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Isogeometric analysis (IGA) is an effective numerical method for connecting computer-aided design and engineering, which has been widely applied in various aspects of computational mechanics. IGA involves Galerkin and collocation formulations. Exploiting the same high-order non-uniform rational B-spline (NURBS) bases that span the physical domain and the solution space leads to increased accuracy and fast computation. Although IGA Galerkin provides optimal convergence, IGA collocation performs better in terms of the ratio of accuracy to computational time. Without numerical integration, by working directly with the strong form of the partial differential equation over the physical domain defined by NURBS geometry, the derivatives of the NURBS-expressed numerical solution at some chosen collocation points can be calculated. In this study, we survey the methodological framework and the research prospects of IGA. The collocation schemes in the IGA collocation method that affect the convergence performance are addressed in this paper. Recent studies and application developments are reviewed as well. [ABSTRACT FROM AUTHOR]

We propose the novel design, development, and implementation of the well-known generalized single step single solve (GS4) family of algorithms into the differential algebraic equation framework which not only allows altogether different numerical time integration algorithms within the GS4 family in each of the different subdomains but also additionally allows for the selection of different space discretized methods such as the finite element method and particle methods, and other spatial methods as well in a single analysis unlike existing state-of-the-art. For the first time, the user has the flexibility and robustness to embed different algorithms for time integration and different spatial methods for space discretization in a single analysis. In addition, the GS4 family enables a wide variety of choices of time integration methods in a single analysis and also ensures the second-order accuracy in time of all primary variables and Lagrange multipliers. This is not possible to date. However, the present framework provides the fusion of a wide variety of choices of time discretized methods and spatial methods and has the bandwidth and depth to engage in various types of research investigations as well and features for fine tuning of numerical simulations. It provides generality/versatility of the computational framework incorporating subdomains with different spatial and time integration algorithms with improved accuracy. The robustness and accuracy of the present work is not feasible in the current state of technology. Various numerical examples illustrate the significant capabilities and generality and effectiveness for general nonlinear dynamics. [ABSTRACT FROM AUTHOR]

The tear test is widely used to measure the fracture toughness of thin rubber sheets and polymer films. More recently, the tear test has been applied to polymer materials produced by melt extrusion additive manufacturing to measure the fracture toughness of a single weld between two printed (extruded) filaments. This paper presents a finite element modeling study of the tearing of a weld between two printed filaments to investigate the mechanics of the tear test and the effects of geometry and material properties on the measured tear energy. The mechanical behavior of the printed filaments was described by a viscoplastic model for glassy polymers and the weld was represented using cohesive surface elements and the Xu-Needleman traction-separation relationship. The geometric model and the material parameters were chosen based on experimental measurements. The tear energy varied with the specimen dimensions, the curvature of the printed filaments, the yield stress relative to the cohesive strength of the weld, and the post-yield stress drop. The effects of the hardening modulus were small. These factors altered the viscoplastic dissipation in the material ahead of the propagating crack tip. The results showed that viscoplastic dissipation could constitute a large fraction of the tear energy and is strongly affected by the specimen dimensions and the geometry and material properties of the printed filament. There was also considerable mode mixty in the tear energy. The findings can be used to design tear tests to measure the intrinsic fracture toughness of the weld. [ABSTRACT FROM AUTHOR]

Laminated glass is a composite made of glass plies sandwiching polymeric interlayers, permanently bonded with a process at high pressure and temperature in autoclave. Within the quasi-elastic approximation, according to which the polymer is linear elastic material whose elastic modulus parametrically depends upon time and environmental temperature, we present a model for inflexed laminated-glass beams in the pre-glass-breakage phase. The approach relies on a modified version of the refined zig-zag theory for composites, in which the glass plies are treated as Euler-Bernoulli beams, whereas the interlayers can only provide a shear-stiffness contribution to the coupling of the glass plies. The kinematic description is greatly simplified and the governing equations can be solved analytically, for laminated packages of any type, when the beam is statically determined. A finite element implementation is proposed for the most general cases. The convergence analysis for the numerical approach and the comparison with the analytical solution in benchmark problems demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Data Driven Computational Mechanics (DDCM) solves the boundary value problem by directly relying on the strain-stress data, bypassing the need for a constitutive model. In presence of materials exhibiting a softening response, Finite Element analyses performed with a constitutive model typically use a length scale, which can be introduced into the problem in multiple ways. A few commonly used ways include the addition of the gradient of damage variable in the energy density functional, using the gradient of strain while evaluating the internal variable, and so on. However, in the context of DDCM, these techniques may not be effective as the internal variables are not explicitly defined. Hence, the current article introduces a regularization technique, where the gradient of strain is constrained to lie within some interval. This prevents strain localization within an element by introducing a length scale into the problem. This article demonstrates the effectiveness of such a regularization technique in the case of 1D problems using a constitutive model while comparing its performance with strain gradient (SG) models. [ABSTRACT FROM AUTHOR]

To reduce the noise in a pump piping system and increase the usage time of equipment, a new type of porous muffler is proposed in this paper. A water guide cone is incorporated into the muffler structure, which may help to redirect the fluid media in the piping system. The porous structure is adapted from a muffler shell, water cone wall and round bottom plate. According to this structure, the muffler sample is made, and a pump pipeline system test bench is set up. The outlet noise of the pump pipeline system is measured after installing the muffler. At the same time, the muffler is numerically simulated by combining computational fluid mechanics and Lighthill acoustic theory. The characteristics of the flow field and external sound field under three different flow conditions of 200 m³ /h, 400 m³ /h and 600 m³ /h are assessed. The numerical simulation results show the same dominant frequency and trend as the experimental results. The rationality of the numerical simulation is verified. Research shows that: the level of sound pressure at the muffler's outlet is lower than at the inlet, causing muffling, and the characteristics of a quadrupole sound source appear at the outlet. The proposed muffler has a certain effect in reducing noise in the pump pipeline system. [ABSTRACT FROM AUTHOR]

Some computational tools intended to educate, illuminate, persuade, or to facilitate scholarship create diagrammatic representations of concepts and ideas. This abstraction, which I call the "indefinite idea plane," often consist of boxes and arrows. Alternative approaches that have been neglected may be found in art and architecture. If an office building "must be every inch a proud and soaring thing," what should we expect of an idea plane unfettered by material physics? [ABSTRACT FROM AUTHOR]

For complex engineering systems, such as trains, planes, and offshore oil platforms, load spectra are cornerstone of their safety designs and fault diagnoses. We demonstrate in this study that well-orchestrated machine learning modeling, in combination with limited experimental data, can effectively reproduce the high-fidelity, history-dependent load spectra in critical sites of complex engineering systems, such as high-speed trains. To meet the need for in-service monitoring, we propose a segmentation and randomization strategy for long-duration historical data processing to improve the accuracy of our data-driven model for long-term load-time history prediction. Results showed the existence of an optimal length of subsequence, which is associated with the characteristic dissipation time of the dynamic system. Moreover, the data-driven model exhibits an excellent generalization capability to accurately predict the load spectra for different levels of passenger-dedicated lines. In brief, we pave the way, from data preprocessing, hyperparameter selection, to learning strategy, on how to capture the nonlinear responses of such a dynamic system, which may then provide a unifying framework that could enable the synergy of computation and in-field experiments to save orders of magnitude of expenses for the load spectrum monitoring of complex engineering structures in service and prevent catastrophic fatigue and fracture in those solids. [ABSTRACT FROM AUTHOR]

In the computational damage mechanics, the coupled elastoplastic damage model involves a nonsymmetric tangent operator. This implies that a sparse matrix solver is needed, which means more computational cost to solve the problem. In the context of Lemaitre's coupled damage model, a new iterative residual-based procedure is proposed to solve the Lemaitre's coupled elastoplastic damage problems. The elastoplastic damaged tangent operator is decomposed into symmetric and nonsymmetric parts. The symmetric part of the tangent operator is contributed to the overall stiffness matrix, while the nonsymmetric part is considered as an additional residual force contributed to the overall force vector. The symmetry and banded format of the stiffness matrix is maintained, consequently the computational costs are largely reduced. The Lemaitre coupled damage model is implemented in ABAQUS commercial Software using a developed user material user subroutine, while the proposed procedure is implemented into a nonlinear 2 D FE model. Two different problems are analyzed to illustrate the applicability and effectiveness of the proposed iterative residual-based procedure. The analysis show that results of the Lemaitre's coupled damage model and the proposed procedure are very close. [ABSTRACT FROM AUTHOR]

The mechanical response of a knot tied in elastic rods strongly depends on the frictional force due to rod-rod contact. The behavior of a knot can be qualitatively different based on the frictional coefficient of the elastic rod. Systematic variation of friction during rod-rod contact is a crucial component of any experimental design to uncover the underlying ingredients behind the mechanics of knots. In this paper, we demonstrate a novel process of controlling the friction of a continuous rod by adhering non-spherical inorganic micro-particles. Polymeric binder is used to deliver the particles as asperities over the rod substrate and by controlling their size and distribution the coefficient of friction of the rod is determined. In parallel, numerical simulations with the discrete elastic rods algorithm are used to reproduce the experimental observations. Tabletop experiments are performed where overhand knots with a variety of unknotting numbers are pulled tight. The force-extension curve of these experiments shows that the proposed process can successfully tune the friction between rods. [ABSTRACT FROM AUTHOR]

Researchers have been studying the pain sensation extensively in the past few decades. Quantitative simulation and theoretical modeling of pain sensation based on experimental results are necessary for pain research. Many theories have been proposed to explain the mechanism of pain from molecular, cellular, and neuron network perspectives. But some phenomena in pain sensation are not fully understood, including wind-up and ramp-off. This paper focused on the theoretical model of wind-up and ramp-off phenomena in the pain sensation. With the addition of the transduction model, the generation mechanism of wind-up and ramp-off is better explained. The simulations were carried out to analyze the skin pain sensation under the mechanical stimulus, consisting of four different parts: the mechanical model of skin, transduction, transmission, modulation, and perception. The stress distribution on the skin was obtained based on the elastic theory. And the modified Hodgkin and Huxley model and the mathematical model of gate control theory were utilized to analyze the process of transduction, modulation, and perception, respectively. The numerical experiments demonstrated the wind-up occurs with a frequent stimulus of 1 Hz and 2 Hz, and ramp-off appears with the withdrawal of constant mechanical stimulus, which could contribute to the understanding of the pain sensation mechanism. [ABSTRACT FROM AUTHOR]

The transition of polymer adhesives from an initially liquid to a fully cured viscoelastic state is accompanied by three phenomenological effects, namely an increase in stiffness and viscosity in conjunction with a decrease in volume (curing shrinkage). Under consideration of these phenomena, some of us (Hossain et al. in Computational Mechanics 46:363-375, 2010) have devised a generic, viscoelastic finite strain framework for the simulation of the curing process of adhesives, which renders a thermodynamically consistent model regardless of the selected free energy density. In the present work, this generic curing framework is modified by means of more precise integration schemes and is applied to a hyperelastic Mooney–Rivlin material based on an additive volumetric-isochoric split of the strain energy density. The benefit of this decomposition is directly related to the distinct material responses of various polymers to volumetric and isochoric deformations [4]. The resulting Mooney–Rivlin curing model provides the foundation for implementing a user-defined material subroutine (UMAT) in Abaqus requiring the Cauchy stress and a non-standard formulation of the tangent operator. To this end, the corresponding transformations are presented. Additionally, a first attempt to determine the evolution of the curing-dependent material parameters through optimization with respect to a photoelasticity measurement is presented. A subset of the material properties, which reflect the emergence of shrinkage stresses inside a ceramic-epoxy composite after its fabrication, is determined via inverse parameter identification. However, due to a lack of experimental data and some rather strong assumptions made on the physics involved, this demonstration can currently be considered only as a proof-of-concept. [ABSTRACT FROM AUTHOR]

Computational modelling of contact problems is still one of the most difficult aspects of non-linear analysis in engineering mechanics. The article introduces an original efficient explicit algorithm for evaluation of impacts of bodies, satisfying the conservation of both momentum and energy exactly. The algorithm is described in its linearized 2-dimensional formulation in details, as open to numerous generalizations including 3-dimensional ones, and supplied by numerical examples obtained from its software implementation. [ABSTRACT FROM AUTHOR]

With advances in materials science and engineering, sandwich panels have evolved over the years. They are now used extensively in many fields, including the construction industry, due to their light weight and ease of construction. In the past, metals and timber-based products constituted most of the facing materials of panels, but plastics, polymers, concrete and other cementitious facings reinforced with glass, steel, carbon, natural fibres or textiles are now finding increasing use as facing materials. Core materials have also evolved and now include balsa and other types of wood, expanded polystyrene, rigid foams and foamed or lightweight cements and concretes. Some of today's novel cores incorporate various lattice-, truss- or pyramid-type structures while others have honeycombs. This study reviews structural sandwich panels with non-profiled faces and a range of innovative core composites and configurations. Particular focus is given to the properties that make panels suitable as structural systems, as well as any inherent weaknesses or peculiarities that require due consideration in design, including their structural response to bending and compression and associated failure modes. Finally, a brief review of theoretical developments is provided, along with representative problems using the theoretical models. [ABSTRACT FROM AUTHOR]

• The INTERNODES method is applied to problems in contact mechanics. • We propose a highly efficient preconditioner to solve the sequence of linear systems. • An algorithm is suggested to cheaply solve linear systems with the preconditioning matrix. • The quality of the preconditioner is assessed on small to medium size 2D problems. The mortar finite element method is a well-established method for the numerical solution of partial differential equations on domains displaying non-conforming interfaces. The method is known for its application in computational contact mechanics. However, its implementation remains challenging as it relies on geometrical projections and unconventional quadrature rules. The INTERNODES (INTERpolation for NOn-conforming DEcompositionS) method, instead, could overcome the implementation difficulties thanks to flexible interpolation techniques. Moreover, it was shown to be at least as accurate as the mortar method making it a very promising alternative for solving problems in contact mechanics. Unfortunately, in such situations the method requires solving a sequence of ill-conditioned linear systems. In this paper, preconditioning techniques are designed and implemented for the efficient solution of those linear systems. [ABSTRACT FROM AUTHOR]

The paper shows research on a closed fermentation chamber (CFC) that is an element of the Biogas Combined Heat and Power Plant located in the Gdańsk East Sewage Treatment Plant. This tank is mounted as an aboveground cylinder-shaped structure covered with a cone-shaped roof. Corrosion and leaks appeared in the tanks during many years of operation. In this work, it was decided to investigate their cause and propose a method of counteracting them. The article presents the research on the influence of individual operational and environmental loads on the stress distributions in the tank structure. Numerical simulations using the Finite Element Method were carried out for shell and solid models. Moreover, the stress distributions in cylindrical steel tanks were compared depending on the shape of the chamber top. The research results allowed us to identify the design errors of the closed fermentation chambers. It finds out that the connection of the cylindrical part of the tank with the conical roof requires reinforcement. A tank repair technology using Belzona composites was proposed to modify the joint geometry. A simulation was performed, taking into account the proposed repair technology. Its results showed a reduction of stresses compared to the state before repair by 19%. [ABSTRACT FROM AUTHOR]

This review discusses the links between the newly introduced concepts of digital twins and more classical finite element modeling, reduced order models, parametric modeling, inverse analysis, machine learning, and parameter identification. The purpose of this article is to demonstrate that development, as almost always is the case, is based on previously developed tools that are currently exploited since the technological tools for their implementation are available and the needs of their usage appear. This fact has rarely been declared clearly in the available literature. The need for digital twins in infrastructures arises due to the extreme loadings applied on energy-related infrastructure and to the higher importance that fatigue effects have. Digital twins promise to provide reliable and affordable models that accompany the structure throughout its whole lifetime, make fatigue and degradation prediction more reliable, and support effective predictive maintenance schemes. [ABSTRACT FROM AUTHOR]

Marine structures are susceptible to corrosion that accelerates material wastage. This phenomenon could lead to thickness reduction to the extent in which local buckling instabilities may occur. The majority of existing repair techniques require welding, which is a restricting factor in flammable environments where hot work is prohibited. A novel repair methodology that has attracted the research focus for over two decades is the adhesive bonding of a composite patch on a ship’s damaged plating. Although most studies have been focused on patch repair against crack propagation, restoring the initial buckling strength of corroded marine plates is of high interest. In this work, this technique is assessed using numerical experimentation through finite element analysis (FEA) with the patch’s dimensions as design parameters. The results are then evaluated using a design-of-experiments (DOE) approach by generating a response surface from central composite design (CCD) points. Applying this methodology to various plates and patches makes it possible to create a repair design procedure that specifies the minimum patch requirements depending on the metal substrate’s dimensions and corrosion realized.

Despite that, an earthquake's occurrence can lead to dramatic effects with significant damage in urban areas, including human and material losses. Fire after an earthquake amplifies the overall impact and becomes a catastrophic event. Most constructions in Algeria are made of reinforced concrete, and current regulations overlook fires after earthquakes. Structural designs are inadequate to handle such events. This study aims to investigate the behaviour of 3D reinforced concrete frames, as part of a residential building, designed according to internal codes, CBA93 and RPA99 v2003. This 3D RC structure is exposed to several load levels of its vertical load bearing capacity. The structural system is assumed to undergo seismic scenarios characterised by various levels of story drift and damage level types. The structure is then exposed to the standard fire ISO834 model. Numerical investigations are carried out for thermo-mechanical analysis using the finite element software ANSYS, taking into account geometric and material non-linearities. Results highlight the significant impact of vertical loads, story drifts, fire scenarios, and structural damage on a building's response to fire following an earthquake. These factors collectively influence the collapse probabilities, underlining the importance of holistic risk assessment in structural design. ● Numerical Investigation of 3D reinforced concrete frames submitted to fire after earthquake (FAE). ● Numerical validation for the earthquake analysis, using the experimental results developed by others. ● Numerical validation for thermal and thermomechanical analysis under fire, using experimental results developed by others. ● New design curves for the fire resistance are presented, depending on the load level, story drift and damage level. ● The failure probability for FAE is presented as a function of time exposed to fire under different load levels. [ABSTRACT FROM AUTHOR]

Fracture analysis of orthotropic materials presents a persistent challenge in computational mechanics, particularly in bond–based peridynamics (BB–PD) framework. This challenge arises from the special material properties of orthotropic materials, presenting difficulties in accurately simulating the mechanical behavior and discerning fracture modes. In particular, the neglect of fracture parameters that profoundly affect the fracture behavior has resulted in an insufficient study of the fracture mechanisms for orthotropic materials. To address this issue, a novel BB–PD model for orthotropic materials was proposed, accompanied by the development of an energy–based failure criterion. The presented BB–PD model has no material parameter limitations and can accurately capture the deformation of orthotropic materials. The energy–based failure criterion considers the variation of fracture energy in different directions and fracture modes, ensuring that the PD calculated fracture energies align with their corresponding theoretical values. To validate the effectiveness of the developed BB–PD model and failure criterion, several numerical examples were performed, including convergence analysis, deformation analysis, and three quasi-static fracture analyses. The results demonstrate that the presented model and failure criterion can accurately predict material deformation and fracture. Furthermore, analysis of fracture modes indicates that the ratio of mode I and mode II fracture energies significantly influences crack paths and fracture modes in orthotropic materials. • A BB–PD model for orthotropic materials is developed that enables arbitrary variation of material parameters. • A new failure criterion is proposed, considering the difference in fracture energies under various directions and modes. • Benchmark numerical examples demonstrate the efficiency of the developed model. • The effect of fracture energies on crack paths and fracture modes is analyzed. [ABSTRACT FROM AUTHOR]

The three-dimensional failure process experimentally observed by synchrotron radiation X-ray computed tomography (SR X-CT) regarding the influence of the interfiber distance is discussed on the basis of the results of numerical experiments. Triaxial stress states in the fracture process zone of carbon fiber reinforced polymers were analyzed on the mesoscale under mode I and mixed-mode (mode I + II) loading. Yield and damage models depending on stress triaxiality were used to accurately simulate three-dimensional stress states in the damage zone around the crack tip. Owing to the heterogeneity of composites, deviatoric stress is prominent in the thin resin region where the interfiber distance is small under mode I loading. On the other hand, matrix resin is triaxially stressed in the middle point between carbon fibers in the thick resin region where the interfiber distance is large. Under mode II loading, the shapes of fiber/matrix debonding depended on the interfiber distance. Areas with stress concentration were found owing to a large debonding area in the thick resin region resulting in a matrix cracking-prone stress state. These findings explain the damage and failure processes well observed by SR X-CT and provide a fundamental understanding of the damage mechanism at a mesoscale. [Display omitted] [ABSTRACT FROM AUTHOR]

Precise simulation of realistic physical phenomena and maintaining high efficiency will be the ultimate goal of computational mechanics. As an effort of such endeavor, an isogeometric analysis (IGA) was proposed by integrating finite element analysis (FEA) and computer-aided design. IGA efficiently predicts a physical behavior with higher fidelity than the original FEA. However, an application to various geometries will be cumbersome owing to the absence of an appropriate pre-processor. To alleviate such limitation, various reinforcements have been attempted, including a finite element (FE)-based IGA. Derived from those initiatives, alternatives will be suggested herein by using a Bernstein–Bézier FE. To obtain approximate C1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$C^1$$\end{document} continuity for a general tetrahedral FE, an approximated Worsey–Piper element split will be presented. Also, Bézier mesh generation will be adopted for an enhanced geometric representation. The present attempt will be validated by comparing the results for various curved geometry. Furthermore, the present method will be applied to a much more complicated configuration to demonstrate the geometric applicability. [ABSTRACT FROM AUTHOR]

The online version of the original article can be found at https://doi.org/10.1007/s00466-024-02458-4.Correction to: Computational Mechanics (2024).https://doi.org/10.1007/s00466-024-02458-4In the original article there are several transcription errors in Appendix A: The stress update algorithm.The correct formulas are shown below.GraphGraphGraphGraphThe original article has been updated.Publisher's NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.By Miroslav Halilovič; Bojan Starman and Sam CoppietersReported by Author; Author; Author [Extracted from the article]

This study presents a rate-dependent cohesive zone model for the fracture of polymeric interfaces and performs a Bayesian calibration, an uncertainty quantification, and a sensitivity analysis for the model. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. Inverse calibration of parameters for such complex models through trial and error is challenging due to the large number of parameters of the model. Moreover, the calibrated parameter values are often non-unique and uncertain when the available experimental data is limited. To tackle this challenge, we employ a Bayesian calibration approach to identify parameters from experimental data, the resulting parameters significantly enhance the accuracy of the model. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. The advantages of the Bayesian calibration over a deterministic parameter fit are demonstrated. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced, which significantly improves the model's prediction. Finally, the total uncertainty of the model is quantified in a predictive setting. A sensitivity analysis is performed to assess how changes in the input variables of the model affect the peak load, facilitating the identification of a concise set of highly influential parameters. The present approach can be used for calibration and uncertainty quantification for other complex computational mechanics models. It should also facilitate the designing of interface materials under uncertainty. • A rate-dependent cohesive zone model for fracture of polymer interfaces is presented. • Bayesian calibration enhances the accuracy of the model significantly. • The total uncertainty of the model is quantified in a predictive setting. • A sensitivity analysis is performed to understand the input-output relationships. [ABSTRACT FROM AUTHOR]

Parallel computing is essential for enhancing computational efficiency and advancing computational mechanics. To reduce the computational cost, peridynamics, a nonlocal numerical method, has been coupled with the finite element method (FEM). However, the accurate modeling of plastic deformation within the coupling framework of the FEM and non-ordinary state-based peridynamics (NOSB-PD) requires further investigation and might add to the computational expense. In this study, the open multi-processing application interface (OpenMP) is implemented for the plastic coupling of the FEM and stabilized NOSB-PD. The framework for the plastic coupling model using OpenMP is described in detail. The implemented code is used to investigate the coupling boundary effect on plastic deformation depending on the size of the coupling zone. After verifying the plastic coupling, the parallelization performance of the coupling model is examined. The efficient coupling model is applied to simulate plastic deformation on a plate with a circular hole, and the displacement results show good agreement with the reference solution. The proposed coupling model can be applied to efficiently solve the plastic deformation and fracture in future studies. • A plastic coupling of the finite element method and peridynamics is developed. • The plastic coupling model is parallelized using OpenMP. • A framework for the coupled code implementation using OpenMP is described. • The coupling boundary effect on plastic deformation is investigated. • The parallelization performance of the coupled code is examined. [ABSTRACT FROM AUTHOR]

This document is a preface to a special issue of the International Journal of Computational Methods on the topic of "Numerical Modelling of Fibre-Reinforced Materials and Structures." The special issue contains selected papers presented at the Fifth Australasian Conference on Computational Mechanics, which focused on the use of computational methods and modelling technology in the field of fibre-reinforced materials and structures. The papers in this special issue cover advanced theory, algorithms, numerical simulations, and novel applications of computational techniques in this area. The research and development of fibre-reinforced materials and structures have been increasing, leading to enhanced structure safety and infrastructure resilience. The preface is written by Sarah (Yixia) Zhang from the School of Engineering, Design and Built Environment at Western Sydney University in Australia. [Extracted from the article]

An isogeometric homogenization (IGH) technique is constructed for the homogenization and localization of unidirectional composites with radially or circumferentially orthotropic carbon/graphite fibers. The proposed theory employs multiple non-conforming Non-Uniform Rational B-Splines (NURBS) patches to depict repeating unit cells (RUCs) representative of composite microstructures. Displacements are formulated using a two-scale expansion that integrates macroscopic and microscopic contributions, with the latter addressed through the isogeometric analysis technique. Nitsche's method is utilized to apply the interfacial traction and displacement continuity and periodicity conditions. The capability and accuracy of the IGH theory were validated upon comparison with the elasticity solutions that take into account explicitly fiber morphologies, along with classical micromechanics solutions based on equivalent fiber moduli. A comparative analysis with conventional finite-element techniques showcases the developed theory's ability to accurately replicate the singular stress field at the fiber center and to capture smooth stress distributions where significant stress gradients are encountered. [Display omitted] [ABSTRACT FROM AUTHOR]

The Node-to-Segment (NTS) method enhanced computational contact mechanics by enabling contact analysis with large deformations with contact location as part of the unknowns. Despite having shortcomings, it is still to this day largely employed by the industry for contact analysis between continuous surfaces due to its low computational cost and scalability, instead of more precise, mathematically sound, but more computationally expensive methods. The method's persistent relevance inspired attempts at improving its performance, usually for first-order elements. It is well known that NTS is not working well for higher orders due to its topological inconsistency. This work proposes a way of reducing the side-effects of the second order penalty-based Node-to-Segment method without adding complexity to contact detection or formulation. This can be achieved using virtual elements to describe the adjacent continuum, because of a filter effect introduced by the polynomial projection used in stress post-processing, which reduces the stress oscillations resulting from higher order penalty-based Node-to-Segment methods. • VEM and NTS are combined in a convenient way to compute elasticity models with contact. • VEM's projection is able to filter the stress oscillations stemming from inconsistent NTS formulation for surfaces. • Improvements in stress results are obtained for both straight and curved contact-boundary problems. [ABSTRACT FROM AUTHOR]

In this paper, a new formulation for large deformation of visco-elastometic materials is derived. The formulation is based on logarithmic strain, and the internal variable is defined as the viscous part of the logarithmic strain. A derivation of thermodynamically consistent formulation for visco-elastomeric materials is provided. The evolution equation which is related to the deviatoric part of the strain for viscoelastic formulation is solved by the implicit trapezoidal integration rule which leads to a recursive relation. [ABSTRACT FROM AUTHOR]

In this work, we proposed a robust radial point interpolation method empowered with neural network solvers (RPIM-NNS) for solving highly nonlinear solid mechanics problems. It is enabled by neural network solvers via minimizing an energy-based functional loss. The RPIM-NNS has the following key ingredients: (1) It uses radial basis functions (RBFs) for displacement interpolation at arbitrary points in the problem domain, permitting irregular node distributions. (2) Nodes are placed also beyond the domain boundary, allowing the convenient implementation of boundary conditions of both Dirichlet and Neumann types. (3) It uses strain energy in an integral form as a part of the loss function, ensuring solution stability. (4) A well-developed gradient descendant algorithm in machine learning is employed to find the optimal solution, enabling robustness and ease in handling material and geometrical nonlinearities. (5) The proposed RPIM-NNS is compatible with parallel computing schemes. The performance of this method is tested using nonlinear problems including Cook's membrane and 3D twisting rubber problems, demonstrating its remarkable stability and robustness. This work, which seamlessly integrates the neural network solvers with mechanics governing equations and computational mechanics techniques, offers an excellent alternative for nonlinear solid mechanics problems. MATLAB codes are made available at https://github.com/JinshuaiBai/RPIM%5fNNS for free downloading. [ABSTRACT FROM AUTHOR]

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. We describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

AbstractThe question of the thickness and diameter report on the performance of the structures is approached in detail in this scientific work. This paper focuses on the stress-strain characteristics, geometry imperfections, damage and deformations that occur inside the materials structure properties. Finite element analysis and experimental results show that, as loading progressed, the strain distribution in the shaft lining structure became approximately uniform indicating the formation of a tied arch mechanism. Concrete strain distribution is nonlinear and non-conform to Bernoulli’s assumptions for strain and stress distribution; this nonlinearity is due to the shear deformations inside the structural element. The study can provide certain reference for practical engineering calculation.

The solubility of a crystalline material can be estimated from the absolute free energy of the solid and the excess solvation free energy. In the earlier work, we presented a general-purpose moleculardynamics-based methodology enabling solubility predictions of crystalline compounds, yielding accurate estimates of the aqueous solubilities of naphthalene at various pressures and temperatures. In the present work, we investigate a number of prototypical complex materials, including phenanthrene, calcite, and aragonite over a range of temperatures and pressures. Our results provide stronger evidence for the power of the methodology for universal solubility predictions. [ABSTRACT FROM AUTHOR]

Deformation of solid or hollow cylinders with transverse isotropic material under axisymmetric loading is one of the oldest problems. A general field solution is highly sought after, as this problem finds application in various fields. In the present work, this problem has been formulated starting with basic curvilinear kinematics and governing equations are derived using Reissner's variational principle. Non-singular solutions have been derived and have been validated with literature for specific cases. [ABSTRACT FROM AUTHOR]

We propose a new methodology to estimate the 3D displacement field of deformable objects from video sequences using standard monocular cameras. We solve in real time the complete (possibly visco-)hyperelasticity problem to properly describe the strain and stress fields that are consistent with the displacements captured by the images, constrained by real physics. We do not impose any ad-hoc prior or energy minimization in the external surface, since the real and complete mechanics problem is solved. This means that we can also estimate the internal state of the objects, even in occluded areas, just by observing the external surface and the knowledge of material properties and geometry. Solving this problem in real time using a realistic constitutive law, usually non-linear, is out of reach for current systems. To overcome this difficulty, we solve off-line a parametrized problem that considers each source of variability in the problem as a new parameter and, consequently, as a new dimension in the formulation. Model Order Reduction methods allow us to reduce the dimensionality of the problem, and therefore, its computational cost, while preserving the visualization of the solution in the high-dimensionality space. This allows an accurate estimation of the object deformations, improving also the robustness in the 3D points estimation. [ABSTRACT FROM AUTHOR]

In this lead article of the special issue, we provide a brief summary of the research developments in Isogeometric Analysis (IGA) for Computational Fluid Dynamics (CFD). We focus on the use of IGA in combination with stabilized and variational multiscale methods in fluids. We highlight the key developments and present results in IGA-based CFD that makes this technology attractive for the computational analysis of complex, unsteady and, often turbulent, flows encountered in modern science and engineering applications. We cover both incompressible and compressible flows, numerical method development and performance evaluation using benchmark problems, and applications ranging from stratified environmental flows over complex terrains to concrete-blast fluid–structure interaction. A short synopsis of each article in the special issue is also provided to help reader quickly see what is in the special issue. [ABSTRACT FROM AUTHOR]

In this essay, we aim to illustrate how Martin Karplus and his research group effectively set in motion the engine of molecular dynamics (MD) simulations of biomolecules. This process saw its prodromes between 1969 and the early 1970s with Karplus' landing in biology, a transition that came to fruition with the treatment of 11-cis-retinal photoisomerization and the development of an allosteric model to account for the mechanism of cooperativity in hemoglobin. In 1977, J. Andrew McCammon, Bruce Gelin, and Martin Karplus published an article in Nature reporting the MD simulation of bovine pancreatic trypsin inhibitor (BPTI). This publication helped initiate the merger of computational statistical mechanics and biochemistry, a process that Karplus undertook at a later stage and whose beginnings we propose to reconstruct in this article through unpublished accounts of the key people who participated in this endeavor. [ABSTRACT FROM AUTHOR]

Twin-wall structures can be cooled both externally and internally, raising great potential for use in high-temperature applications. However, their increased geometric complexity imposes a range of potential failure mechanisms for consideration in design. The primary aim of this study is to identify the nature of such mechanisms by constructing Bree type interaction diagrams for idealized double-wall systems under cyclic thermomechanical loading that shows the combination of loading conditions for which cyclic plasticity (leading to fatigue failure)-creep ratchetting occur. Through an extension of the classical Bree analysis, we determine analytical boundaries between different regimes of behavior. We also quantify the effects of wall thickness ratio, temperature field, and yield and creep material properties. Local cyclic plasticity is shown to dominate over structural/global ratchetting when the yield strength reduces with temperature and/or when the temperature gradient through the hot wall thickness dominates over the temperature difference between the walls. Thus, we conclude that global ratchetting is unlikely to occur in the practical loading range of Nickel-based twin-wall turbine blades, but instead these systems suffer from local fatigue at cooling holes and excessive creep deformation. This is verified by 3D cyclic finite element (FE) simulations, demonstrating that the analytical approach provides a powerful, cost-effective strategy for providing physical insight into possible deformation mechanisms in a range of thin-walled components; highlighting the key trade-offs to be considered in design; and directing the use of computer methods toward more detailed calculations. [ABSTRACT FROM AUTHOR]

Numerical modeling methods have been used to study the effect of an emergency stop of the fuel mixture supply through individual burners on the aerodynamics of the flow in the combustion chamber of a power boiler. The performed computational experiments made it possible to obtain the main aerodynamic characteristics of heat and mass transfer processes (full velocity vector, pressure, kinetic energy of turbulence and dissipation energy) in the volume of the combustion chamber and at the exit from it in emergency mode (two swirl burners are operating) and compare them with traditional solid fuel combustion (basic mode - four direct-flow burners are working). The results obtained indicate that with a vortex fuel supply in the central region of the combustion chamber, a sharp change in aerodynamic characteristics is observed with the formation of a vortex flow, which weakens as the pulverized coal flow and combustion products move to the exit. The presence of a vortex flow causes stable combustion of solid fuel and uniform distribution of heat flows along the walls of the combustion chamber. In addition, the vortex nature of the flow increases the residence time of coal particles in the combustion chamber, which contributes to a more complete burnout and a decrease in the mechanical underburning of the fuel mixture. Such a detailed study of the aerodynamic flow pattern that takes place in the combustion chamber of power boilers of operating TPPs can only be obtained by numerical simulation methods and by performing computational experiments. The highly informative results obtained make it possible to develop "clean" energy production technologies and solve environmental problems of the emission of harmful substances into the environment. [ABSTRACT FROM AUTHOR]

Convolutional neural networks (CNNs) perform well for crack detection in concrete structures. However, a large dataset with accurate labeling is required for CNN training. The generation of large datasets by capturing real images and applying manual image labeling is a time- and labor-intensive task. Hence, large dataset generation and labeling are critical for crack detection. Among the existing methods of dataset generation, random cropping is the most effective. For crack detection, only crack images are required for the crack dataset. However, no-crack images are also generated from crack sample images by random cropping, which is a major issue. Here, an image-augmentation method; namely, the crack-cropping method, is proposed for generating a large training dataset for concrete walls. The proposed method solves the issue of random cropping by discarding no-crack images at the time of crack dataset generation. In addition, image labeling was automatically applied using the proposed method. [ABSTRACT FROM AUTHOR]

The article presents the application of swarming algorithms in heat conduction, taking into account the continuity of the boundary condition (type IV). The influence of the input parameters of the bee and ant algorithm and tessellation on the selection of the heat conduction coefficient between the casting mold and the casting in computer simulations was presented. The results were compared for two different finite element grids, a different number of individuals, and a different number of iterations. The study also considered the magnitude of the reference temperature disturbance as the input temperature for numerical calculations. The analysis showed that the relative error of reproducing the value of the thermal conductivity coefficient in the continuity condition did not exceed 1.5% of the reference value of this coefficient. [ABSTRACT FROM AUTHOR]

The present work is focused on the investigation of tetra-anti-chiral structures by means of numerical and analytical methods. Specimens were evaluated under compressive load using analytical and numerical methods. The paper summarizes a theoretical solution for the estimate of Poisson's ratio and the plateau force. The models can handle structures with various configurations, such as the radius of the connection node, lengths, and thickness of the ligaments. A section dedicated to the evaluation of the buckling load is included to extend the investigation of the behavior under compressive loads. The theoretical model is based on Euler's formula, and a series of amendments are performed to adapt the formula to the analysis of chiral structures. Throughout the paper, theoretical results are compared with results from the simulations to validate the principles stated. Two sets of numerical models were developed: a fully 3D model using hexahedral finite elements and a 2.5D model using a beam finite element model. An overall comparison of results is presented, showing a good agreement between datasets. The present work might set the background for future activities, allowing for a selection of individual investigation methods. [ABSTRACT FROM AUTHOR]

Nozzle facilities, which can generate high Mach number flows, are the core portions of the supersonic wind tunnel. Different from traditional fixed nozzles, a flexible nozzle can deform to designed contours and supply steady core flows in several Mach numbers. Due to the high-quality demands from the thermo-aerodynamic testing, the deformation of the flexible nozzle plate should be carefully designed. This problem is usually converted into the large deformation problem of a cantilever with movable hinge boundary conditions. In this paper, a generalized variational method is established to analyze the deformation behavior of the flexible nozzle. By introducing axial deformation constraint and Lagrange multiplier, an analytical model is derived to predict the deformed morphology of the flexible plate. Finite element analyses (FEA) of a single-jack flexible nozzle model is performed to examine the predicted deformations and reaction forces. Furthermore, the large deformation experiments of an elastic cantilever with a movable hinge connection are carried out to simulate the scenarios in supersonic flexible nozzle facility. Both the FEA and experimental results show high accuracy of current theoretical model in deformation predictions. This method can also serve as a general approach in the design of flexible mechanisms with movable boundaries. [ABSTRACT FROM AUTHOR]

Mechanical failure and its interference with electrochemistry are a roadblock in deploying high-capacity electrodes for Li-ion batteries. Computational prediction of the electrochemomechanical behavior of high-capacity composite electrodes is a significant challenge because of (i) complex interplay between mechanics and electrochemistry in the form of stress-regulated Li transport and interfacial charge transfer, (ii) thermodynamic solution non-ideality, (iii) nonlinear deformation kinematics and material inelasticity, and (iv) evolving material properties over the state of charge. We develop a computational framework that integrates the electrochemical response of batteries modulated by large deformation, mechanical stresses, and dynamic material properties. We use silicon as a model system and construct a microstructurally resolved porous composite electrode model. The model concerns the effect of large deformation of silicon on charge conduction and electrochemical response of the composite electrode, impact of mechanical stress on Li transport and interfacial charge transfer, and asymmetric charging/discharging kinetics. The study captures the rate-dependent, coupled electrochemomechanical behavior of high-capacity composite electrodes that agrees well with experimental results. [ABSTRACT FROM AUTHOR]

We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and accurate methodology to account for the effect of long-range (nonlocal) interactions in curved structures. More specifically, the use of frame-invariant fractional-order kinematic relations enables a physically, mathematically, and thermodynamically consistent formulation to model the nonlocal elastic interactions. To evaluate the response of these nonlocal shells under practical scenarios involving generalized loads and boundary conditions, the fractional-finite element method (f-FEM) is extended to incorporate shell elements based on the first-order shear-deformable displacement theory. Finally, numerical studies are performed exploring both the linear and the geometrically nonlinear static response of nonlocal cylindrical shell panels. This study is intended to provide a general foundation to investigate the nonlocal behavior of curved structures by means of fractional-order models. [ABSTRACT FROM AUTHOR]

We compare and contrast three different, but complementary views of "structure" and "pattern" in spatial processes. For definiteness and analytical clarity, we apply all three approaches to the simplest class of spatial processes: one-dimensional Ising spin systems with finite-range interactions. These noncritical systems are well-suited for this study since the change in structure as a function of system parameters is more subtle than that found in critical systems where, at a phase transition, many observables diverge, thereby making the detection of change in structure obvious. This survey demonstrates that the measures of pattern from information theory and computational mechanics differ from known thermodynamic and statistical mechanical functions. Moreover, they capture important structural features that are otherwise missed. In particular, a type of mutual information called the excess entropy—an information theoretic measure of memory—serves to detect ordered, low entropy density patterns. It is superior in several respects to other functions used to probe structure, such as magnetization and structure factors. ϵ -Machines—the main objects of computational mechanics—are seen to be the most direct approach to revealing the (group and semigroup) symmetries possessed by the spatial patterns and to estimating the minimum amount of memory required to reproduce the configuration ensemble, a quantity known as the statistical complexity. Finally, we argue that the information theoretic and computational mechanical analyses of spatial patterns capture the intrinsic computational capabilities embedded in spin systems—how they store, transmit, and manipulate configurational information to produce spatial structure. [ABSTRACT FROM AUTHOR]

This article aims at analytically solving the free vibration problem of rectangular thin plates with one corner free and its opposite two adjacent edges rotationally-restrained, which is difficult to handle by conventional semi-inverse approaches such as the Levy solution and Naiver solution, etc. Based on the classical Fourier series theory, this work presents a first endeavor to treat the two-dimensional half-sinusoidal Fourier series, which is quite similar to the Navier's form solution, as the solution form of plate deflection. By utilizing the orthogonality of the present trial function and the Stoke's transformation technique, the present solution procedure converts the complicated plate problem into solving sets of linear algebra equations, which heavily decreases the difficulties. Therefore, the present approach enables one to solve the title problem in a unified, simple and straightforward way, which is very easily implemented by researchers. Another advantage of the present method over other analytical approaches is that it has general applicability to various boundary conditions through utilizing different types of Fourier series and it can be extended for further dynamic/static analysis of plates under different shear deformation theories. Moreover, without any extra derivation processes, new, precise analytical free vibration solutions for plates under three non-Levy-type boundary conditions are also obtained by choosing different rotating fixed coefficients. Consequently, we present more than 400 comprehensive free vibration results for plates with classical/non-classical boundaries, all the present results are confirmed by FEM/analytical solutions and can be used as benchmark data for further research. [ABSTRACT FROM AUTHOR]