Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Full-field experiment-aided virtual modelling framework for inverse-based stochastic prediction of structures with elastoplasticity","authors":"","doi":"10.1016/j.cma.2024.117284","DOIUrl":"10.1016/j.cma.2024.117284","url":null,"abstract":"<div><p>Forecasting of stochastic ductile failures in fabrication and service stages are challenging tasks of advanced structures in practical engineering. Due to the prohibitive costs of repetitive experimental tests to quantify optimal failure-related parameters, numerous studies have turned to simulation-based uncertainty quantification. However, the credibility of these approaches is frequently doubted by the function-generated distribution of random data involved. Thus, an accurate assessment of the material parameters ascertains the appropriate estimation of uncertain parameters, which is essential for the risk/safety assessment of structures in different stages. In this paper, a full-field experiment-aided virtual modelling framework for inverse-based prediction of stochastic elastoplastic failure (EVMF-ISP) is proposed to deliver precise insights regarding the effective distribution range of mechanical parameters. To this end, all available experiment observations serve as the reference for assessing the prior and posterior probability density of the unknown parameters through the real-time inverse uncertainty quantification (UQ) module. The framework can be divided into three parts, where initially a pre-virtual model (PRVM) is formulated, and Bayesian inference is implemented to propagate the experiment observations backwards to ascertain the uncertain parameters. Then, an advanced multidimensional slice sampling method is developed to deal with the derived complex posterior probability density function (PDF) of mechanical parameters. In the end, a reliable stochastic elastoplastic analysis can be conducted with the revised uncertain samples and finalised with post-virtual models (POVMs) for the concerned structures. Such that, accurate and efficient determination of nonlinear response of structures can be directly predicted. The EVMF-ISP framework is logically presented and thoroughly illustrated with practical applications.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045782524005401/pdfft?md5=f3d82201febf6d54ed6b4de506a7232d&pid=1-s2.0-S0045782524005401-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142041190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Model-free chemomechanical interfaces: History-dependent damage under transient mass diffusion","authors":"","doi":"10.1016/j.cma.2024.117286","DOIUrl":"10.1016/j.cma.2024.117286","url":null,"abstract":"<div><p>This paper presents a data-driven framework based on distance functional for chemo-mechanical cohesive interfaces to capture transient diffusion and resulting interfacial damage evolution. The framework eliminates reliance on complex constitutive models and phenomenological assumptions, especially avoiding the coupling tangent terms with a given material database. The interfacial chemical potential and its jumps are used to expand the phase space for describing the chemical states of interfaces. Subsequently, a novel chemo-mechanical distance norm, including traction-separation pair, interfacial chemical potential-concentration pair and corresponding chemical potential jump-flux pair, is presented. Momentum conservation law for interfacial tractions and mass conservation law for interfacial concentration are enforced via Lagrange multipliers. For tracking the history-dependent state of the interface damage, an internal variable, termed interface integrity, is introduced to condition the interfacial database and manage the subsets mapping strategies, following physically motivated evolution constraints. Numerical examples are conducted to investigate the efficiency and capability of the present framework. A monotonic loading test validates a good numerical convergence relative to the number of data points. Subsequent cyclic loading simulations, compared with the reference solutions, show that the algorithm is well suitable to predict the history-dependent interface damage evolution under complex loading paths. Finally, the chemo-mechanically coupled examples capture phenomena such as interfacial swelling and interface degradation induced by transient diffusion and stress-driven diffusion. The current work provides a promising tool for understanding chemo-mechanical behaviors of interfaces within heterogeneous composites.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142040223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Data-driven methods for computational mechanics: A fair comparison between neural networks based and model-free approaches","authors":"","doi":"10.1016/j.cma.2024.117289","DOIUrl":"10.1016/j.cma.2024.117289","url":null,"abstract":"<div><p>We present a comparison between two approaches to modelling hyperelastic material behaviour using data. The first approach is a novel approach based on Data-driven Computational Mechanics (DDCM) that completely bypasses the definition of a material model by using only data from simulations or real-life experiments to perform computations. The second is a neural network (NN) based approach, where a neural network is used as a constitutive model. It is trained on data to learn the underlying material behaviour and is implemented in the same way as conventional models. The DDCM approach has been extended to include strategies for recovering isotropic behaviour and local smoothing of data. These have proven to be critical in certain cases and increase accuracy in most cases. The NN approach contains certain elements to enforce principles such as material symmetry, thermodynamic consistency, and convexity. In order to provide a fair comparison between the approaches, they use the same data and solve the same numerical problems with a selection of problems highlighting the advantages and disadvantages of each approach. Both the DDCM and the NNs have shown acceptable performance. The DDCM performed better when applied to cases similar to those from which the data is gathered from, albeit at the expense of generality, whereas NN models were more advantageous when applied to wider range of applications.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142012238","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A B-spline based gradient-enhanced micropolar implicit material point method for large localized inelastic deformations","authors":"","doi":"10.1016/j.cma.2024.117291","DOIUrl":"10.1016/j.cma.2024.117291","url":null,"abstract":"<div><p>The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045782524005474/pdfft?md5=9bf64ed7c2399ba88f7cce52fe705a69&pid=1-s2.0-S0045782524005474-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142012236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive methods with C1 splines for multi-patch surfaces and shells","authors":"","doi":"10.1016/j.cma.2024.117287","DOIUrl":"10.1016/j.cma.2024.117287","url":null,"abstract":"<div><p>We introduce an adaptive isogeometric method for multi-patch surfaces and Kirchhoff–Love shell structures with hierarchical splines characterized by <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> continuity across patches. We extend the construction of smooth hierarchical splines from the multi-patch planar setting to analysis suitable <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> surfaces. The adaptive scheme to solve fourth order partial differential equations is presented in a general framework before showing its application for the numerical solution of the bilaplacian and the Kirchhoff–Love model problems. A selection of numerical examples illustrates the performance of hierarchical adaptivity on different multi-patch surface configurations.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045782524005437/pdfft?md5=854105ba2c70eb6a4311e75392f8aea3&pid=1-s2.0-S0045782524005437-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142012234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A mortar segment-to-segment frictional contact approach in material point method","authors":"","doi":"10.1016/j.cma.2024.117294","DOIUrl":"10.1016/j.cma.2024.117294","url":null,"abstract":"<div><p>Handling contact problems in the Material Point Method (MPM) has long been a challenge. Traditional grid-based contact approaches often face issues with mesh dependency, while material point-based methods can be computationally intensive. To address these challenges, this study develops a novel mortar segment-to-segment frictional contact approach for MPM. We first introduce boundary vertices and propose an innovative kinematic update scheme for precise representation of the boundaries of the continuum media and their continuously evolving contact normals throughout the contact process. Then, we construct a weak form of contact constraints based on the mortar method to facilitate a stable segment-to-segment contact detection. To rigorously ensure the non-penetration condition, the energetic barrier method is further adopted and implemented in MPM for enforcing the contact constraints. The proposed kinematic update scheme for boundary vertices is first verified through a cantilever beam benchmark test. The verified framework is further examined through a wide range of contact scenarios, including rolling, sliding, collision of two rings, and multi-body contacts, in both small and finite deformations. The simulation results are thoroughly discussed, highlighting the significant improvements in accuracy and versatility. Potential limitations of the proposed method are also examined.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142012237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy-stable auxiliary variable viscosity splitting (AVVS) method for the incompressible Navier–Stokes equations and turbidity current system","authors":"","doi":"10.1016/j.cma.2024.117295","DOIUrl":"10.1016/j.cma.2024.117295","url":null,"abstract":"<div><p>In this work, we develop a novel energy-stable linear approach, which we name as auxiliary variable viscosity splitting (AVVS) method, to efficiently solve the incompressible fluid flows. Different from the projection-type methods with pressure correction, the AVVS method adopts the viscosity splitting strategy to split the original momentum equation into an intermediate momentum equation without divergence-free constraint and an advection-free momentum equation. A time-dependent auxiliary variable which has exact value 1 is introduced to construct a supplementary equation. The new model not only inherits the same dynamics of original incompressible Navier–Stokes equations, but also facilitates us to design linearly decoupled and energy-stable time-marching scheme. Comparing with the conventional projection-type schemes, the present method leads to an energy dissipation law with respect to kinetic energy instead of a modified energy including velocity and pressure gradient. In each time step, only two parabolic equations with constant coefficients and one Poisson equation need to be solved. Therefore, the numerical implementation is highly efficient. Moreover, the proposed AVVS method can be directly extended to construct linear, decoupled, and energy-stable scheme for the turbidity current system with slight modifications on the right-hand side of supplementary equation. Extensive numerical experiments are implemented to validate the accuracy, energy stability, and capability in complex fluid simulations.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142007047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence of multirate fixed stress split iterative schemes for a fractured Biot model","authors":"","doi":"10.1016/j.cma.2024.117253","DOIUrl":"10.1016/j.cma.2024.117253","url":null,"abstract":"<div><p>This paper considers the convergence analysis of a coupled mixed dimensional flow and mechanics problem in a fractured poro-elastic medium. In this mixed dimensional type system, the flow equation on a <span><math><mi>d</mi></math></span> dimensional porous matrix is coupled to the flow equation on a <span><math><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></math></span> dimensional fracture surface. The fracture geometry is treated as a possibly non-planar interface, and the fracture is assumed to remain open (<em>i.e.</em>, ignoring contact mechanics boundary conditions). The main contribution is developing a multirate scheme in which flow takes multiple fine time steps within one coarse mechanics time step using the standard fixed stress splitting approach. In this coupled system, the linear quasi-static Biot model is assumed for the porous matrix, and the lubrication-type system (Girault et al., 2015) is assumed for the fracture. More specifically, two variations (<em>i.e.</em>, algorithms) of the multirate scheme are formulated and their convergence analyses are established. The convergence analysis is based on proving a Banach fixed-point contraction argument which establishes the geometric convergence, and hence, the uniqueness of the obtained solution for both algorithms. The theoretical investigations are supplemented by preliminary numerical results validating the theoretical findings.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142007044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks","authors":"","doi":"10.1016/j.cma.2024.117290","DOIUrl":"10.1016/j.cma.2024.117290","url":null,"abstract":"<div><p>Kolmogorov–Arnold Networks (KANs) were recently introduced as an alternative representation model to MLP. Herein, we employ KANs to construct physics-informed machine learning models (PIKANs) and deep operator models (DeepOKANs) for solving differential equations for forward and inverse problems. In particular, we compare them with physics-informed neural networks (PINNs) and deep operator networks (DeepONets), which are based on the standard MLP representation. We find that although the original KANs based on the B-splines parameterization lack accuracy and efficiency, modified versions based on low-order orthogonal polynomials have comparable performance to PINNs and DeepONet, although they still lack robustness as they may diverge for different random seeds or higher order orthogonal polynomials. We visualize their corresponding loss landscapes and analyze their learning dynamics using information bottleneck theory. Our study follows the FAIR principles so that other researchers can use our benchmarks to further advance this emerging topic.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142007046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fast implicit update schemes for Cahn–Hilliard-type gradient flow in the context of Fourier-spectral methods","authors":"","doi":"10.1016/j.cma.2024.117220","DOIUrl":"10.1016/j.cma.2024.117220","url":null,"abstract":"<div><p>This work discusses a way of allowing fast implicit update schemes for the temporal discretization of phase-field models for gradient flow problems that employ Fourier-spectral methods for their spatial discretization. Through the repeated application of the Sherman–Morrison formula we provide a rule for approximations of the inverted tangent matrix of the corresponding Newton–Raphson method with a selectable order. Since the representation of this inversion is exact for a sufficiently high approximation order, the proposed scheme is shown to provide a fixed-point-type iterative solver for gradient flow problems that require the solution of linear systems in the context of an implicit time-integration. While the proposed scheme is applicable to general gradient flow phase-field models, we discuss the scheme in the context of the Cahn–Hilliard equation, the Swift–Hohenberg equation, and the phase-field crystal equation for which we demonstrate the performance of the proposed method in comparison with classical solvers.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045782524004766/pdfft?md5=0f1cab81751dc7da18c718fb80da9194&pid=1-s2.0-S0045782524004766-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141994748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}