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In the field of materials engineering, the accurate prediction of material behavior under various loading conditions is crucial. Machine Learning (ML) methods have emerged as promising tools for generating constitutive models straight from data, capable of describing complex material behavior in a more flexible way than classical constitutive models. Yield functions, which serve as foundation of constitutive models for plasticity, can be properly described in a data-oriented manner using ML methods. However, the quality of these descriptions heavily relies on the availability of sufficient high-quality and representative training data that needs to be generated by fundamental numerical simulations, experiments, or a combination of both. The present paper addresses the issue of data selection, by introducing an active learning approach for Support Vector Classification (SVC) and its application in training an ML yield function with suitable data. In this regard, the Query-By-Committee (QBC) algorithm was employed, guiding the selection of new training data points in regions of the feature space where a committee of models shows significant disagreement. This approach resulted in a marked reduction in the variance of model predictions throughout the active learning process. It was also shown that the rate of decrease in the variance went along with an increase in the quality of the trained model, quantified by the Matthews Correlation Coefficient (MCC). This demonstrated the effectiveness of the approach and offered us the possibility to define a dynamic stopping criterion based on the variance in the committee results. [ABSTRACT FROM AUTHOR]

Numerical simulations consist of many components that affect the simulation accuracy and the required computational resources. However, finding an optimal combination of components and their parameters under constraints can be a difficult, time-consuming and often manual process. Classical adaptivity does not fully solve the problem, as it comes with significant implementation cost and is difficult to expand to multi-dimensional parameter spaces. Also, many existing data-based optimization approaches treat the optimization problem as a black-box, thus requiring a large amount of data. We present a constrained, model-based Bayesian optimization approach that avoids black-box models by leveraging existing knowledge about the simulation components and properties of the simulation behavior. The main focus of this paper is on the stochastic modeling ansatz for simulation error and run time as optimization objective and constraint, respectively. To account for data covering multiple orders of magnitude, our approach operates on a logarithmic scale. The models use a priori knowledge of the simulation components such as convergence orders and run time estimates. Together with suitable priors for the model parameters, the model is able to make accurate predictions of the simulation behavior. Reliably modeling the simulation behavior yields a fast optimization procedure because it enables the optimizer to quickly indicate promising parameter values. We test our approach experimentally using the multi-scale muscle simulation framework OpenDiHu and show that we successfully optimize the time step widths in a time splitting approach in terms of minimizing the overall error under run time constraints. [ABSTRACT FROM AUTHOR]

3D Concrete Printing (3DCP) is a rapidly evolving technology that allows for the efficient and accurate construction of complex concrete objects. In this paper, a numerical modelling approach is presented for the simulation of the printing process of cementitious materials, based on the homogeneous fluid assumption. To cope with the large deformations of the domain and the nonlinearity resulting from the use of a non-Newtonian rheological law, the Navier–Stokes equations are solved in the framework of the Particle Finite Element Method (PFEM). Furthermore, tailored solutions have been formulated and implemented for the time-dependent moving boundary conditions at the nozzle outlet and for the efficient handling of the inter-layer contact in the same PFEM framework. The overall computational cost is decreased by the implementation of an adaptive de-refinement technique, which drastically reduces the number of degrees of freedom in time. The proposed modelling approach is finally validated by simulating the printing process of six rectilinear layers and one multi-layer "wall". The results show good agreement with the experimental data and provide valuable insights into the printing process, paving the way for the use of numerical modelling tools for the optimization of materials and processes in the field of 3D Concrete Printing. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is the numerical analysis of a class of mathematical models that describe the contact between a thermo-piezoelectric body and a conductive foundation. Under the assumption of a static process, the material's behavior is modeled with a linear thermo-electro-elastic constitutive law and the frictional contact with Signorini's and Tresca's laws. A variational problem is derived and the existence of a unique weak solution is proved by combining arguments from the theory of variational inequalities with linear strongly monotone Lipschitz continuous operators. A successive iteration technique to linearize the problem by transforming it into an incremental recursive form is proposed, and its convergence is established. An Augmented Lagrangian variant, known as the Alternating Direction Multiplier Method (ADMM), is employed to split the original problem into two subproblems, resolve them sequentially, as well as update the dual variables at each iteration. To illustrate the performance of the proposed approach, several numerical simulations on two-dimensional test problems are carried out. [ABSTRACT FROM AUTHOR]

The paper deals with the gradient based shape optimization of the biaxial X0-specimen, which has been introduced and examined in various papers, under producibility restrictions and the related experimental verification. The original, engineering based design of the X0-specimen has been applied successfully to different loading conditions persisting the question if relevant stress states could be reached by optimizing the geometry. Specimens with the initial as well as with the two load case dependent optimized geometries have been fabricated of the aluminum alloy sheets (AlSi1MgMn; EN AW 6082-T6) and tested. The strain fields in critical regions of the specimens have been recorded by digital image correlation technique. In addition, scanning electron microscope analysis of the fracture surfaces clearly indicate the stress state dependent damage processes. Consequently, the presented gradient based optimization technique facilitated significant improvements to study the damage and fracture processes in a more purposeful way. [ABSTRACT FROM AUTHOR]

Numerical simulation based on FEM/IGA methods is the standard approach for the approximated solution of applied physical problems. In this context, the differentiation of the numerical counterpart of mechanical fields is required. Moreover, the differentiated function can have a complicated shape, depend on many variables and change within the process. Many state-of-the-art numerical differentiation methods are not suitable for this kind of applications and the common way is to exploit analytical differentiation. Thus, an on-the-fly differentiation method is desirable particularly when the process is complicated and when new mechanical models are under development. In this paper, a new method is proposed for a precise computation of the gradient and Hessian. This method has been applied to nonlinear analysis of Kirchhoff–Love shells, which can be considered as an appropriate test bench to prove the reliability in relevant physical context. Numerical experiments show the advantages of the proposed techniques with respect to standard approaches. [ABSTRACT FROM AUTHOR]

This paper deals with the computational homogenization and numerical model reduction of deformation driven pressure diffusion in fractured porous rock. Exposed to seismic waves, the heterogeneity of the material leads to local fluid pressure gradients which are equilibrated via pressure diffusion. However, a macroscopic observer is not able to measure the diffusion process directly but senses the intrinsic attenuation of an apparently monophasic viscoelastic solid. The aim of this paper is to establish a reliable, yet numerically efficient, computational homogenization method to identify the viscoelastic properties of the macroscopic substitute model. Inspired by the Nonuniform Transformation Field Analysis, we incorporate a Numerical Model Reduction procedure. The proposed method is validated for several scenarios ranging from pressure diffusion in an unfractured poroelastic matrix, via localized pressure diffusion in interconnected fractures embedded in an impermeable matrix, to the fully coupled pressure diffusion both in fractures and the embedding poroelastic matrix. [ABSTRACT FROM AUTHOR]

In this paper, a direct data-driven approach for the modeling of isotropic, tension–compression asymmetric, elasto-plastic materials is proposed. Our approach bypasses the conventional construction of explicit mathematical function-based elasto-plastic models, and the need for parameter-fitting. In it, stress update is driven directly by a set of stress–strain data that is generated from uniaxial tension and compression experiments (physical). Particularly, for compression experiments, digital image correlation and homogenization are combined to further improve modeling accuracy. Two representative tension–compression asymmetric materials, titanium alloy TC4ELI and high-density polyethylene, are chosen to illustrate the effectiveness and accuracy of our proposed approach. Results indicate that our data-driven approach can predict the mechanical response of elasto-plastic materials that exhibit tension–compression asymmetry, within the small deformation regime. This data-driven approach provides a practical way to model such materials directly from physical experimental data. Our current implementation is limited, however, by a small reduction to computational efficiency, when compared to typical function-based approaches. Moreover, our present formulation is focused on tension–compression asymmetric elasto-plastic materials that are isotropic. [ABSTRACT FROM AUTHOR]

In this paper, a type of numerical simulation of a three-dimensional (3D) bionic bird with flapping wings in a viscous flow is studied. The model is a self-propelled flying bird capable of free rotation and translation whose flying motion follows the laws of conservation of momentum and angular momentum. The bird is propelled and lifted through flapping and rotating wings and most of thrust force and lift force are exerted on both wings. Both the vortex structures and the flight characteristics are also presented. The relationship between both wings' movement and the vortex structures as well as that between both wings' movement and flight characteristics are also analyzed in this paper. The study uses a 3D computational fluid dynamics package that includes the combined immersed boundary method, volume of fluid method, adaptive multigrid finite volume method, and control strategy for swimming and flying. [ABSTRACT FROM AUTHOR]

In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE 2 methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible dynamic effects arising from micro heterogeneities. A finite-strain formulation is adapted to account for geometrical nonlinearities enabling the study of e.g. plasticity or fiber pullout, which may be associated with large deformations. A consistent kinematic scale link is established as displacement constraint on the whole representative volume element. The consistent macroscopic material tangent moduli are derived including micro inertia in closed form. These can easily be calculated with a loop over all microscopic finite elements, only applying existing assembly and solving procedures. Thus, making it suitable for standard finite element program architectures. Numerical examples of a layered periodic material are presented and compared to direct numerical simulations to demonstrate the capability of the proposed framework. In addition, a simulation of a split Hopkinson tension test showcases the applicability of the framework to engineering problems. [ABSTRACT FROM AUTHOR]

Model reduction techniques such as the proper orthogonal decomposition (POD) method can be used to reduce the computational effort of simulations with a very large number of degrees-of-freedom. The reduction of finite element models including elastoplastic material behavior is still far from being trivial and inevitably leads to problems of efficiency and accuracy. One aim of the present paper is to combine the two methods-sub-structuring and POD-based model reduction-to overcome these difficulties. A typical field of application where plasticity dominates the material behavior are forming processes. The second aim of the paper is to investigate the applicability of the new approach in this context. The presented combined approach selective POD (SPOD) where the reduction is only applied in sub-domains with approximately elastic behavior shows higher accuracy than the general POD method. In this paper, the SPOD method is extended by an adaptive method of sub-structuring (A-SPOD) in which the sub-domain where model reduction is applied is determined automatically. While achieving errors of the same magnitude as by means of SPOD, the computational effort can be reduced significantly by using the A-SPOD approach. [ABSTRACT FROM AUTHOR]

The numerical simulation of contact problems is nowadays a standard procedure in many engineering applications. The contact constraints are usually formulated using either the Lagrange multiplier, the penalty approach or variants of both methodologies. The aim of this paper is to introduce a new scheme that is based on a space filling mesh in which the contacting bodies can move and interact. To be able to account for the contact constraints, the property of the medium, that imbeds the bodies coming into contact, has to change with respect to the movements of the bodies. Within this approach the medium will be formulated as an isotropic/anisotropic material with changing characteristics and directions. In this paper we will derive a new finite element formulation that is based on the above mentioned ideas. The formulation is presented for large deformation analysis and frictionless contact. [ABSTRACT FROM AUTHOR]

This paper is concerned with the energy-dissipation Brezis–Ekeland–Nayroles variational principle (BEN principle) for the numerical study of quasi-static elastoplastic and viscoplastic problems in small strains. This principle is based on the dissipation potential and its Fenchel transform and allows to have a consistent view of the whole evolution by computing the nonlinear response along the whole time history as a solution of a suitable minimization problem. In the present work, the BEN principle is applied to address the elastic perfectly plastic and viscoplastic thick hollow cylinder subjected to internal pressure. It turns out that the BEN variational formulation is based on a two-field functional, that leads naturally to discretize the displacement and stress fields. We present the detailing of the discretization and the numerical implementation of the minimization problem by using the mixed finite element method which is more efficient to enforce the yield condition. Computational accuracy and efficiency of the BEN principle is assessed by comparing the numerical results with the analytical ones and the simulations derived by the classical step-by-step finite element procedure. [ABSTRACT FROM AUTHOR]

In this paper we investigate the application of the localized method of fundamental solutions (LMFS) for solving three-dimensional inhomogeneous elliptic boundary value problems. A direct Chebyshev collocation scheme (CCS) is employed for the approximation of the particular solutions of the given inhomogeneous problem. The Gauss–Lobatto collocation points are used in the CCS to ensure the pseudo-spectral convergence of the method. The resulting homogeneous equations are then calculated by using the LMFS. In the framework of the LMFS, the computational domain is divided into a set of overlapping local subdomains where the traditional MFS formulation and the moving least square method are applied. The proposed CCS-LMFS produces sparse and banded stiffness matrix which makes the method possible to perform large-scale simulations on a desktop computer. Numerical examples involving Poisson, Helmholtz as well as modified-Helmholtz equations (with up to 1,000,000 unknowns) are presented to illustrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In the numerical simulation of impact phenomena, artificial oscillations can occur due to an instantaneous change of velocity in the contact area. In this paper, a nonlinear penalty regularization is used to avoid these oscillations. A particular focus is the investigation of higher order methods in space and time to increase the computational efficiency. The spatial discretization is realized by higher order spectral element methods that are characterized by a diagonal mass matrix. The time integration scheme is based on half-explicit Runge-Kutta scheme of fourth order. For the conditionally stable scheme, the critical time step is influenced by the penalty regularization. A framework is presented to adjust the penalty stiffness and the time step for a specific mesh to avoid oscillations. The methods presented in this paper are applied to 1D-simulations of a split Hopkinson pressure bar, which is commonly used for the investigation of materials under dynamic loading. [ABSTRACT FROM AUTHOR]

This paper presents an integrated model-free data-driven approach to solid mechanics, allowing to perform numerical simulations on structures on the basis of measures of displacement fields on representative samples, without postulating a specific constitutive model. A material data identification procedure, allowing to infer strain–stress pairs from displacement fields and boundary conditions, is used to build a material database from a set of mutiaxial tests on a non-conventional sample. This database is in turn used by a data-driven solver, based on an algorithm minimizing the distance between manifolds of compatible and balanced mechanical states and the given database, to predict the response of structures of the same material, with arbitrary geometry and boundary conditions. Examples illustrate this modelling cycle and demonstrate how the data-driven identification method allows importance sampling of the material state space, yielding faster convergence of simulation results with increasing database size, when compared to synthetic material databases with regular sampling patterns. [ABSTRACT FROM AUTHOR]

This paper builds on a recently developed immersogeometric fluid-structure interaction (FSI) methodology for bioprosthetic heart valve (BHV) modeling and simulation. It enhances the proposed framework in the areas of geometry design and constitutive modeling. With these enhancements, BHV FSI simulations may be performed with greater levels of automation, robustness and physical realism. In addition, the paper presents a comparison between FSI analysis and standalone structural dynamics simulation driven by prescribed transvalvular pressure, the latter being a more common modeling choice for this class of problems. The FSI computation achieved better physiological realism in predicting the valve leaflet deformation than its standalone structural dynamics counterpart. [ABSTRACT FROM AUTHOR]

In this paper, an actual landslide process that occurred in Southern China is simulated by a continuum approach, the particle finite element method (PFEM). The PFEM attempts to solve the boundary-value problems in the framework of solid mechanics, satisfying the governing equations including momentum conservation, displacement-strain relation, constitutive relation as well as the frictional contact between the sliding mass and the slip surface. To warrant the convergence behaviour of solutions, the problem is formulated as a mathematical programming problem, while the particle finite element procedure is employed to tackle the issues of mesh distortion and free-surface evolution. The whole procedure of the landslide, from initiation, sliding to deposition, is successfully reproduced by the continuum approach. It is shown that the density of the mass has little influence on the sliding process in the current landslide, whereas both the geometry and the roughness of the slip surface play important roles. Comparative studies are also conducted where a satisfactory agreement is obtained. [ABSTRACT FROM AUTHOR]

In this paper, an enriched FEM technique is employed for thermo-mechanical contact problem based on the extended finite element method. A fully coupled thermo-mechanical contact formulation is presented in the framework of X-FEM technique that takes into account the deformable continuum mechanics and the transient heat transfer analysis. The Coulomb frictional law is applied for the mechanical contact problem and a pressure dependent thermal contact model is employed through an explicit formulation in the weak form of X-FEM method. The equilibrium equations are discretized by the Newmark time splitting method and the final set of non-linear equations are solved based on the Newton-Raphson method using a staggered algorithm. Finally, in order to illustrate the capability of the proposed computational model several numerical examples are solved and the results are compared with those reported in literature. [ABSTRACT FROM AUTHOR]

This paper deals with adhesive frictionless normal contact between one elastic flat solid and one stiff solid with rough surface. After computation of the equilibrium solution of the energy minimization principle and respecting the contact constraints, we aim at studying the stability of this equilibrium solution. This study of stability implies solving an eigenvalue problem with inequality constraints. To achieve this goal, we propose a proximal algorithm which enables qualifying the solution as stable or unstable and that gives the instability modes. This method has a low computational cost since no linear system inversion is required and is also suitable for parallel implementation. Illustrations are given for the Hertzian contact and for rough contact. [ABSTRACT FROM AUTHOR]

Acoustic metamaterials (AMs) are man-made composite materials. However, the random uncertainties are unavoidable in the application of AMs due to manufacturing and material errors which lead to the variance of the physical responses of AMs. In this paper, an uncertainty model based on the change of variable perturbation stochastic finite element method (CVPS-FEM) is formulated to predict the probability density functions of physical responses of AMs with random parameters. Three types of physical responses including the band structure, mode shapes and frequency response function of AMs are studied in the uncertainty model, which is of great interest in the design of AMs. In this computation, the physical responses of stochastic AMs are expressed as linear functions of the pre-defined random parameters by using the first-order Taylor series expansion and perturbation technique. Then, based on the linear function relationships of parameters and responses, the probability density functions of the responses can be calculated by the change-of-variable technique. Three numerical examples are employed to demonstrate the effectiveness of the CVPS-FEM for stochastic AMs, and the results are validated by Monte Carlo method successfully. [ABSTRACT FROM AUTHOR]

This paper presents an isogeometric formulation for frictionless contact between deformable bodies, based on the recently proposed concept of the third medium. This concept relies on continuum formulations not only for the contacting bodies but also for a fictitious intermediate medium in which the bodies can move and interact. Key to the formulation is a suitable definition of the constitutive behavior of the third medium. In this work, based on a number of numerical tests, the role of the material parameters of the third medium is systematically assessed. We also assess the rate of spatial convergence for higher-order discretizations, stemming from the regularization of the non-smooth contact problem inherent to the third medium approach. Finally, problems with self contact are considered and turn out to be an attractive application of the method. [ABSTRACT FROM AUTHOR]

Distance fields are scalar functions defining the minimum distance of a given point in the space from the boundary of an object. Crack surfaces are geometric entities whose shapes can be arbitrary, often described with ruled surfaces or polygonal subdivisions. The derivatives of distance functions for such surfaces are discontinuous across the surface, and continuous all around the edges. These properties of the distance function were employed to build intrinsic enrichments of the underlying mesh-free discretisation for efficient simulation of three-dimensional crack propagation, removing the limitations of existing criteria (reviewed in this paper). Examples show that the proposed approach is able to introduce quite convoluted crack paths. The incremental nature of the developed approach does not require re-computation of the enrichment for the entire crack surface as advancing crack front extends incrementally as a set of connected surface facets. The concept is based on purely geometric representation of discontinuities thus addressing only the kinematic aspects of the problem, such to allow for any constitutive and cohesive interface models to be used. [ABSTRACT FROM AUTHOR]

The elastic energy in the conventional Cauchy continuum model depends on the gradient of the displacement field, which is not adequate to show the behavior of a system under point and line forces. Applying these kinds of boundary conditions to the continuum will lead to singularities. To overcome this problem, a generalization of the Cauchy continuum concept is a choice. In this paper, isogeometric analysis is used to simulate the behavior of second- and third-gradient materials. As expected, a significant improvement in the efficiency and accuracy of the attained results compared to the conventional finite element method is noticed. [ABSTRACT FROM AUTHOR]

In this paper, a numerical approach with an experimental validation is introduced for modelling high-speed metal grinding processes in 6061-T6 aluminum alloys. The derivation of the present numerical method starts with an establishment of a stabilized particle Galerkin approximation. A non-residual penalty term from strain smoothing is introduced as a means of stabilizing the particle Galerkin method. Additionally, second-order strain gradients are introduced to the penalized functional for the regularization of damage-induced strain localization problem. To handle the severe deformation in metal grinding simulation, an adaptive anisotropic Lagrangian kernel is employed. Finally, the formulation incorporates a bond-based failure criterion to bypass the prospective spurious damage growth issues in material failure and cutting debris simulation. A three-dimensional metal grinding problem is analyzed and compared with the experimental results to demonstrate the effectiveness and accuracy of the proposed numerical approach. [ABSTRACT FROM AUTHOR]

Many atomistic-continuum coupling techniques employ an overlapping subdomain to suppress spurious wave reflections. In this paper, we propose the imposition of a new damping condition on the overlapping subdomain to enhance the capability of such methods in eliminating spurious wave reflections. In this technique, the total displacements of the atoms in the overlapping subdomain are decomposed into fine and coarse scales. The fine scale displacements represent the oscillations which cannot be resolved by the continuum mesh and must be eliminated to avoid the artificial reflections. This is achieved by modifying the equations of motion of the fine scale displacements to include a damping term. The flexibility of the proposed technique is verified by applying it to the bridging scale method and bridging domain method. Numerical simulations of one- and two-dimensional problems demonstrate the effectiveness of the technique in enhancing the elimination of the spurious wave reflections in coupled atomistic-continuum techniques. [ABSTRACT FROM AUTHOR]

In this paper, we present a dynamic refinement algorithm for the smoothed particle Hydrodynamics (SPH) method. An SPH particle is refined by replacing it with smaller daughter particles, which positions are calculated by using a square pattern centered at the position of the refined particle. We determine both the optimal separation and the smoothing distance of the new particles such that the error produced by the refinement in the gradient of the kernel is small and possible numerical instabilities are reduced. We implemented the dynamic refinement procedure into two different models: one for free surface flows, and one for post-failure flow of non-cohesive soil. The results obtained for the test problems indicate that using the dynamic refinement procedure provides a good trade-off between the accuracy and the cost of the simulations. [ABSTRACT FROM AUTHOR]

In this paper is proposed an extended Bouc–Wen model for improving its capability to approximate experimental symmetric hysteretic loops. On the basis of the generalized equation there are defined integral and differential conditions that describe the essential geometric properties of a hysteretic curve. Next, a new method based on Genetic Algorithms is developed to identify the Bouc–Wen model parameters from experimental hysteretic loops obtained from periodic loading tests. The performance of presented approach is illustrated for two types of seismic protection devices with hysteretic characteristics: elastomeric base isolators and buckling restrained dissipative braces. The applicability of proposed method is highlighted by using the derived models to analyse by numerical simulation the efficiency of these devices for reducing seismic response of a three stories civil structure. [ABSTRACT FROM AUTHOR]

This paper proposes the use of a specific combination of discrete and finite element methods for the simulation of systems of deformable bodies in order to reduce the computational cost, when certain assumptions can be made. In particular, the Updated Lagrangian finite element formulation and the central difference time integration method are employed together with certain simplifying assumptions in order to linearize this highly nonlinear contact problem and obtain solutions with realistic computational cost and sufficiently good accuracy. Furthermore, the paper discusses software implementation issues and the advantages that the Java technologies can offer in the development of such engineering applications. [ABSTRACT FROM AUTHOR]

The paper proposes and investigates an efficient two-scale approach to describe the material behavior of technical textiles. On the macroscopic scale the considered textile materials are modeled as homogeneous by means of shell elements. The heterogeneous microstructure, which consists e.g. of woven fibers, is explicitly resolved in representative volume elements (RVE). A shell-specific homogenization scheme is applied to connect the macro and the micro scale. The simultaneous solution of the macroscopic and the nonlinear microscopic simulations, e.g. by means of the FE $$^2$$ -method, is very expensive. Therefore, a different approach is applied here: the macro constitutive response is computed in advance and tabulated for a certain RVE and for different loading scenarios. These homogenized stress and tangent values are then used in a macroscopic simulation without the need to explicitly resort to the microscopic simulations. The efficiency of the approach is analyzed by means of numerical examples. [ABSTRACT FROM AUTHOR]

Tracking algorithms constitute an efficient numerical technique for modelling fracture in quasi-brittle materials. They succeed in representing localized cracks in the numerical model without mesh-induced directional bias. Currently available tracking algorithms have an important limitation: cracking originates either from the boundary of the discretized domain or from predefined 'crack-root' elements and then propagates along one orientation. This paper aims to circumvent this drawback by proposing a novel tracking algorithm that can simulate cracking starting at any point of the mesh and propagating along one or two orientations. This enhancement allows the simulation of structural case-studies experiencing multiple cracking. The proposed approach is validated through the simulation of a benchmark example and an experimentally tested structural frame under in-plane loading. Mesh-bias independency of the numerical solution, computational cost and predicted collapse mechanisms with and without the tracking algorithm are discussed. [ABSTRACT FROM AUTHOR]

Self-healing hydrogels exhibit enhanced toughness due to their unique microstructures consisting of an extensible and loose crosslinked polymer network, and a brittle but healable network with tightly connected sacrificial bonds. Due to the time-dependent breaking–healing kinetics of the sacrificial network, the constitutive models of self-healing hydrogels are commonly in the form of convolution-like integral, which imposes great challenges to the numerical simulation with intolerable computational cost. In this study, we propose to solve this issue by incorporating a generalized recursive integration algorithm into the finite element (FE) framework for the simulation of the convolution-like constitutive behaviors. With the recursive algorithm, the time-dependent breaking–healing kinetics are numerically solved only based on the results from the previous last time step. The deformation behaviors of one typical self-healing hydrogel with ionic sacrificial bonds are then modeled with the proposed FE framework by adopting the full Newton–Raphson formulation, in which the recursive algorithm is expanded into the tensor space to determine the convolution-like stress and material stiffness tensors. The merits of this numerical framework in simulation capabilities and accuracy are witnessed by different case studies under both transient and equilibrium loading conditions. This proposed FE framework can also be expanded to incorporate different self-healing mechanisms of hydrogels, which is expected to act as a general avenue to numerically simulate the time/history-dependent constitutive behaviors of soft materials. [ABSTRACT FROM AUTHOR]

In this paper, a 3D computational model has been developed to investigate biofilms in a multi-physics framework using smoothed particle hydrodynamics (SPH) based on a continuum approach. Biofilm formation is a complex process in the sense that several physical phenomena are coupled and consequently different time-scales are involved. On one hand, biofilm growth is driven by biological reaction and nutrient diffusion and on the other hand, it is influenced by fluid flow causing biofilm deformation and interface erosion in the context of fluid and deformable solid interaction. The geometrical and numerical complexity arising from these phenomena poses serious complications and challenges in grid-based techniques such as finite element. Here the solution is based on SPH as one of the powerful meshless methods. SPH based computational modeling is quite new in the biological community and the method is uniquely robust in capturing the interface-related processes of biofilm formation such as erosion. The obtained results show a good agreement with experimental and published data which demonstrates that the model is capable of simulating and predicting overall spatial and temporal evolution of biofilm. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional (2D)-three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier-Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations. [ABSTRACT FROM AUTHOR]

In the present paper, a finite strain model for complex combined isotropic-kinematic hardening is presented. It accounts for finite elastic and finite plastic strains and is suitable for any anisotropic yield criterion. In order to model complex cyclic hardening phenomena, the kinematic hardening is described by several back stress components. To that end, a new procedure is proposed in which several multiplicative decompositions of the plastic part of the deformation gradient are considered. The formulation incorporates a completely general format of the yield function, which means that any yield function can by employed by following a procedure that ensures the principle of material frame indifference. The constitutive equations are derived in a thermodynamically consistent way and numerically integrated by means of a backward-Euler algorithm based on the exponential map. The performance of the constitutive model is assessed via numerical simulations of industry-relevant sheet metal forming processes (U-channel forming and draw/re-draw of a panel benchmarks), the results of which are compared to experimental data. The comparison between numerical and experimental results shows that the use of multiple back stress components is very advantageous in the description of springback. This holds in particular if one carries out a comparison with the results of using only one component. Moreover, the numerically obtained results are in excellent agreement with the experimental data. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the coupling of reduced models for the simulation of structures involving localized geometrical details. Herein, we use the Arlequin method, originally designed to deal with multimodel and multiscale analyses of mechanical problems, to mix reduced models built using the proper generalized decomposition. Instead of solving the global coupled problem in a monolithic way, the LATIN strategy is used to propose a decoupled algorithm. The numerical examples demonstrate the feasibility of the approach and in particular its potentiality in terms of flexibility. [ABSTRACT FROM AUTHOR]

In industry, particle-laden fluids, such as particle-functionalized inks, are constructed by adding fine-scale particles to a liquid solution, in order to achieve desired overall properties in both liquid and (cured) solid states. However, oftentimes undesirable particulate agglomerations arise due to some form of mutual-attraction stemming from near-field forces, stray electrostatic charges, process ionization and mechanical adhesion. For proper operation of industrial processes involving particle-laden fluids, it is important to carefully breakup and disperse these agglomerations. One approach is to target high-frequency acoustical pressure-pulses to breakup such agglomerations. The objective of this paper is to develop a computational model and corresponding solution algorithm to enable rapid simulation of the effect of acoustical pulses on an agglomeration composed of a collection of discrete particles. Because of the complex agglomeration microstructure, containing gaps and interfaces, this type of system is extremely difficult to mesh and simulate using continuum-based methods, such as the finite difference time domain or the finite element method. Accordingly, a computationally-amenable discrete element/discrete ray model is developed which captures the primary physical events in this process, such as the reflection and absorption of acoustical energy, and the induced forces on the particulate microstructure. The approach utilizes a staggered, iterative solution scheme to calculate the power transfer from the acoustical pulse to the particles and the subsequent changes (breakup) of the pulse due to the particles. Three-dimensional examples are provided to illustrate the approach. [ABSTRACT FROM AUTHOR]

Gaining insights into the effects of microstructural details on materials behavior may be achieved by incorporating their attributes into numerical modeling. This requires us to make considerable efforts to feature heterogeneity morphology distributions and their spatial arrangement. This paper focuses on modeling the scatter observed in materials heterogeneity geometry. The proposed strategy is based on the development of a 1D-shape signature function representing the 2D-section of a given shape, on Fourier basis functions. The Fourier coefficients are then considered as random variables. This methodology has been applied to flax fibers which are gradually introduced into composite materials as a potential alternative to synthetic reinforcements. In this contribution, the influence of some underlying assumptions regarding the choice of one 1D-shape signature function, its discretization scheme and truncation level, and the best way of modeling the associated random variables is also investigated. Some configurations coming from the combination of these tuning parameters are found to be sufficiently relevant to render efficiently the morphometric factors of the observed fibers statistically speaking. [ABSTRACT FROM AUTHOR]

For multi-field simulations involving a larger number of different physical fields and in cases where the involved fields or simulation codes change due to new modelling insights, e.g., flexible and robust partitioned coupling schemes are an important prerequisite to keep time-to-solution within reasonable limits. They allow for a fast, almost plug-and-play combination of existing established codes to the respective multi-field simulation environment. In this paper, we study a class of coupling approaches that we originally introduced in order to improve the parallel scalability of partitioned simulations. Due to the symmetric structure of these coupling methods and the use of 'long' vectors of coupling data comprising the input and output of all involved codes at a time, they turn out to be particularly suited also for simulations involving more than two coupled fields. As standard two-field coupling schemes are not suited for such cases as shown in our numerical results, this allows the simulation of a new range of applications in a partitioned way. [ABSTRACT FROM AUTHOR]

This paper considers numerical simulations of fluid-structure interaction (FSI) problems in hemodynamics for idealized geometries of healthy cerebral arteries modeled by both nonlinear isotropic and anisotropic material constitutive laws. In particular, it focuses on an anisotropic model initially proposed for cerebral arteries to characterize the activation of collagen fibers at finite strains. In the current work, this constitutive model is implemented for the first time in the context of an FSI formulation. In this framework, we investigate the influence of the material model on the numerical results and, in the case of the anisotropic laws, the importance of the collagen fibers on the overall mechanical behavior of the tissue. With this aim, we compare our numerical results by analyzing fluid dynamic indicators, vessel wall displacement, Von Mises stress, and deformations of the collagen fibers. Specifically, for an anisotropic model with collagen fiber recruitment at finite strains, we highlight the progressive activation and deactivation processes of the fibrous component of the tissue throughout the wall thickness during the cardiac cycle. The inclusion of collagen recruitment is found to have a substantial impact on the intramural stress, which will in turn impact the biological response of the intramural cells. Hence, the methodology presented here will be particularly useful for studies of mechanobiological processes in the healthy and diseased vascular wall. [ABSTRACT FROM AUTHOR]

This paper proposes for the first time an intrinsic enrichment for extremely curved cracks in a meshfree framework. The unique property of the proposed method lies in the exact geometric representation of cracks using non-uniform rational B-splines (NURBS). A distance function algorithm for NURBS is presented, resulting in a spatial field which is simultaneously discontinuous over the (finite) curved crack and continuous all around the crack tips. Numerical examples show the potential of the proposed approach and illustrate its advantages with respect to other techniques usually employed to model fracture, including standard finite elements with remeshing and the extended finite element method. This work represents a further step in an ongoing effort in the community to integrate computer aided design with numerical simulations. [ABSTRACT FROM AUTHOR]

A GSM-CFD solver for incompressible flows is developed based on the gradient smoothing method (GSM). A matrix-form algorithm and corresponding data structure for GSM are devised to efficiently approximate the spatial gradients of field variables using the gradient smoothing operation. The calculated gradient values on various test fields show that the proposed GSM is capable of exactly reproducing linear field and of second order accuracy on all kinds of meshes. It is found that the GSM is much more robust to mesh deformation and therefore more suitable for problems with complicated geometries. Integrated with the artificial compressibility approach, the GSM is extended to solve the incompressible flows. As an example, the flow simulation of carotid bifurcation is carried out to show the effectiveness of the proposed GSM-CFD solver. The blood is modeled as incompressible Newtonian fluid and the vessel is treated as rigid wall in this paper. [ABSTRACT FROM AUTHOR]

This paper focuses on the numerical simulation of martensitic transformations in shape memory alloys (SMAs) using a phase-field model. We developed a dynamic thermo-mechanical model for SMAs, using strain based order parameter, having a bi-directional coupling between structural and thermal physics via strain, strain rate and temperature. The model involves fourth order spatial derivatives representing a domain wall. We propose an isogeometric analysis numerical formulation for straightforward solution to the fourth order differential equations. We present microstructure evolution under different loading conditions and dynamic loading simulations of the evolved microstructures of SMAs of different geometries to illustrate the flexibility, accuracy and stability of our numerical method. The simulation results are in agreement with the numerical and experimental results from the literature. [ABSTRACT FROM AUTHOR]

A monolithic numerical solution of a partial differential equation (PDE) model for shear bands, which includes a thermal softening rate dependent plastic flow rule and finite thermal conductivity, is presented. The formulation accounts for large deformation kinematics and includes incrementally objective treatment of the hypoplastic constitutive relations. Regularization is achieved by including finite thermal conductivity, which informs the PDE system of a length scale, governed by competition between shear heating and thermal diffusion. The monolithic solution scheme is then used to eliminate splitting errors during the solution of the discretized system. The scheme is presented in a general, mixed formulation, which allows for many choices of shape functions. We study and compare two elements, which have been implemented with the monolithic nonlinear solver: the Irreducible Shear Band Quad (ISBQ) and the Pian Sumihara Shear Band Quad (PSSBQ). ISBQ employs the same interpolation as an irreducible four node quad while PSSBQ is a mixed, assumed stress element. The algorithmic approximations to the Lie derivative and Jaumann rate of Kirchhoff stress are available in the literature for ISBQ type elements, and are derived in this paper for the PSSBQ. These expressions are used to achieve an incrementally objective formulation. It is found that the PSSBQ converges faster than the ISBQ with mesh refinement, and that the convergence of the ISBQ can be improved with a remeshing procedure. [ABSTRACT FROM AUTHOR]

The understanding and the prediction of the failure behaviour of materials with pronounced microstructural effects is of crucial importance. This paper presents a novel computational methodology for the handling of fracture on the basis of the microscale behaviour. The basic principles presented here allow the incorporation of an adaptive discretization scheme of the structure as a function of the evolution of strain localization in the underlying microstructure. The proposed quasi-discrete methodology bridges two scales: the scale of the material microstructure, modelled with a continuum type description; and the structural scale, where a discrete description of the material is adopted. The damaging material at the structural scale is divided into unit volumes, called cells, which are represented as a discrete network of points. The scale transition is inspired by computational homogenization techniques; however it does not rely on classical averaging theorems. The structural discrete equilibrium problem is formulated in terms of the underlying fine scale computations. Particular boundary conditions are developed on the scale of the material microstructure to address damage localization problems. The performance of this quasi-discrete method with the enhanced boundary conditions is assessed using different computational test cases. The predictions of the quasi-discrete scheme agree well with reference solutions obtained through direct numerical simulations, both in terms of crack patterns and load versus displacement responses. [ABSTRACT FROM AUTHOR]

Finite element based formulations for flexible multibody systems are becoming increasingly popular and as the complexity of the configurations to be treated increases, so does the computational cost. It seems natural to investigate the applicability of parallel processing to this type of problems; domain decomposition techniques have been used extensively for this purpose. In this approach, the computational domain is divided into non-overlapping sub-domains, and the continuity of the displacement field across sub-domain boundaries is enforced via the Lagrange multiplier technique. In the finite element literature, this approach is presented as a mathematical algorithm that enables parallel processing. In this paper, the divided system is viewed as a flexible multibody system, and the sub-domains are connected by kinematic constraints. Consequently, all the techniques applicable to the enforcement of constraints in multibody systems become applicable to the present problem. In particular, it is shown that a combination of the localized Lagrange multiplier technique with the augmented Lagrange formulation leads to interesting solution strategies. The proposed algorithm is compared with the well-known FETI approach with regards to convergence and efficiency characteristics. The present algorithm is relatively simple and leads to improved convergence and efficiency characteristics. Finally, implementation on a parallel computer was conducted for the proposed approach. [ABSTRACT FROM AUTHOR]

The paper reviews the construction of cloaks for 2D acoustic or electromagnetic waves using the Piola transform, and shows how the knowledge of the transform leads to the construction of a quasi-optimal test norm for the Discontinuous Petrov-Galerkin (DPG) method with optimal test functions for this class of problems. Numerical experiments for cylindrical and square cloaks illustrate the discussed concepts and demonstrate the effectiveness of the DPG method in cloak simulations. [ABSTRACT FROM AUTHOR]

The numerical simulation of contact problems is still a delicate matter especially when large transformations are involved. In that case, relative large slidings can occur between contact surfaces and the discretization error induced by usual finite elements may not be satisfactory. In particular, usual elements lead to a facetization of the contact surface, meaning an unavoidable discontinuity of the normal vector to this surface. Uncertainty over the precision of the results, irregularity of the displacement of the contact nodes and even numerical oscillations of contact reaction force may result of such discontinuity. Among the existing methods for tackling such issue, one may consider mortar elements (Fischer and Wriggers, Comput Methods Appl Mech Eng 195:5020-5036, ; McDevitt and Laursen, Int J Numer Methods Eng 48:1525-1547, ; Puso and Laursen, Comput Methods Appl Mech Eng 93:601-629, ), smoothing of the contact surfaces with additional geometrical entity (B-splines or NURBS) (Belytschko et al., Int J Numer Methods Eng 55:101-125, ; Kikuchi, Penalty/finite element approximations of a class of unilateral contact problems. Penalty method and finite element method, ASME, New York, ; Legrand, Modèles de prediction de l'interaction rotor/stator dans un moteur d'avion Thèse de doctorat. PhD thesis, École Centrale de Nantes, Nantes, ; Muñoz, Comput Methods Appl Mech Eng 197:979-993, ; Wriggers and Krstulovic-Opara, J Appl Math Mech (ZAMM) 80:77-80, ) and, the use of isogeometric analysis (Temizer et al., Comput Methods Appl Mech Eng 200:1100-1112, ; Hughes et al., Comput Methods Appl Mech Eng 194:4135-4195, ; de Lorenzis et al., Int J Numer Meth Eng, in press, ). In the present paper, we focus on these last two methods which are combined with a finite element code using the bi-potential method for contact management (Feng et al., Comput Mech 36:375-383, ). A comparative study focusing on the pros and cons of each method regarding geometrical precision and numerical stability for contact solution is proposed. The scope of this study is limited to 2D contact problems for which we consider several types of finite elements. Test cases are given in order to illustrate this comparative study. [ABSTRACT FROM AUTHOR]

New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. These results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations. [ABSTRACT FROM AUTHOR]

Parametric studies and identification problems require to perform repeated analyses, where only a few input parameters are varied among those defining the problem of interest, often associated to complex numerical simulations. In fact, physical phenomena relevant to several practical applications involve coupled material and geometry non-linearities. In these situations, accurate but expensive computations, usually carried out by the finite element method, may be replaced by numerical procedures based on proper orthogonal decomposition combined with radial basis function interpolation. Besides drastically reducing computing times and costs, this approach is capable of retaining the essential features of the considered system responses while filtering most disturbances. These features are illustrated in this paper with specific reference to some elastic-plastic problems. The presented results can however be easily extended to other meaningful engineering situations. [ABSTRACT FROM AUTHOR]