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This paper discusses the process of optimizing the shape of systems that are controlled by the Stokes flow with threshold leak boundary conditions. In the theoretical part it focuses on studying the stability of solutions to the state problem in relation to a specific set of domains. In order to facilitate computation, the slip term and impermeability condition are regulated. In the computational part, the optimized portion of the boundary is defined using Bézier polynomials, in order to create a finite dimensional optimization problem. The paper also includes numerical examples to demonstrate the computational efficiency of this approach. [ABSTRACT FROM AUTHOR]

This paper proposes a smooth finite element method (S-FEM) for efficient and accurate analysis of motor magnetic fields. The edge-based smooth finite element (ES-FEM) formulations are derived for two-dimensional triangular element meshes suitable for multi-material motor structures, and then a magnetic flux density calculation method appropriate for S-FEM to calculate nonlinear electromagnetic fields is introduced. In the calculation of motor magnetic field, ES-FEM has a proper softening effect on the stiffness matrix of the finite elements, which makes the calculation more accurate and more efficient than FEM. The magnetic flux intensity calculation method introduced in this paper is not only appropriate for ES-FEM to calculate the nonlinear electromagnetic field of motor, but also can improve the calculation accuracy of magnetic flux density. In the calculation of nonlinear magnetic field of motor, ES-FEM can also improve the calculation accuracy of magnetic field analysis compared with FEM. Several numerical examples demonstrate the improving effect of the ES-FEM discussed above on the motor's magnetic field calculation. [ABSTRACT FROM AUTHOR]

• A mechanical invariance based on the interaction consistency between the FEM and the PD is derived. • An arbitrary switching FEM - PD coupling at the particle level was developed. • The surface effect of PD boundary and FEM - PD coupling interface is eliminated. • The mechanical behavior of the composite materials at the interface can be captured accurately. The issue of coupling the finite element method (FEM) and peridynamics (PD) is a critical concern of widespread attention in PD. In this paper, some essential insights into particle interfaces are presented to address the challenges of coupling PD with FEM and to mitigate surface effects. The interaction consistency between FEM and PD is demonstrated, and then a mechanical invariance of interactions is derived. This mechanical invariance serves as the foundation for an arbitrary switching FEM - PD coupling (ASC), which allows for arbitrary switching between the two methods without introducing artificial deviations. Moreover, a strain - based surface effect correction (SB - SEC) is developed to rectify surface effects by leveraging the symmetry of the strain tensor. This correction allows for the direct application of FEM boundary conditions onto PD boundary, thereby enhancing the precision of simulation results. The reliability of ASC is validated through quantitative deformation and fracture examples, while the excellent mitigation effect of SB - SEC is illustrated. Furthermore, the examples related to composite materials highlight the promising potential of the proposed method for simulating composite materials. [ABSTRACT FROM AUTHOR]

This paper presents the application of the Galerkin Finite Block Method (GFBM) to address cracked solids associated with Functionally Graded Materials (FGMs), leveraging the foundational principles of the Galerkin method. The equilibrium equations pertinent to FGMs are articulated in their weak form. Employing Chebyshev polynomials as shape functions, the GFBM integrates mapping techniques to accommodate irregular finite or semi-infinite physical domains. Boundary and continuity conditions are enforced through the Lagrange Multiplier Method. The domain integrals are calculated through either analytical or numerical integration. The proposed method can easily solve the edge crack or diagonal crack problem by using the crack opening displacement method. The accuracy and convergence of the proposed method are illustrated through a selection of numerical examples. The obtained numerical solutions are verified with analytical solutions and the results from the Finite Element Method. [ABSTRACT FROM AUTHOR]

The Generalized Finite Element Method (GFEM) is developed from the Partition of the Unity Method (PUM), which expands the standard finite element space by using non-polynomial function spaces called the enrichment spaces. GFEM has been successfully applied to various problems, but it still has some drawbacks. It lacks robustness in adjusting meshes when solving interface problems, and the condition number of the stiffness matrix will increase dramatically when the interface is close to the mesh boundary. This phenomenon can lead to ill-conditioned linear equations. A stable GFEM called SGFEM is proposed for the Stokes interface problem in this paper, which modifies the enrichment space. The SGFEM space of the velocity is divided into a basic part S F E M and an enrichment part S E N R ∗. The discretization of space (S F E M × Q h) uses Q 1 − Q 0 element or the Taylor-Hood element for the study. S E N R ∗ uses different interpolation functions. Numerical studies show that SGFEM has the optimal convergence order of the error and robustness. The growth rate of the scaled condition number of the stiffness matrix is the same as that of a standard FEM. • The stable GFEM is proposed for the Stokes interface problems. • Error convergence order same as FEM solving Stokes equation without interface. • Scaled condition number of stiffness matrix is the same growth order as standard FEM. [ABSTRACT FROM AUTHOR]

In this paper, a linear smoothing scheme over eight-node Reissner-Mindlin plate element under the framework of the CS-FEM is employed to buckling analysis of laminated composite plates based on the first-order shear deformation theory. The modified stain matrix is computed by the divergence theorem between the nodal shape functions and their derivatives using Taylor's expansion. Isoparametric mapping and the computation of interior derivatives of shape function is not required in the proposed method, furthermore, all the computation are based on the global Cartesian coordinates. Some numerical examples are given at the end to demonstrate that the present method has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive coupling approach between meshless Smoothed Point Interpolation Methods (SPIMs) and the Finite Element Method (FEM) for the physically nonlinear analysis of quasi-brittle media. The nonlinear behaviour is represented by scalar damage and smeared-crack models. In the proposed adaptive coupling approach, the domain is initially discretised with a relatively coarse FEM mesh. During the solution process, FEM patches are replaced by meshless discretisations according to certain selection criteria. Refinement is also considered. • A new meshless-FEM adapting coupling is proposed. • The Kronecker delta property of smoothed point interpolation methods allows a straightforward coupling. • After each mesh modification the iterative process is repeated to guarantee the equilibrium of the model. • The irreversibility of damage is guaranteed throughout the adaptive process. [ABSTRACT FROM AUTHOR]

Piezoelectric materials find widespread applications in high-precision actuators and sensors. However, the traditional finite element method falls short in meeting the simulation needs of piezoelectric structures due to complexities in mesh generation and precision requirements for accurate simulations. This paper focuses on adapting and generalizing the meshless modeling technique based on the radial point interpolation method to address three-dimensional simulations of piezoelectric structures and accurately model positive and inverse piezoelectric behaviors. The piezoelectric body is discretized into point cloud data, and displacement and potential are approximated by interpolating values through the radial point interpolation method. Subsequently, a 3D meshless model for general piezoelectric structures is formulated based on the principle of minimum potential energy. The influences of key factors on interpolation accuracy and computational cost were discussed. Numerical examples, featuring a 3D piezoelectric bimorph beam as actuators and sensors, validate the efficacy of this extended approach. Results affirm that the three-dimensional meshless method, rooted in the radial point interpolation technique, achieves superior accuracy in predicting piezoelectric behavior compared to the traditional finite element method. This adaptation not only enhances the applicability of meshless modeling but also represents a significant advancement in accurately simulating complex three-dimensional piezoelectric structures. • Multi-field coupling meshless modeling for 3D piezoelectric structures based on RPIM. • Valuable insights are provided for selecting meshless model parameters. • Uniformly distributed nodes helps improve the numerical calculation accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a weak Galerkin finite element method is implemented to solve the one-dimensional singularly perturbed reaction–diffusion equation. This weak Galerkin finite element scheme uses piecewise polynomial with degree k ≥ 1 in the interior part of each element and piecewise constant function at the nodes of each element. The existence and uniqueness of the weak Galerkin finite element solution are proved. Based on the interpolation operator and the corresponding approximation properties, an ɛ − uniform error bound of O (N − (k + 1) + ɛ (N − 1 ln N) k) in the energy-like norm is investigated rigorously. Furthermore, an ɛ − uniform error bound of O (N − (k + 1 / 2) + (N − 1 ln N) k) in the balanced norm is established by the weighted local L 2 projection and its corresponding approximation properties. Finally, numerical experiments validate the theoretical results. Moreover, numerical results show that this weak Galerkin finite element solution achieves the convergence rate of O ( (N − 1 ln N) k + 1) in the L 2 norm and the discrete L ∞ norm uniformly with respect to the singular perturbation parameter ɛ. [ABSTRACT FROM AUTHOR]

It is well known that the analytical matrices arising from the discretization of distributed parameter systems using the finite element technique are usually symmetric and banded. How to preserve the coefficient matrices of the updated model being of the same band structure is an important yet difficult challenge for model updating in structural dynamics. In this paper, an iterative method for updating mass, damping and stiffness matrices simultaneously based on partial modal measured data is provided. By the method, the optimal updated matrices can be obtained within finite iteration steps by choosing a special kind of initial matrix triplet. The proposed approach not only preserves the physical connectivity of the original model, but also the updated model reproduces the measured modal data, which can be utilized for various finite element model updating problems. Numerical examples confirm the effectiveness of the introduced method. • An iterative updating method for damped structure systems is established. • The proposed approach preserves the physical connectivity of the original model. • The updated model can reproduce the measured modal data. • The deviation between the updated model and the original model is minimal. [ABSTRACT FROM AUTHOR]

In the present paper, a previously introduced numerical method, GDDR (Generalized Differential Dynamic Relaxation), is developed to analyze ratcheting behavior of moderately thick rectangular plates. The validity of the method is verified by comparison with literature data and finite element method results. Classical Plate Theory (CPT) and First-order Shear Deformation Theory (FSDT) are utilized to define the displacement field of plates. Incremental strain equations are derived according to von Karman relations. Prandtl-Reuss flow rule and von Mises yield criterion and are used to express the behavior of the plates in the plastic region. The Armstrong-Frederick nonlinear kinematic hardening model is incorporated for elastic-plastic analyses. Finally the results of ratcheting analysis obtained by GDDR method based on two mentioned theories are compared. Results showed that higher amounts of strains are predicted when FSDT theory is employed. Moreover, the area of hysteresis loops obtained by FSDT analysis are larger than those of CPT analysis, meaning that FSDT approach predicts more energy dissipation during each cycle of loading compared with CPT approach. Finally, comparing the results for different ratios of thickness to width shows that GDDR method can predict more accurate results, especially for higher ratios, when it utilizes FSDT theory. [ABSTRACT FROM AUTHOR]

• The polyhedral formula of the Cosserat theory has been derived. • The precision of the proposed method can approach that of quadratic elements. • The meshing performance is enhanced benefiting efficient octree techniques. The Cosserat continuum offers high accuracy in micro-structure analysis and stress concentration simulation due to its consideration of mechanical factors such as coupled stress and internal length scale. However, existing methods are mainly developed based on the isoparametric conventional continuum framework, with relatively simple element shapes and weak adaptability to complex geometries. Therefore, this paper proposes an improved Cosserat continuum theory based on the three-dimensional (3D) polyhedral scale boundary finite element method (PSBFEM). The main work is as follows: (1) The Cosserat continuum theory formula is deduced within the SBFEM framework by integrating a polygon mean-value shape function; (2) The analytical accuracy of the proposed method is examined through classical micro-structure test examples; (3) An efficient octree algorithm is introduced to evaluate the comprehensive performance of the proposed method for the analysis of complex structures, and the selection and impact of the internal length scale are discussed. The results indicate that the proposed method incorporates the good performance of SBFEM and the Cosserat continuum, and its accuracy can approach the traditional quadratic Cosserat continuum elements; The stress concentration problem can be effectively addressed, leading to a more accurate representation of structural stress characteristics. Additionally, complex polyhedral elements can be directly calculated, and the element library of traditional Cosserat theory has been greatly expanded. [ABSTRACT FROM AUTHOR]

Time-domain boundary element method (TDBEM) can be applied in studying transient acoustic wave problems, especially in solving exterior problems. However, in order to avoid calculations of coefficients at different time steps, TDBEM usually requires storing or recomputing the coefficients at each time step. This can lead to significant amount of memory usage or long computing time. In this paper, an acoustic TDBEM based on a kernel-function library (KFL-BEM) is proposed, in order to reduce the memory consumption of the time-domain conventional BEM (CBEM) and speedup the computation. In this approach, the storage requirement is reduced from O (N 2 N t min) to O (N 2), where N represents the number of degrees of freedom of the model, and N t min is the minimum number of time steps for which coefficients need to be computed and stored. To demonstrate the effectiveness of the KFL-BEM, two verification examples are presented using the problems of a pulsating sphere and sound propagating in a channel. Compared with the CBEM, the KFL-BEM can save significantly the memory storage as it does not require storing coefficients for any previous time steps. This method can also be applied to solve vibro-acoustic problems in the time domain. As an example, the acoustic radiation responses of a tuning fork under different striking loads are studied using the finite element method and the proposed KFL-BEM, which clearly shows the potentials of the KFL-BEM in solving time-domain acoustic problems. [ABSTRACT FROM AUTHOR]

In this paper, we consider an enriched cut finite element method (ECFEM) with interface-unfitted meshes for solving Stokes interface equations consisting of two incompressible fluids with different viscosities. By approximating the velocity with the enriched P 1 element and the pressure with the P 0 element, and stabilizing the Galerkin variational formulation with suitable ghost penalty terms, we propose the new ECFEM and prove that it is well-posed and has the optimal a priori error estimate in the energy norm. All derived results are independent of the interface position. Moreover, compared with other conforming finite element methods with the optimal rate in convergence, the proposed scheme here not only has the minimum degrees of freedom, but also avoids using the derivative of the pressure in the penalty term. The presented numerical examples validate the theoretical predictions. [ABSTRACT FROM AUTHOR]

Models involving interfaces with discontinuities or even singularities of some fields across them are very frequent in real life problems modelling. In the last decades, the use of the eXtended Finite Element Method (XFEM) instead of the traditional FEM has become more and more popular, mainly because of two advantages: the mesh of the domain can be independent of the interface position, therefore avoiding remeshing, and it allows to enrich an area with specific shape functions fitted to the particular properties (singularities, discontinuities) of the expected solution, obtaining more accurate results with less computational efforts. Nevertheless, a critical point of XFEM is its implementation since it varies from one problem to another, due to the different kind (and number) of degrees of freedom on each node. A diligent organization of nodes, degrees of freedom and enrichment functions is fundamental to achieve an efficient implementation. Our aim in this paper is to provide a common reference framework for the implementation of XFEM from a mathematical point of view, providing the readers with a set of tools that will allow them to apply it to any kind of problem. To this aim, we present a detailed description of XFEM implementation, with special emphasis on the terms that involve integration over interfaces. The proposed tools are presented in a general context, and as an example, we will apply them to a problem of solids mechanics. In particular, we will contextualize the procedure on a Rayleigh waves propagation problem in a cracked structure considering a Signorini contact condition on the crack sides. [ABSTRACT FROM AUTHOR]

This paper presents a nonlocal energy-informed neural network to address the inherent zero-energy mode instability in peridynamic correspondence material models. Starting from the principle of virtual work, the task of solving peridynamic equilibrium equation is reformulated as a variational minimum problem of total potential energy, serving as the natural loss function for neural network. By minimizing the potential energy of the peridynamic body, the proposed neural network effectively eliminates the zero-energy modes. Importantly, this approach preserves the original peridynamic formulation without introducing a supplementary force vector state or modifying the nonlocal deformation gradient tensor. Additionally, there is no need for an artificial damping coefficient in adaptive dynamic relaxation, and the high memory consumption in implicit schemes is avoided. To improve the prediction accuracy near boundaries and to impose boundary conditions consistently with the local continuum theory, variable horizon method is introduced. Comparative studies of the proposed neural network with analytical solutions, finite element analyses or other control methods are conducted to verify the feasibility and accuracy of the proposed neural network in suppressing zero-energy mode oscillations. Furthermore, the convergence of the proposed approach and the influence of different activation functions on the prediction accuracy and convergence rate are investigated. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic analysis of shear deformable shells was conducted using the hybrid displacement boundary element method (HD-BEM). The approach involved utilizing the fundamental solution as a trial function to derive the 8-node element stiffness matrix, while approximating the boundary variables with quadratic shape functions. To ensure efficient computations and avoid singular integrals, the source points were strategically positioned outside the domain. For accurate calculations of the proposed 8-node element mass matrix, only four Gauss points were relied upon. It is important to note that both the element mass and stiffness matrices demonstrate symmetry. Throughout the study, free, forced, and harmonic analyses were considered. Encouragingly, the results obtained from the study exhibited exceptional accuracy levels, even when employing a coarse discretization approach. [ABSTRACT FROM AUTHOR]

In this paper, a semi-analytical method is employed to model a Cosserat continuum. The spatial discretization is based on quadtree decomposition, a hierarchical structure. The hanging nodes as a result of quadtree decomposition are naturally handled by the scaled boundary finite element framework without requiring additional constraints/shape functions. The accuracy and convergence properties of the proposed framework is demonstrated with four numerical examples of varying complexity. From the numerical study, it is opined the framework yields accurate results. The influence of characteristic length ℓ and the Cosserat constant a on the stress distribution in a masonry structure and in the vicinity of the hole and crack tip is systematically studied. [ABSTRACT FROM AUTHOR]

The traditional finite element analysis for irregular design domains often encounters challenges such as intricate mesh discretization and inaccurate boundary description. In this paper, we propose a quadtree scaled boundary finite element method based on NURBS curves where the boundaries can be accurately represented. Quadtree decomposition, which satisfies the 2:1 rule, is employed to rapidly subdivide the analysis domain. The scaled boundary finite element method (SBFEM) is utilized to analyze the internal elements and address the displacement incompatibility issue of hanging nodes in the quadtree. Furthermore, the boundary element is discretized into boundary curves and internal lines, whose displacement fields are respectively constructed by the NURBS shape functions and the Lagrange shape functions, and then the subsequent analysis of the boundary element is completed by SBFEM. Finally, numerical examples are tested to demonstrate the feasibility of the proposed method, which effectively enhances computational efficiency and accuracy in solving irregular design domains. [ABSTRACT FROM AUTHOR]

Studying dynamic response and damage assessment of mountain tunnels is paramount in earthquake engineering. This paper proposed a novel method, the indirect boundary element method-finite element method (IBEM-FEM) coupled method, aimed to concurrently simulate the amplification effect of kilometer-scale mountain topography and the damage evolution in a centimeter-scale lining tunnel section. The proposed method involves two fundamental steps. Initially, the input motion on the truncation boundary within the mountain is accurately determined using the indirect boundary element method (IBEM). Subsequently, the nonlinear dynamic behavior of the tunnel structure and its adjacent area is analyzed by the finite element method (FEM) based on the results from the previous step. This study numerically simulates the seismic damage and failure mechanisms of a mountain tunnel considering three influence factors: incident wave types, incident wave intensities, and surrounding rock mass grades. The results indicate that mountain topography amplifies the seismic response, thereby affecting the dynamic behavior of the tunnel. Under the incidence of SV-waves and P-waves, the dynamic damage distribution patterns of the tunnel lining are significantly different. Moreover, as seismic wave intensity increases, the peak values of tunnel stress exhibit a non-monotonic increasing trend. The surrounding rock mass grade also significantly affects the dynamic response and damage distribution of the mountain tunnel. Overall, the proposed IBEM-FEM coupled method can effectively consider complex mountain topography and is applicable for evaluating the nonlinear seismic response of mountain tunnels. [ABSTRACT FROM AUTHOR]

• 'Repeated winding' method is used to improve Lagrange hole elements. • 8, 12 and 16-node trigonometric hole elements are derived. • Adaptive element sub-division method is used to deal with the near-singularity. • Node distribution ways on ellipse of the hole elements are discussed in detail. Structures with holes are prevalent in engineering applications. Analyzing the stress concentration effects caused by holes using the finite element method (FEM) or the boundary element method (BEM) is challenging and time-consuming. Typically, a large number of elements are necessary in the vicinity of holes to achieve accurate results. In this paper, a series of improved hole elements and tube elements are constructed for simulating the holes and cylinders, respectively. Two construction methods for hole elements, based on Lagrange and trigonometric interpolations, respectively, are introduced. The general formulas for evaluating singular integrals over the proposed elements are derived. Additionally, the adaptive element sub-division technique is applied to address the nearly singular integrals over these elements and account for the interactions of multiple holes. Five numerical examples are studied to demonstrate the accuracy and efficiency of the proposed elements. The results demonstrate that employing hole and tube elements can reduce the number of nodes while maintaining stress accuracy, in comparison to using several quadratic elements. [ABSTRACT FROM AUTHOR]

High computational cost in elastoplastic analysis is often handled by the use of high performance parallel computers. However, the presence of both elastic and plastic states leads to the branching issue, which prevents the realization of true parallel performance. The computational efficiency of an elastoplastic analysis using finite element method is largely determined by the performance of repeated solution of linearized system of equations. In this paper, we propose GPU-based matrix-free strategies to compute sparse matrix–vector multiplication (SpMV) in Conjugate Gradient (CG) iterative solver for the acceleration of solution of linear system of equations. Matrix-free solvers never assemble large sparse global tangent matrix and perform the computation directly with small dense elemental matrices, reducing the storage requirement and preventing the use of problematic sparse storage formats. A uniform treatment of elements in elastic and plastic regions is achieved by the proposed single kernel strategy, which prevents branching, avoids redundant computation and provides efficient memory access. In addition, we propose node-based and degrees-of-freedom (DOF)-based parallel strategies for effective implementation of matrix-free SpMV on a GPU. The proposed strategies use single elemental tangent matrix for all elements in elastic region and individual tangent matrices in plastic region. The computational experiments over three large-scale benchmark examples of elastoplasticity reveal that the performance of the node-based and DOF-based parallelization strategies depends on the amount of plasticity in the body. At low plasticity levels, node-based strategy performs best, achieving 3.2 × speedup over an existing GPU-based matrix-free SpMV strategy in the literature. For moderate to high amount of plasticity, the DOF-based strategy outperforms every other strategy and obtains speedups of up to 3.5 × over the existing SpMV strategy. [ABSTRACT FROM AUTHOR]

Time domain obstacle scattering widely exists in the scientific fields of geophysics, remote sensing, seismology, and medicine. However, it is difficult to solve the time domain scattering problems with arbitrarily shaped obstacles only within the fixed domain of interest. In this paper, an edge-based smoothed finite element method using linear triangular elements (ES-FEM-T3) combined with the Newmark method is proposed for the two-dimensional time domain acoustic scattering by an arbitrarily shaped obstacle. In the algorithm, a time domain transparent boundary condition (TBC) and the Newmark method are introduced to transform the time domain problem in an unbounded domain into a series of steady-state PDEs on a bounded domain, which is suitable for an arbitrary shaped obstacle scattering problem. In the numerical discretization, ES-FEM-T3 is used to construct a close-to-exact stiffness matrix by the smoothed gradient technique, making it space stable and obtaining more accurate results compared to FEM-T3. Especially, through in advance calculating the function σ(t), the convolution term in the time-domain TBC can be quickly calculated. Finally, through the numerical experiments, the effectiveness of the proposed method is demonstrated. Especially, ES-FEM-T3 can better improve the time convergence stability of the Newmark method and have better accuracy at γ = 0.5 compared to FEM-T3. [ABSTRACT FROM AUTHOR]

Open pit mines are large geotechnical structures. Their stability is an important consideration in the mining industry. The deformations of geotechnical structures often involve the coupled interaction between the pore fluid pressure and the nonlinear deformation of soil, characterised by poro-elasto-plastic behaviour. This paper develops the scaled boundary finite element method (SBFEM) to address poro-elasto-plastic in slope stability problems. It builds upon a previously developed elasto-plastic formulation to consider the effect of pore fluid pressure and its interaction with the nonlinear deformation within the soil. The pore pressure field introduces an additional variable in the governing equations that is similarly discretised using SBFEM shape functions. The SBFEM is implemented together with a pixel-based quadtree mesh generation technique, enabling automatic meshing directly from digital images. This leads to efficient automation when modelling problems with iterative changes in the geometry such as in optimisation of construction processes during the rehabilitation of slopes. The formulation is validated first using a standard numerical benchmark. Application of the developed technique in construction applications in slopes where the stability and effect of pore water pressure is considered e.g., tailings dam construction and optimisation of backfilling process is demonstrated in three examples to demonstrate feasibility. [ABSTRACT FROM AUTHOR]

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics (MHD) problem. This model consists of Cahn–Hilliard equations, Navier–Stokes equations and Poisson equation. We propose a linear and decoupled finite element method to solve this highly nonlinear and multi-physics system. For the time variable, the discretization is a combination of the first order Euler semi-implicit scheme, several first-order stabilization terms and implicit–explicit treatments for coupling terms. For the space variables, we adopt the finite element discretization. Especially, we approximate the current density and electric potential by inf–sup stable face-volume mixed finite element pairs. With these techniques, the scheme only involves a sequence of decoupled linear equations to solve at each time step. We show that the scheme is provably mass-conservative, charge-conservative and unconditionally energy stable. Numerical experiments are performed to illustrate the properties, accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

• Lagrange's equation for fluid mechanics is proposed with power functional. • Fluid part of VFIFE method is explored via fractional steps. • A MATLAB program based on VFIFE-LES turbulence model is developed. • Theoretical basis for the unified fluid-solid dynamics in VFIFE is provided. • The method is effective in improving the convergence and numerical oscillation. Vector form of intrinsic finite element (VFIFE) is a numerical method widely used in solid mechanics. However, it's hard to extend the VFIFE method to fluid mechanics since the traditional VFIFE method fails to reflect the analytical equilibrium of multiple variables in the continuum. Therefore, under the framework of analytical mechanics, this paper proposes Lagrange's equation of the second kind in fluid mechanics with the extremum condition of Lagrange power functional. And a vectorized motion equation of incompressible viscous fluids is deduced from Lagrange's equation. By using several efficient algorithms in the finite difference method (FDM) and the finite element method (FEM), the NS equation is decomposed into four governing equations of vector form for fluid mechanics. In addition, with the application of the classic Smagorinsky sub-grid scale model in large eddy simulation (LES), this paper puts forward turbulence modelling with VFIFE procedure, and a corresponding MATLAB program is developed. Two typical examples are given to demonstrate the applicability and efficiency of the proposed large eddy simulation with VFIFE method. The proposed algorithm can effectively eliminate the non-physical oscillation of the pressure, and obtain much accurate results with a small number of grids. [ABSTRACT FROM AUTHOR]

This paper presents the lowest-order weak Galerkin finite element method for linear elasticity problems on the convex polygonal meshes. This method uses piecewise constant vector-valued spaces on element interiors and edges. The discrete weak gradient space introduced by this paper is the matrix version of C W 0 space. The discrete weak divergence space is piecewise constant space on each element. This method is simple, efficient, stabilizer-free and symmetric positive-definite. The optimal error estimates in discrete H 1 and L 2 norms are presented. Numerical results are given to demonstrate the efficiency of algorithm and the locking-free property. • The matrix version of C W 0 element for discrete weak gradient is introduced. • The lowest-order weak Galerkin finite element space ( P 0 2 , P 0 2 , C W 0 2 , P 0 ) is adopted. • Our method is suitable for the polygonal and hybrid meshes. [ABSTRACT FROM AUTHOR]

In this paper, a novel and fast two-grid finite element method (FEM) is proposed for efficiently solving semilinear time-fractional diffusion equations with variable coefficients. To handle the initial singularity, the nonuniform L1 scheme is employed in the temporal domain. A novel two-grid FEM technique is used in the spatial domain to reduce computational cost. The two-grid algorithm solves the original nonlinear fractional equation on a much coarser grid with size H , obtaining the coarse-grid solution u H n based on the fine-grid solutions at previous time levels. This approach avoids repetitive discrete convolutional summation when approximating the Caputo derivative on the coarse grid, resulting in reduced computational cost. Furthermore, a fast nonuniform L1 scheme with two-grid technique is developed to accelerate the evaluation of the Caputo derivative. The paper also proposes a novel, fast and highly accurate algorithm for computing the coefficients involved in the discretized Caputo fractional derivative. The α -robust stability and optimal L 2 - and H 1 -norm error estimates for fully discrete scheme are derived, where the error bound remains valid as α → 1 − . Numerical results validate the theoretical findings and demonstrate the superior efficiency of the proposed two-grid algorithms compared to the standard FEM. • A novel, fast two-grid FEM is proposed for time-fractional diffusion equations. • A innovative method for computing the discrete convolution kernels is proposed. • The α -robust stability and optimal L 2 - and H 1 -norm error estimates are derived. • Numerical results show the efficiency and accuracy of the proposed algorithms. [ABSTRACT FROM AUTHOR]

As new supercomputer architectures become more heavily focused on using hardware accelerators, in particular general-purpose graphical processors, it is therefore relevant that algorithms for computational fluid dynamics, especially those targeting scale-resolving simulations, be designed in such a way as to make efficient use of such hardware. In this paper, we propose one such hardware-accelerated Continuous Galerkin Finite Elements model, aimed at handling simulations of turbulent compressible flows over complex geometries. As this model is intended for use in Large-Eddy and Direct Numerical simulations, it is necessary that the resulting scheme introduces only small amounts of artificial (numerical) diffusion for stabilization purposes. We achieve this through a combination of Spectral Finite Elements, operator splittings on the convective term, and the use of the Entropy Viscosity stabilization model adapted to spectral elements scheme. The paper will present the resulting algorithm, how it is made to work efficiently on the accelerators, and results obtained that demonstrate its high-accuracy capabilities. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the convergence of an adaptive two-grid weak Galerkin (ATGWG) finite element method for second order semilinear elliptic partial differential equations (PDEs). First, we propose an ATGWG method and then prove that the sum of the energy error and the error estimator of ATGWG method between two consecutive adaptive loops is a contraction. The weak Galerkin (WG) elements (P j (T) , P ℓ (∂ T) , R T j (T)) (Wang and Ye, 2013) are studied in this paper and numerical experiments based on the lowest order case with j = l = 0 are provided to support the theoretical results. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the strong mutual influence between the flow and the physical processes involved in the heart function, the development of accurate and efficient CFD solvers for cardiovascular flows is still a challenging task. In this paper we present life▪-cfd, an open-source CFD solver for cardiovascular simulations based on the life▪ finite element library, written in modern C++ and exploiting distributed memory parallelism. We model blood flow in both physiological and pathological conditions via the incompressible Navier-Stokes equations, accounting for moving cardiac valves, moving domains, and transition-to-turbulence regimes. In this paper, we provide an overview of the underlying mathematical formulation, numerical discretization, implementation details and examples on how to use life▪-cfd. We verify the code through rigorous convergence analyses, and we show its almost ideal parallel speedup. We demonstrate the accuracy and reliability of the numerical methods implemented through a series of idealized and patient-specific vascular and cardiac simulations, in different physiological flow regimes. The life▪-cfd source code is available under the LGPLv3 license, to ensure its accessibility and transparency to the scientific community, and to facilitate collaboration and further developments. Program Title: life▪-cfd CPC Library link to program files: https://doi.org/10.17632/hzsnc3jgds.1 Developer's repository link: https://gitlab.com/lifex/lifex-cfd Licensing provisions: LGPLv3 Programming language: C++ (standard ≥17) Supplementary material: https://doi.org/10.5281/zenodo.7852088 contains the application executable in binary form, compatible with any recent enough x86-64 Linux system, assuming that glibc version ≥ 2.28 is installed. Data and parameter files necessary to replicate the test cases described in this manuscript are also available. Nature of problem: The program allows to run computational fluid dynamics simulations of cardiovascular blood flows in physiological and pathological conditions, modeled through incompressible Navier-Stokes equations, including moving cardiac valves, moving domains (such as contracting cardiac chambers) in the arbitrary Lagrangian-Eulerian framework, and transition-to-turbulence flow. Given the scale of the typical applications, the program is designed for parallel execution. Solution method: The equations are discretized using the Finite Element method, on either tetrahedral or hexahedral meshes. The software builds on top of deal.II, implementing the mathematical models and numerical methods specific for CFD cardiovascular simulations. Parallel execution exploits the MPI paradigm. The software supports both Trilinos and PETSc as linear algebra backends. Additional comments including restrictions and unusual features: The program provides a general-purpose executable that can be used to run CFD simulations without having to access or modify the source code. The program allows to setup simulations through a user-friendly yet flexible interface, by means of readable and self-documenting parameter files. On top of that, more advanced users can modify the source code to implement more sophisticated test cases. life▪-cfd supports checkpointing, i.e. simulations can be stopped and restarted at a later time. [ABSTRACT FROM AUTHOR]

• The framework of the semi-analytical wavelet finite element (SAWFE) is proposed. • Dispersion curves of aluminium plates and rectangular rods are calculated. • The present method shows high precision and efficiency in comparison with the semi-analytical finite element (SAFE)method. Prior knowledge of the dispersion curves and mode shapes of guided waves provides valuable information for wave mode selection and excitation in the field of non-destructive evaluation (NDE) and structural health monitoring (SHM). They are typically computed by the matrix methods, the finite element (FE) and semi-analytical finite element (SAFE) methods. However, the former is prone to numerical instability, and the latter two are limited by the refinement level of the FE mesh. In this paper, a semi-analytical wavelet finite element (SAWFE) method is presented to characterize wave propagation in rectangular rods. The piecewise polynomial interpolation functions of the SAFE method are replaced by two-dimensional scaling functions of the B-spline wavelet on the interval (BSWI). To demonstrate the accuracy of the proposed SAWFE technique, the propagation of guided waves in an aluminium plate is studied first. Then, the propagation of guided waves in rectangular rods of arbitrary aspect ratio is investigated. The results of this work clearly show that the SAWFE method presented here has higher accuracy and efficiency than the SAFE method. [ABSTRACT FROM AUTHOR]

In general, the laminated composite plates and stiffeners may exhibit the bending-extension coupling effect with the transverse shear deformations significantly induced. In this paper, for the first time we develop the associated boundary element method (BEM) for bending-extension coupling shear deformable laminated composite plates with multiple beams attached as stiffeners. Based upon the first order shear deformation theory, the individual boundary integral equations (BIEs) for plates and stiffeners are obtained from their corresponding matrix-form basic equations. To account for perfect bonding conditions between plate and stiffeners, we establish displacement continuity and interaction load equilibrium relations at their interfaces. To calculate the domain integrals related to unknown interaction loads, we discretize each stiffener into a series of cells using quadratic interpolation. By collecting the individual BIEs for plates and stiffeners and employing the continuity and equilibrium relations at the interfaces, we construct the entire system of linear equations to solve for all the unknown nodal quantities. Additionally, the complete solutions at the plate boundary, at internal points or along a stiffener are provided. The correctness of our present BEM formulation is verified through two representative examples by comparison with the commercial finite element software ANSYS. The numerical results demonstrate that our BEM formulation surpasses the conventional finite element method and is highly desirable for general stiffened laminated plates with bending-extension coupling and transverse shear deformations. [ABSTRACT FROM AUTHOR]

In this paper, the unconditional stability and optimal error estimate of the velocity, pressure and angular velocity for the modified characteristics FEMs of the unsteady Micropolar Naiver–Stokes Equations (MNSE) are presented. In this method, the nonlinear equation is linearized by the characteristic finite element method for dealing with the time derivative term and the convection term. Basing on the characteristic time-discrete system, the error function is split into a temporal error and a spatial error. With a rigorous analysis to the characteristic time-discrete system, we prove that the error between the numerical solution and the solution of the time-discrete system is τ -independent, where τ denotes the time stepsize. The stability results and optimal error estimates in L 2 norm and H 1 norm will be given. Finally, some numerical results will be provided to confirm our theoretical analysis. • The unconditional stability and optimal error estimate for the modified characteristics FEMs are presented. • The nonlinear equation is linearized by the characteristic method. • Basing on the characteristic time-discrete system, the error function is split into a temporal error and a spatial error. • The stability results and optimal error estimates in $L̂2$ norm and $Ĥ1$ norm will be given. [ABSTRACT FROM AUTHOR]

In this paper, based on the scalar auxiliary variable (SAV) approach, the superconvergence error analysis is investigated for the time-dependent Navier–Stokes equations. In which, an equivalent system of the Navier–Stokes equations with three variables and a fully-discrete scheme is developed with semi-implicit Euler discretization for the temporal direction and low-order bilinear-constant finite element discretization for the spatial direction, respectively. With the help of the high-precision estimations of the bilinear-constant finite element pair on the rectangular meshes, the superclose error estimates for velocity in H 1 -norm and pressure in L 2 -norm are obtained by treating the trilinear term carefully and skillfully. The global superconvergence results are also derived in terms of a simple and efficient interpolation post-processing technique. Finally, some numerical results are provided to demonstrate the correctness of the theoretical analysis. • A semi-implicit SAV Galerkin FEM is investigated for the time-dependent N–S equations. • The high-precision estimations are employed in the error analysis. • The trilinear term is treated skillfully in the error analysis. • The superclose and superconvergence results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we propose a second-order decoupled finite element method based on lagging a part of the interfacial coupling terms for the time dependent Stokes–Darcy problem, which only need to solve two sub-physical problems sequentially. Under a modest time step restriction Δ t ≤ C (physical parameters), the optimal long time error estimates are obtained both in the L 2 norm and in the H 1 norm. Numerical results are provided to illustrate the convergence rate O (Δ t 2) of the temporal approximation. • A second-order decoupled finite element method based on lagging a part of the interfacial coupling terms is proposed. • The optimal long time error estimates are obtained in the L 2 norm. • The optimal long time error estimates are obtained in the H 1 norm. [ABSTRACT FROM AUTHOR]

This paper presents a Crank–Nicolson leap-frog (CNLF) scheme for the unsteady incompressible magnetohydrodynamics (MHD) equations. The spatial discretization adopts the Galerkin finite element method (FEM), and the temporal discretization employs the CNLF method for linear terms and the semi-implicit method for nonlinear terms. The first step uses Stokes style's scheme, the second step employs the Crank–Nicolson extrapolation scheme, and others apply the CNLF scheme. We establish that the fully discrete scheme is stable and convergent when the time step is less than or equal to a positive constant. Firstly, we show the stability of the scheme by means of the mathematical induction method. Next, we focus on analyzing error estimates of the CNLF method, where the convergence order of the velocity and magnetic field reach second-order accuracy, and the pressure is the first-order convergence accuracy. Finally, the numerical examples demonstrate the optimal error estimates of the proposed algorithm. • Crank–Nicolson leap-frog (CNLF) scheme for the unsteady incompressible magnetohydrodynamics (MHD) equations. • The CNLF method for linear terms and the semi-implicit method for nonlinear terms. • Fully discrete scheme is stable and convergent. • The convergence order of the velocity and magnetic field reach second-order accuracy. [ABSTRACT FROM AUTHOR]

This paper considers the finite element method to solve a generalized constant delay diffusion equation. The regularity of the solution of the considered model is investigated, which is the first time to discover that the solution has non-uniform multi-singularity in time compared with Tan et al. (2022). To overcome the multi-singularity, a symmetrical graded mesh is used to devise the fully discrete finite element scheme for the considered problem based on L1 formula of the Caputo fractional derivative and fractional trapezoidal formula of the Riemann–Liouville fractional integral. Then we investigate the unconditional stability of this scheme. Next, the local truncation errors of the L1 formula and the fractional trapezoidal formula are analyzed in detail, especially the later one is discussed at the first time, under the multi-singularity of the solution and the symmetrical graded mesh. Using these error results, we obtain the convergence of the proposed numerical scheme. Finally, some numerical tests are provided to verify the obtained theoretical results. • The regularity of the solution is investigated and shows multi-singularity in time. • A symmetrical graded mesh is used to overcome the multi-singularity. • The unconditional stability and optimal temporal convergence rate are obtained. • The truncation errors of L1 formula and fractional trapezoidal formula are discussed. • Some numerical tests are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents the properties of electromagnetic vibration in a submerged tubular linear induction motor through an analytical model. Firstly, the spatial and temporal characteristics of electromagnetic force acting in the stator are analyzed. Subsequently, based on the wave propagation approach, an analytical model is established to calculate the vibration response of the stator, which is simplified as a finite-length cylindrical shell. The accuracy of the proposed model is verified by comparing natural frequencies of axial breathing modes and frequency response with the finite element method. Finally, the effects of the position of electromagnetic force, the spatial distribution of electromagnetic force, radial static pressure and structure parameters on vibration response are investigated and discussed. Some conclusions are outlined, which is of great importance to reduce electromagnetic vibrations by optimizing the structure design of the motor. • An analytical model is established to calculate the vibration response of the stator, the accuracy of which is verified by comparing natural frequencies of axial breathing modes and frequency response with the finite element method. • The effects of the position of electromagnetic force, the spatial distribution of electromagnetic force, radial static pressure and structure parameters on vibration response are investigated and discussed. • Some key conclusions are outlined, which is of great importance to reduce electromagnetic vibrations by optimizing the design of the motor body. [ABSTRACT FROM AUTHOR]

We describe a data-driven, multiscale technique to model reactive wetting of a silver–aluminum alloy on a Kovar™ (Fe-Ni-Co alloy) surface. We employ molecular dynamics simulations to elucidate the dependence of surface tension and wetting angle on the drop's composition and temperature. A design of computational experiments is used to efficiently generate training data of surface tension and wetting angle from a limited number of molecular dynamics simulations. The simulation results are used to parameterize models of the material's wetting properties and compute the uncertainty in the models due to limited data. The data-driven models are incorporated into an engineering-scale (continuum) model of a silver–aluminum sessile drop on a Kovar™ substrate. Model predictions of the wetting angle are compared with experiments of pure silver spreading on Kovar™ to quantify the model-form errors introduced by the limited training data versus the simplifications inherent in the molecular dynamics simulations. The paper presents innovations in the determination of "convergence" of noisy MD simulations before they are used to extract the wetting angle and surface tension, and the construction of their models which approximate physio-chemical processes that are left unresolved by the engineering-scale model. Together, these constitute a multiscale approach that integrates molecular-scale information into continuum scale models. • Constructed a data-driven wetting model from molecular dynamics simulations. • Studied wetting of molten silver-aluminum alloy on a Kovar™ substrate for brazing. • Performed molecular dynamics simulation to predict surface tension & wetting angle. • Calibrated probabilistic, data-driven surrogate model using limited training data. • Integrated wetting model into engineering-scale finite element brazing model. • Compared model to experiment, identifying missing physics in simulations. [ABSTRACT FROM AUTHOR]

The stability of blood vessels is essential for maintaining their functions, while severe blood vessel tortuosity leads to various clinical complications. The growth and remodeling of blood vessels, which are regulated by mechanical and biochemical cues, cause residual stresses that affect vessel stability. In this paper, we combine theory and simulations to study the mechanobiological behavior of blood vessels with stress-modulated growth and remodeling. Effects of the volumetric growth of the matrix and the turnover and reorientation of collagen fibers are accounted for. Linear stability analysis is first carried out to investigate the mechanobiological stability of blood vessels. By developing a finite element method that incorporates stress-modulated growth and remodeling, we validate the theoretical solution of the critical state and further capture the postbuckling evolution of blood vessels. Our results show that an increased internal pressure can lead to the thickening of the vessel wall, which stabilizes the blood vessels mechanically, whereas the effect of internal pressure on the mechanobiological buckling is nonmonotonic. Compared to the mechanical instability, the mechanobiological buckling results in a larger mode number and a shorter wavelength, as usually observed in varicose veins. Vessels during postbuckling may exhibit non-uniform wall thicknesses, in consistency with the experimental observation on tortuous aortas. These findings highlight the crucial role of mechanical remodeling in tissue morphogenesis and could deepen the understanding of mechanobiological mechanisms underlying the formation and development of blood vessel tortuosity. [ABSTRACT FROM AUTHOR]

This paper presents dual-robust iterative algorithms for the 2D/3D steady thermally coupled inductionless magnetohydrodynamics (IMHD) system in a general Lipschitz domain. Both velocity and current density are discretized by the divergence-conforming elements. Furthermore, we utilize an interior penalty discontinuous Galerkin (IPDG) approach to guarantee the H 1 -continuity of velocity. With the system's strong nonlinearity, we propose three iterative algorithms (Stokes, Newton and Oseen iterations) and provide analytical proofs for their stability and convergence. And the feature of these methods is that they simultaneously ensure the complete divergence-free of discrete velocity and discrete current density. Finally, the numerical simulations verify theoretical analysis and the effectiveness of proposed algorithms. • H(div)-conforming IPDG finite element method. • The approximations for velocity and current density are exactly divergence-free. • Iterative analysis based on pressure robustness and electric potential robustness. • The theoretical analysis is validated by numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we propose two Multipoint Stress Mixed Finite Element (MSMFE) methods for linear viscoelasticity with weak symmetry on quadrilateral grids. The methods are constructed based on the lowest order Brezzi–Douglas–Marini mixed finite element spaces for elastic and viscous stress, piecewise constant velocity and piecewise constant (linear) vorticity. A special quadrature rule is applied for local stress and vorticity elimination. This results in a positive definite cell centered velocity–vorticity or only velocity system at each time step. Unconditional energy-dissipation of the MSMFE methods is proved rigorously. The accuracy of all the numerical solutions in their nature norms are established to be first order space convergence, both for the semi-discrete and fully-discrete formulations. Numerical results validate the theory results of the proposed methods. • We propose two efficient multipoint stress mixed finite element methods. • The resulting system can be deduced as positive definite cell-centered velocity–vorticity or only velocity system. • The accuracy of all the numerical solutions in their nature norms are established. • Several numerical examples validate the theory results. [ABSTRACT FROM AUTHOR]

In this paper, we present a new static and time-dependent MagnetoHydroDynamic (MHD) equilibrium code, TokaMaker, for axisymmetric configurations of magnetized plasmas, based on the well-known Grad-Shafranov equation. This code utilizes finite element methods on an unstructured triangular grid to enable capturing accurate machine geometry and simple mesh generation from engineering-like descriptions of present and future devices. The new code is designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. A detailed description of the numerical methods of the code, including a novel formulation of the boundary conditions for free-boundary equilibria, and validation of the implementation of those methods using both analytic test cases and cross-code validation is shown. Results show expected convergence across tested polynomial degree for analytic and cross-code test cases. [ABSTRACT FROM AUTHOR]

This paper develops a weak Galerkin (WG) finite element method of arbitrary order for the steady incompressible Magnetohydrodynamics equations. The WG scheme uses piecewise polynomials of degrees k (k ≥ 1) , k , k − 1 and k − 1 respectively for the approximations of the velocity, the magnetic field, the pressure, and the magnetic pseudo-pressure in the interior of elements, and uses piecewise polynomials of degree k for their numerical traces on the interfaces of elements. The method is shown to yield globally divergence-free approximations of the velocity and magnetic fields. We give existence and uniqueness results for the discrete scheme and derive optimal a priori error estimates. We also present a convergent linearized iterative algorithm. Numerical experiments are provided to verify the obtained theoretical results. • We develop a weak Galerkin method of arbitrary order for the steady incompressible MHD equations. • The method is shown to yield globally divergence-free approximations of the velocity and magnetic fields. • We give existence and uniqueness results for the discrete scheme and derive optimal a priori error estimates. • We also present a convergent linearized iterative algorithm. • Numerical experiments confirm the theoretical results. [ABSTRACT FROM AUTHOR]

The prediction of compressible nonisothermal flows of viscoelastic fluids is important in many industrial processes. Until relatively recently, there was a lack of tractable thermodynamically consistent mathematical models for this class of flows. In this paper a stabilised finite element scheme is presented for the models developed by the authors Mackay and Phillips (2019) which incorporates compressibility and nonisothermal effects. Numerical results are presented for variants of a couple of benchmark problems: the lid driven cavity and the natural convection problems. The temporal discretisation is based on the Taylor–Galerkin method. A compressible version of the discrete elastic viscous split stress (DEVSS) formulation is used to stabilise the numerical scheme. The combined and separate influence of compressible, viscoelastic and thermal effects on the characteristics of these benchmark flows is studied for the first time. • Numerical schemes for compressible, nonisothermal viscoelastic flows are presented. • The influence of stabilisation methods on convergence is explored. • The influence of compressible, viscoelastic and thermal effects is studied. • For lid-driven cavity flow, viscoelasticity increases elastic energy while compressibility decreases it. • Viscoelasticity reduces overall heat transfer in a convection cell. [ABSTRACT FROM AUTHOR]

• Thermomechanical interaction in NiTi strips at different displacement rates. • Full-field deformation and temperature monitoring using DIC and IR. • Single surface fully coupled thermomechanical constitutive model. • Up-down-up softening branches for modeling inhomogeneous deformation. • Thermomechanics of phase transforming materials. The paper uses tensile experiments on NiTi strips at different displacement rates to establish and simulate the thermomechanical interactions caused by the latent heat of the reversible transformation between the austenitic and martensitic phases. The evolution of deformation in the specimen is synchronously monitored with digital image correlation, and the temperature field through infrared imaging, essential for structural modeling. Transformation leads to localized deformation that propagates through the specimen, while the latent heat released/absorbed at the propagating fronts locally heats/cools the specimen. The sensitivity of the transformation stress to temperature results in a complex interaction between the heat transfer conditions and the nucleation and evolution of transformation in the specimen. At low rates of loading, the alternate phase propagates nearly isothermally with a small number of fronts producing relatively flat stress plateaus. Higher rates lead to significant heating/cooling that results in progressive nucleation of multiple fronts and apparent "hardening" responses. The experiments are simulated in a three-dimensional static displacement transient temperature finite element analysis, using a new fully coupled thermomechanical constitutive model. Transformation strain and entropy are its internal variables whose evolution is governed by the motion in the stress-temperature space of a single transformation surface governing both transformations. The prevailing localization is captured by the introduction of softening over the unstable branches of the recorded isothermal material response. The results demonstrate how the important role of the thermal interaction between the specimen and the environment can be addressed. This, together with appropriate calibration of the constitutive and structural model, enable the analysis to reproduce the effect of rate on the recorded response, the evolution of localization patterns, and the associated thermal fields. The results can guide the development of constitutive and structural models of phase transforming materials with strong thermomechanical interactions. [ABSTRACT FROM AUTHOR]

This paper aims to study an H 1 -Galerkin mixed finite element method (FEM) for Klein–Gordon–Zakharov (KGZ) equations with power law nonlinearity. The bilinear element and zero-order Raviart–Thomas element ( Q 11 / Q 10 × Q 01 ) are taken as approximation spaces for the original variables p , ϕ and the auxiliary variables u = ∇ p and ψ = ∇ ϕ , respectively. The supercloseness and superconvergence estimates of order O (h 2 + τ 2) are presented for p and ϕ in the H 1 norm and u and ψ in the L 2 norm, which improve the known results that the original variable ϕ can only reach optimal error estimate shown in numerical experiments without theoretical analysis. Here h is the subdivision parameter and τ is the time step. Finally, some numerical results are provided to support the theoretical analysis. • An H 1 -Galerkin mixed FEM for nonlinear KGZ equations is studied. • The superconvergence estimates are presented, which improve the known results. • The results are also valid to the nonconforming FE pair E Q 1 r o t / Q 10 × Q 01 . [ABSTRACT FROM AUTHOR]

• Detachment experiments for mushroom-shaped adhesive structures are conducted at different retraction velocities spanning 4 orders of magnitude. • At an intermediate mushroom cap thickness, the transition from edge-crack mode to center-crack mode as the retraction velocity increases is observable. • The crucial scaling law of pull-off force with retraction velocity is demonstrated. • Finite element analysis of the viscoelastic detachment uncovers the stress redistribution mechanism. Dynamic adhesion characteristics of synthetic adhesives have attracted massive attention recently. Specific to the mushroom-shaped adhesive structures with outperformed adhesion properties, a clear understanding of the pull-off dynamics, especially the role of retraction velocity, has not been addressed yet. In this paper, based on a custom-built adhesion test apparatus allowing in-situ high-speed measurement of the interface failure, we conducted detachment tests on hundreds-micrometer-scale mushroom-shaped adhesive structures with different cap thicknesses at a retraction velocity range spanning 4 orders of magnitude. It is found that the crack propagation mode for a thin or thick cap remains the same at different retraction velocities, whereas for an intermediate cap the transition from the edge-crack mode to the center-crack mode is observable. Notably, for center-crack mode, the crack area at pull-off remains relatively constant at different velocities. The variation of the pull-off forces with velocity exhibits a scaling law at high velocity regardless of the propagation mode. Dynamic detachment models are developed by considering the rate-dependent work of adhesion to demonstrate the critical-crack-dimension invariance at different velocities and the scaling law of pull-off force with the velocity with the same scaling exponent for center- and edge-crack mode. The theoretical scaling agrees well with experiments. Furthermore, finite element analysis of the viscoelastic detachment demonstrates the stress redistribution against retraction velocities. A prominent feature is the increasing length of the cohesive zone at pull-off with the increasing velocity, indicating a potential trend of a transition to a long-range adhesive interaction. At a sufficiently large velocity, the stress spike at the crack tip disappears and a theoretical strength is almost obtained at the region beneath the stalk. [ABSTRACT FROM AUTHOR]

Axonal beading or formation of multiple beads along an axon is characteristic of many brain pathological states like Alzheimer's, Parkinson's and traumatic injuries. Despite the many existing experimental studies, the underlying mechanisms of this shape instability remain still poorly understood. In this paper, we establish a combined theoretical and numerical framework to study the governing key factors of this morphological transformation. We develop a three-dimensional (3D) non-equilibrium large deformation thermodynamic model with two main parts: the central axoplasm which is considered as a polyelectrolyte hydrogel and the encapsulating cortical membrane which is modeled as an incompressible hyperelastic layer with surface energy and growing surface. The model constitutive and evolution equations are then extracted employing thermodynamic balance principles for both bulk and surface material points. It is shown that the second law of thermodynamics indicates that the axolemma growth rate is proportional to the membrane tension which is in perfect agreement with the available experimental findings. While the developed model is general and can be extended to cover other types of axonal beadings, for the sake of simplicity, here, we focus on osmotically driven axisymmetric beadings which are compressible viscoelastic periodic modulations. We solve the corresponding governing equations using the linear perturbation method. This perturbation analysis proves that: 1) the beading instability is a rate dependent phenomenon that is controlled by the axolemma growth, 2) the initially dominant beading waves (the fastest waves) might be replaced only by longer waves which are more stable and 3) the wavelength of the fastest beads should vary roughly linearly with the axonal radius. These main findings are all in good agreement with the existing experimental results. Finally, the finite element implementation of the model is also presented to verify the results of the linear stability analysis for slow waves. The obtained axisymmetric finite element results are in good agreement with the corresponding theoretical findings. [ABSTRACT FROM AUTHOR]