Showing papers in "Computational Mechanics in 2022"
TL;DR: In this article , the authors focus on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems and evaluate them in terms of their computational effort and predictive capabilities.
Abstract: Abstract Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized.
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TL;DR: In this article , a phase-field formulation for fracture based on the framework of representative crack elements is extended to transient thermo-mechanics, which allows to predict realistic deformation kinematics and heat fluxes at cracks.
Abstract: Abstract The phase-field formulation for fracture based on the framework of representative crack elements is extended to transient thermo-mechanics. The finite element formulation is derived starting from the variational principle of total virtual power. The intention of this manuscript is to demonstrate the potential of the framework for multi-physical fracture models and complex processes inside the crack. The present model at hand allows to predict realistic deformation kinematics and heat fluxes at cracks. At the application of fully coupled, transient thermo-elasticity to a pre-cracked plate, the opened crack yields thermal isolation between both parts of the plate. Inhomogeneous thermal strains result in a curved crack surface, inhomogeneous recontact and finally heat flow through the crack regions in contact. The novel phase-field framework further allows to study processes inside the crack, which is demonstrated by heat radiation between opened crack surfaces. Finally, numerically calculated crack paths at a disc subjected to thermal shock load are compared to experimental results from literature and a curved crack in a three-dimensional application are presented.
13 citations
TL;DR: In this article , the authors extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials, where every Gauss point of the macroscopic finite element model is equipped with a deep material network.
Abstract: Abstract We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN serves as a high-fidelity surrogate model for full-field solutions on the microscopic scale of inelastic, non-isothermal constituents. Building on the homogenization framework of Chatzigeorgiou et al. (Int J Plast 81:18–39, 2016), we extend the framework of DMNs to thermomechanical composites by incorporating the two-way thermomechanical coupling, i.e., the coupling from the macroscopic onto the microscopic scale and vice versa, into the framework. We provide details on the efficient implementation of our approach as a user-material subroutine (UMAT). We validate our approach on the microscopic scale and show that DMNs predict the effective stress, the effective dissipation and the change of the macroscopic absolute temperature with high accuracy. After validation, we demonstrate the capabilities of our approach on a concurrent thermomechanical two-scale simulation on the macroscopic component scale.
12 citations
TL;DR: In this article , the authors proposed a bi-fidelity modeling approach for complex physical systems, where they model the discrepancy between the true system's response and a low fidelity response using a deep operator network, a neural network architecture suitable for approximating nonlinear operators.
Abstract: Recent advances in modeling large-scale, complex physical systems have shifted research focuses towards data-driven techniques. However, generating datasets by simulating complex systems can require significant computational resources. Similarly, acquiring experimental datasets can prove difficult. For these systems, often computationally inexpensive, but in general inaccurate models, known as the low-fidelity models, are available. In this paper, we propose a bi-fidelity modeling approach for complex physical systems, where we model the discrepancy between the true system’s response and a low-fidelity response in the presence of a small training dataset from the true system’s response using a deep operator network, a neural network architecture suitable for approximating nonlinear operators. We apply the approach to systems that have parametric uncertainty and are partially unknown. Three numerical examples are used to show the efficacy of the proposed approach to model uncertain and partially unknown physical systems.
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TL;DR: In this paper , a hyperelastic extended Kirchhoff-love shell model with out-of-plane normal stress is presented, where the traction acting on the shell can be specified on the upper and lower surfaces separately.
Abstract: Abstract This is the first part of a two-part article on a hyperelastic extended Kirchhoff–Love shell model with out-of-plane normal stress. We present the derivation of the new model, with focus on the mechanics of the out-of-plane deformation. Accounting for the out-of-plane normal stress distribution in the out-of-plane direction affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the shell. The improvement is beyond what we get from accounting for the out-of-plane deformation mapping. By accounting for the out-of-plane normal stress, the traction acting on the shell can be specified on the upper and lower surfaces separately. With that, the new model is free from the “midsurface” location in terms of specifying the traction. We also present derivations related to the variation of the kinetic energy and the form of specifying the traction and moment acting on the upper and lower surfaces and along the edges. We present test computations for unidirectional plate bending, plate saddle deformation, and pressurized cylindrical and spherical shells. We use the neo-Hookean and Fung’s material models, for the compressible- and incompressible-material cases, and with the out-of-plane normal stress and without, which is the plane-stress case.
TL;DR: In this paper , a layer of fictitious nodes around the body, the displacements of which are determined by multiple Taylor series expansions based on the nearest-node strategy is introduced to mitigate the surface effect and impose Dirichlet and Neumann boundary conditions in a peridynamic way.
Abstract: Abstract Peridynamics is a non-local continuum theory which is able to model discontinuities in the displacement field, such as crack initiation and propagation in solid bodies. However, the non-local nature of the theory generates an undesired stiffness fluctuation near the boundary of the bodies, phenomenon known as “surface effect”. Moreover, a standard method to impose the boundary conditions in a non-local model is not currently available. We analyze the entity of the surface effect in ordinary state-based peridynamics by employing an innovative numerical algorithm to compute the peridynamic stress tensor. In order to mitigate the surface effect and impose Dirichlet and Neumann boundary conditions in a peridynamic way, we introduce a layer of fictitious nodes around the body, the displacements of which are determined by multiple Taylor series expansions based on the nearest-node strategy. Several numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.
TL;DR: In this paper , a high-resolution space-time (ST) isogeometric analysis of car and tire aerodynamics with near-actual tire geometry, road contact, and tire deformation and rotation is presented.
Abstract: Abstract We are presenting high-resolution space–time (ST) isogeometric analysis of car and tire aerodynamics with near-actual tire geometry, road contact, and tire deformation and rotation. The focus in the high-resolution computation is on the tire aerodynamics. The high resolution is not only in space but also in time. The influence of the aerodynamics of the car body comes, in the framework of the Multidomain Method (MDM), from the global computation with near-actual car body and tire geometries, carried out earlier with a reasonable mesh resolution. The high-resolution local computation, carried out for the left set of tires, takes place in a nested MDM sequence over three subdomains. The first subdomain contains the front tire. The second subdomain, with the inflow velocity from the first subdomain, is for the front-tire wake flow. The third subdomain, with the inflow velocity from the second subdomain, contains the rear tire. All other boundary conditions for the three subdomains are extracted from the global computation. The full computational framework is made of the ST Variational Multiscale (ST-VMS) method, ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods, ST Isogeometric Analysis (ST-IGA), integrated combinations of these ST methods, element-based mesh relaxation (EBMR), methods for calculating the stabilization parameters and related element lengths targeting IGA discretization, Complex-Geometry IGA Mesh Generation (CGIMG) method, MDM, and the “ST-C” data compression. Except for the last three, these methods were used also in the global computation, and they are playing the same role in the local computation. The ST-TC, for example, as in the global computation, is making the ST moving-mesh computation possible even with contact between the tire and the road, thus enabling high-resolution flow representation near the tire. The CGIMG is making the IGA mesh generation for the complex geometries less arduous. The MDM is reducing the computational cost by focusing the high-resolution locally to where it is needed and also by breaking the local computation into its consecutive portions. The ST-C data compression is making the storage of the data from the global computation less burdensome. The car and tire aerodynamics computation we present shows the effectiveness of the high-resolution computational analysis framework we have built for this class of problems.
TL;DR: In this paper , a data-driven concurrent n-scale modeling approach was adopted for woven composites utilizing a mechanistic reduced order model (ROM) called Self-consistent Clustering Analysis (SCA).
Abstract: Concurrent analysis of composite materials can provide the interaction among scales for better composite design, analysis, and performance prediction. A data-driven concurrent n-scale modeling approach ( $$\text {FExSCA}^\text {n-1}$$ ) is adopted in this paper for woven composites utilizing a mechanistic reduced order model (ROM) called Self-consistent Clustering Analysis (SCA). We demonstrated this concurrent multiscale modeling theory with a $$\text {FExSCA}^2$$ approach to study the 3-scale woven carbon fiber reinforced polymer (CFRP) laminate structure. $$\text {FExSCA}^2$$ significantly reduced expensive 3D nested composite representative volume element (RVE) computation for woven and unidirectional (UD) composite structures by developing a material database. The modeling procedure is established by integrating the material database into a woven CFRP structural numerical model, formulating a concurrent 3-scale modeling framework. This framework provides an accurate prediction for the structural performance (e.g., nonlinear structural behavior under tensile load), as well as the woven and UD physics field evolution. The concurrent modeling results are validated against physical tests that link structural performance to the basic material microstructures. The proposed methodology provides a comprehensive predictive modeling procedure applicable to general composite materials aiming to reduce laborious experiments needed.
TL;DR: In this paper , a non-negative least square solver is proposed to ensure the generation of positive weights when solving the moment fitting equations, which can be achieved by employing a so-called nonnegative least-squares solver, and the performance of the nonnegative moment fitting scheme is illustrated using different numerical examples in hyperelasticity and elastoplasticity.
Abstract: Abstract Fictitious domain methods, such as the finite cell method, simplify the discretization of a domain significantly. This is because the mesh does not need to conform to the domain of interest. However, because the mesh generation is simplified, broken cells with discontinuous integrands must be integrated using special quadrature schemes. The moment fitting quadrature is a very efficient scheme for integrating broken cells since the number of integration points generated is much lower as compared to the commonly used adaptive octree scheme. However, standard moment fitting rules can lead to integration points with negative weights. Whereas negative weights might not cause any difficulties when solving linear problems, this can change drastically when considering nonlinear problems such as hyperelasticity or elastoplasticity. Then negative weights can lead to a divergence of the Newton-Raphson method applied within the incremental/iterative procedure of the nonlinear computation. In this paper, we extend the moment fitting method with constraints that ensure the generation of positive weights when solving the moment fitting equations. This can be achieved by employing a so-called non-negative least square solver. The performance of the non-negative moment fitting scheme will be illustrated using different numerical examples in hyperelasticity and elastoplasticity.
TL;DR: In this paper , the authors propose an adaptive strategy that continuously updates the hyperparameters on the basis of an approximate tangent of the hidden constitutive manifold, which can substantially reduce the computational cost and at the same time also improve the accuracy of the distance-minimizing method.
Abstract: Abstract Data-driven constitutive modeling in continuum mechanics assumes that abundant material data are available and can effectively replace the constitutive law. To this end, Kirchdoerfer and Ortiz proposed an approach, which is often referred to as the distance-minimizing method. This method contains hyperparameters whose role remains poorly understood to date. Herein, we demonstrate that choosing these hyperparameters equal to the tangent of the constitutive manifold underlying the available material data can substantially reduce the computational cost and improve the accuracy of the distance-minimizing method. As the tangent of the constitutive manifold is typically not known in a data-driven setting, and as it can also change during an iterative solution process, we propose an adaptive strategy that continuously updates the hyperparameters on the basis of an approximate tangent of the hidden constitutive manifold. By several numerical examples we demonstrate that this strategy can substantially reduce the computational cost and at the same time also improve the accuracy of the distance-minimizing method.
TL;DR: In this article , the authors generalize composite voxels towards composite boxels (ComBo) that are non-equiaxed, a feature that can pay off for materials with a preferred direction such as pseudo-uni-directional fiber composites.
Abstract: Abstract Computational homogenization is the gold standard for concurrent multi-scale simulations (e.g., FE2) in scale-bridging applications. Often the simulations are based on experimental and synthetic material microstructures represented by high-resolution 3D image data. The computational complexity of simulations operating on such voxel data is distinct. The inability of voxelized 3D geometries to capture smooth material interfaces accurately, along with the necessity for complexity reduction, has motivated a special local coarse-graining technique called composite voxels (Kabel et al. Comput Methods Appl Mech Eng 294: 168–188, 2015). They condense multiple fine-scale voxels into a single voxel, whose constitutive model is derived from the laminate theory. Our contribution generalizes composite voxels towards composite boxels (ComBo) that are non-equiaxed, a feature that can pay off for materials with a preferred direction such as pseudo-uni-directional fiber composites. A novel image-based normal detection algorithm is devised which (i) allows for boxels in the firsts place and (ii) reduces the error in the phase-averaged stresses by around 30% against the orientation cf. Kabel et al. (Comput Methods Appl Mech Eng 294: 168–188, 2015) even for equiaxed voxels. Further, the use of ComBo for finite strain simulations is studied in detail. An efficient and robust implementation is proposed, featuring an essential selective back-projection algorithm preventing physically inadmissible states. Various examples show the efficiency of ComBo against the original proposal by Kabel et al. (Comput Methods Appl Mech Eng 294: 168–188, 2015) and the proposed algorithmic enhancements for nonlinear mechanical problems. The general usability is emphasized by examining various Fast Fourier Transform (FFT) based solvers, including a detailed description of the Doubly-Fine Material Grid (DFMG) for finite strains. All of the studied schemes benefit from the ComBo discretization.
TL;DR: In this paper , the use of the node-dependent kinematics concept for the geometrical nonlinear analysis of composite one-dimensional structures is proposed with the present approach.
Abstract: Abstract In this paper, the use of the node-dependent kinematics concept for the geometrical nonlinear analysis of composite one-dimensional structures is proposed With the present approach, the kinematics can be independent in each element node. Therefore the theory of structures changes continuously over the structural domain, describing remarkable cross-section deformation with higher-order kinematics and giving a lower-order kinematic to those portion of the structure which does not require a refinement. In this way, the reliability of the simulation is ensured, keeping a reasonable computational cost. This is possible by Carrera unified formulation, which allows writing finite element nonlinear equilibrium and incremental equations in compact and recursive form. Compact and thin-walled composite structures are analyzed, with symmetric and unsymmetric loading conditions, to test the present approach when dealing with warping and torsion phenomena. Results show how finite element models with node-dependent behave as well as ones with uniform highly refined kinematic. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by node-dependent kinematics analysis.
TL;DR: In this paper , a mixed formulation of classical and data-driven modeling is obtained, where the data set is augmented with directions in the tangent space of points in stress-strain space.
Abstract: Abstract Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the data set is minimized, subject to equilibrium and compatibility constraints. Although this method operates well for non-linear elastic problems, there are challenges dealing with history-dependent materials, since one and the same point in stress-strain space might correspond to different material behaviour. In recent literature, this issue has been treated by including local histories into the data set. However, there is still the necessity to include models for the evolution of specific internal variables. Thus, a mixed formulation of classical and data-driven modeling is obtained. In the presented approach, the data set is augmented with directions in the tangent space of points in stress-strain space. Moreover, the data set is divided into subsets corresponding to different material behaviour. Based on this classification, transition rules map the modeling points to the various subsets. The approach will be applied to non-linear elasticity and elasto-plasticity with isotropic hardening.
TL;DR: In this article , the Grassmannian exponential map and the optimal injectivity condition of this map, related to the cut-locus of Grassmann manifolds, were established and used to determine the loss of injectivity in practical pMOR applications.
Abstract: Proper Orthogonal Decomposition (POD) basis interpolation on Grassmann manifolds has been successfully applied to problems of parametric model order reduction (pMOR). In this work we address the necessary stability conditions for the interpolation, all defined from strong mathematical background. A first condition concerns the domain of definition of the logarithm map. Second, we show how the stability of interpolation can be lost if certain geometrical requirements are not satisfied by making a concrete elucidation of the local character of linearization. To this effect, we draw special attention to the Grassmannian exponential map and the optimal injectivity condition of this map, related to the cut–locus of Grassmann manifolds. From this, an explicit stability condition is established and can be directly used to determine the loss of injectivity in practical pMOR applications. A third stability condition is formulated when increasing the number p of POD modes, deduced from the principal angles of subspaces of different dimensions p. Definition of this condition leads to an understanding of the non-monotonic oscillatory behavior of the Reduced Order Model (ROM) error-norm with respect to the number of POD modes, and on the contrary, the well-behaved monotonic decrease of the error-norm in the two numerical examples presented herein. We have chosen to perform pMOR in hyperelastic structures using a non-intrusive approach for inserting the interpolated spatial POD ROM basis in a commercial FEM code. The accuracy is assessed by a posteriori error norms defined using the ROM FEM solution and its high-fidelity counterpart simulation. Numerical studies successfully ascertained and highlighted the implication of stability conditions which are general and can be applied to a variety of other linear or nonlinear problems involving parametrized ROMs generation based on POD basis interpolation on Grassmann manifolds.
TL;DR: In this paper , an advanced continuum macro-scale model based on a two-scale nonlinear description for masonry material is presented, where a 3D distribution of embedded internal layers allows for the anisotropic mesoscale features at the local level.
Abstract: Abstract A great proportion of the existing architectural heritage, including historical and monumental constructions, is made of brick/block masonry. This material shows a strong anisotropic behaviour resulting from the specific arrangement of units and mortar joints, which renders the accurate simulation of the masonry response a complex task. In general, mesoscale modelling approaches provide realistic predictions due to the explicit representation of the masonry bond characteristics. However, these detailed models are very computationally demanding and mostly unsuitable for practical assessment of large structures. Macroscale models are more efficient, but they require complex calibration procedures to evaluate model material parameters. This paper presents an advanced continuum macroscale model based on a two-scale nonlinear description for masonry material which requires only simple calibration at structural scale. A continuum strain field is considered at the macroscale level, while a 3D distribution of embedded internal layers allows for the anisotropic mesoscale features at the local level. A damage-plasticity constitutive model is employed to mechanically characterise each internal layer using different material properties along the two main directions on the plane of the masonry panel and along its thickness. The accuracy of the proposed macroscale model is assessed considering the response of structural walls previously tested under in-plane and out-of-plane loading and modelled using the more refined mesoscale strategy. The results achieved confirm the significant potential and the ability of the proposed macroscale description for brick/block masonry to provide accurate and efficient response predictions under different monotonic and cyclic loading conditions.
TL;DR: In this paper , the displacement field is augmented by enriched terms associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces, which effectively produces an enriched node-to-node discretization.
Abstract: Abstract We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multi-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. We show that the node-to-node enrichment ensures continuity of the displacement field—without locking—in mesh coupling problems, and that tractions are transferred accurately at contact interfaces without the need for stabilization. We also show the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.
TL;DR: In this article , the authors propose a continuous version of a trainable convolutional filter able to work also with unstructured data, which allows exploring CNNs beyond discrete domains, enlarging the usage of this important learning technique for many more complex problems.
Abstract: Abstract Convolutional Neural Network (CNN) is one of the most important architectures in deep learning. The fundamental building block of a CNN is a trainable filter, represented as a discrete grid, used to perform convolution on discrete input data. In this work, we propose a continuous version of a trainable convolutional filter able to work also with unstructured data. This new framework allows exploring CNNs beyond discrete domains, enlarging the usage of this important learning technique for many more complex problems. Our experiments show that the continuous filter can achieve a level of accuracy comparable to the state-of-the-art discrete filter, and that it can be used in current deep learning architectures as a building block to solve problems with unstructured domains as well.