Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Modeling via peridynamics for damage and failure of hyperelastic composites","authors":"Binbin Yin ,&nbsp;Weikang Sun ,&nbsp;Chuan Wang ,&nbsp;K.M. Liew","doi":"10.1016/j.cma.2024.117494","DOIUrl":"10.1016/j.cma.2024.117494","url":null,"abstract":"<div><div>Modeling damage and failure behaviors of hyperelastic composites under large deformations is pivotal for advancing the design of cutting-edge elastomers used in biomedical engineering and soft robotics. However, existing methods struggle with capturing the non-linearities and singularities in the displacement field under such conditions. To address these difficulties, we propose a novel bond-based peridynamics (PD) framework with multiple advancements. First, we develop a PD bond strain model grounded in the nonlinear Piola-Kirchhoff stress-stretch relationship, precisely capturing hyperelasticity and ensuring full compliance with thermodynamic laws and kinematics in large deformation scenarios. Second, our framework employs a particle discretization technique that not only sidesteps the mesh distortion issues commonly encountered in grid-based methods subjected to large deformation but also significantly lowers the computational complexity due to the ease of numerical implementation of random inclusion distributions. Third, we propose, for the first time, a refined 3D hyperelastic model within the PD framework that enables a more comprehensive and accurate prediction of material responses to external loads, surpassing the limitations of conventional 2D simulations. Validation against experimental data demonstrates that our model accurately captures key physical phenomena in hyperelastic composites, such as spontaneous crack initiation and propagation, interface debonding, crack coalescence, and the formation of non-smooth crack surfaces. Crucially, this framework is versatile and adaptable to a wide range of engineered composite systems with different inclusions and matrices, making it a powerful tool for predicting and analyzing large deformation behaviors in various advanced applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117494"},"PeriodicalIF":6.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578366","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":"GDSW preconditioners for composite Discontinuous Galerkin discretizations of multicompartment reaction–diffusion problems","authors":"Ngoc Mai Monica Huynh ,&nbsp;Luca F. Pavarino ,&nbsp;Simone Scacchi","doi":"10.1016/j.cma.2024.117501","DOIUrl":"10.1016/j.cma.2024.117501","url":null,"abstract":"<div><div>The aim of the present work is to design, analyze theoretically, and test numerically, a generalized Dryja–Smith–Widlund (GDSW) preconditioner for composite Discontinuous Galerkin discretizations of multicompartment parabolic reaction–diffusion equations, where the solution can exhibit natural discontinuities across the domain. We prove that the resulting preconditioned operator for the solution of the discrete system arising at each time step converges with a scalable and quasi-optimal upper bound for the condition number. The GDSW preconditioner is then applied to the EMI (Extracellular - Membrane - Intracellular) reaction–diffusion system, recently proposed to model microscopically the spatiotemporal evolution of cardiac bioelectrical potentials. Numerical tests validate the scalability and quasi-optimality of the EMI-GDSW preconditioner, and investigate its robustness with respect to the time-step size as well as jumps in the diffusion coefficients.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117501"},"PeriodicalIF":6.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578367","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 novel framework for fatigue cracking and life prediction: Perfect combination of peridynamic method and deep neural network","authors":"Liwei Wu ,&nbsp;Han Wang ,&nbsp;Dan Huang ,&nbsp;Junbin Guo ,&nbsp;Chuanqiang Yu ,&nbsp;Junti Wang","doi":"10.1016/j.cma.2024.117515","DOIUrl":"10.1016/j.cma.2024.117515","url":null,"abstract":"<div><div>This paper presents an innovative methodology that seamlessly integrates the peridynamic method with advanced deep learning techniques, specifically utilizing the Gated Recurrent Unit (GRU) neural network. This integration results in the development of a highly accurate and efficient model for predicting fatigue cracking and life. This model can effectively forecast the fatigue crack patterns and fatigue life, effectively addressing the limitations of existing data-driven models, which often struggle with accurately predicting fatigue crack growth. One of the key advancements of this study is the significant enhancement in numerical efficiency, reducing the computational cost to mere hundreds of seconds, a substantial improvement over traditional peridynamic simulations. The study begins by establishing a peridynamic fatigue damage model, which is used to generate a comprehensive dataset of mechanical behavior under fatigue loading. A strategy is developed to convert the mechanical data into a suitable format for deep learning, which enables the creation of well-structured training and testing datasets. The Peridynamic-Gated Recurrent Unit (PD-GRU) data-driven model is then proposed, demonstrating exceptional numerical performance and operational efficiency. Through a series of rigorous numerical analyses, the PD-GRU model's capabilities are validated, highlighting its potential as an innovative perspective and groundbreaking tool in the fatigue analysis of materials and structures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117515"},"PeriodicalIF":6.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578370","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 Bayesian framework for constitutive model identification via use of full field measurements, with application to heterogeneous materials","authors":"Abbas Jafari ,&nbsp;Konstantinos Vlachas ,&nbsp;Eleni Chatzi ,&nbsp;Jörg F. Unger","doi":"10.1016/j.cma.2024.117489","DOIUrl":"10.1016/j.cma.2024.117489","url":null,"abstract":"<div><div>In this paper, we present a Bayesian framework for the identification of the parameters of nonlinear constitutive material laws using full-field displacement measurements. The concept of force-based Finite Element Model Updating (FEMU-F) is employed, which relies on the availability of measurable quantities such as displacements and external forces. The proposed approach particularly unfolds the advantage of FEMU-F, as opposed to the conventional FEMU, by directly incorporating information from full-field measured displacements into the model. This feature is well-suited for heterogeneous materials with softening, where the localization zone depends on the random microstructure. Besides, to account for uncertainties in the measured displacements, we treat displacements as additional unknown variables to be identified, alongside the constitutive parameters. A variational Bayesian scheme is then employed to identify these unknowns via approximate posteriors under the assumption of multivariate normal distributions. An optimization problem is then formulated and solved iteratively, aiming to minimize the discrepancy between true and approximate posteriors. The benefit of the proposed approach lies in the stochastic nature of the formulation, which allows to tackle uncertainties related to model parameters and measurement noise. We verify the efficacy of our proposed framework on two simulated examples using gradient damage model with a path-dependent nonlinear constitutive law. Based on a nonlocal equivalent strain norm, this constitutive model can simulate a localized damage zone representing softening and cracking. The first example illustrates an application of the FEMU-F approach to cracked structures including sensitivity studies related to measurement noise and parameters of the prior distributions. In this example, the variational Bayesian solver demonstrates a sizable advantage in terms of computational efficiency compared to a traditional least-square optimizer. The second example demonstrates a sub-domain analysis to tackle challenges associated with limited domain knowledge such as uncertain boundary conditions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117489"},"PeriodicalIF":6.9,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142578368","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 computational framework for well production simulation: Coupling transient Darcy flow and channel flow by SGBEM–FEM","authors":"Jing Hu ,&nbsp;Mark E. Mear","doi":"10.1016/j.cma.2024.117491","DOIUrl":"10.1016/j.cma.2024.117491","url":null,"abstract":"<div><div>An efficient SGBEM–FEM framework for predicting transient hydrocarbon production by coupling transient Darcy flow and channel flow is proposed, which extends the steady state analysis framework developed in Hu and Mear (2022). The governing equation of transient Darcy flow in the matrix is formulated by an integral equation method, and that of channel flow in the fracture is cast in a weak form suitable for treatment with the standard finite element method. An asymptotic analysis is conducted for the transient flux field around the crack front in porous media, and a special tip element is developed to capture the dominant asymptotic field. Cracks in an unbounded domain as well as a layered domain are treated. For the layered domain simulation, a fast algorithm is developed for evaluating the bounded layer kernel based upon Ewald summation. The numerical implementation is verified with the solution to the decoupled transient Darcy flow equation and the coupled equations, respectively. Numerical examples consisting of sequential circular cracks, sequential long cracks and petal cracks are presented to demonstrate the capability of the proposed framework. The proposed framework could potentially be a useful basis for extensions to model related engineering processes involving fluid flows in fractured subsurfaces (such as contaminant transport, nuclear waste disposal, and carbon capture).</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117491"},"PeriodicalIF":6.9,"publicationDate":"2024-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572626","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":"Bayesian neural networks for predicting uncertainty in full-field material response","authors":"George D. Pasparakis,&nbsp;Lori Graham-Brady,&nbsp;Michael D. Shields","doi":"10.1016/j.cma.2024.117486","DOIUrl":"10.1016/j.cma.2024.117486","url":null,"abstract":"<div><div>Stress and material deformation field predictions are among the most important tasks in computational mechanics. These predictions are typically made by solving the governing equations of continuum mechanics using finite element analysis, which can become computationally prohibitive considering complex microstructures and material behaviors. Machine learning (ML) methods offer potentially cost effective surrogates for these applications. However, existing ML surrogates are either limited to low-dimensional problems and/or do not provide uncertainty estimates in the predictions. This work proposes an ML surrogate framework for stress field prediction and uncertainty quantification for diverse materials microstructures. A modified Bayesian U-net architecture is employed to provide a data-driven image-to-image mapping from initial microstructure to stress field with prediction (epistemic) uncertainty estimates. The Bayesian posterior distributions for the U-net parameters are estimated using three state-of-the-art inference algorithms: the posterior sampling-based Hamiltonian Monte Carlo method and two variational approaches, the Monte-Carlo Dropout method and the Bayes by Backprop algorithm. A systematic comparison of the predictive accuracy and uncertainty estimates for these methods is performed for a fiber reinforced composite material and polycrystalline microstructure application. It is shown that the proposed methods yield predictions of high accuracy compared to the FEA solution, while uncertainty estimates depend on the inference approach. Generally, the Hamiltonian Monte Carlo and Bayes by Backprop methods provide consistent uncertainty estimates. Uncertainty estimates from Monte Carlo Dropout, on the other hand, are more difficult to interpret and depend strongly on the method’s design.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117486"},"PeriodicalIF":6.9,"publicationDate":"2024-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572627","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 Review of Recent Advances in Surrogate Models for Uncertainty Quantification of High-Dimensional Engineering Applications","authors":"Zeynab Azarhoosh,&nbsp;Majid Ilchi Ghazaan","doi":"10.1016/j.cma.2024.117508","DOIUrl":"10.1016/j.cma.2024.117508","url":null,"abstract":"<div><div>In fields where predictions may have vital consequences, <em>uncertainty quantification</em> (UQ) plays a crucial role, as it enables more accurate forecasts and mitigates the potential risks associated with decision-making. However, performing uncertainty quantification in real-world scenarios necessitates multiple evaluations of complex computational models, which can be both costly and time-consuming. To address these challenges, surrogate models (also known as meta-models)—which are low-cost approximations of computational models—can be an influential tool. Nonetheless, as the complexity of the problem increases and the number of input variables grows, the computational burden of constructing an efficient surrogate model also rises, leading to the so-called <em>curse of dimensionality</em> in <em>uncertainty propagation</em> from inputs to outputs. Additionally, dealing with constraints, ensuring the robustness and generalization of surrogate models across different inputs, and interpreting the output results can present significant difficulties. Therefore, techniques must be implemented to enhance the performance of these models. This paper reviews the developments of the past years in surrogate modeling for <em>high-dimensional</em> inputs, with the goal of quantifying output uncertainty. It proposes general approaches, including dimension reduction techniques, multi-fidelity surrogate models, and advanced sampling schemes, to overcome challenges in various practical problems. This comprehensive study provides an initial guide for effective surrogate modeling in engineering practices by outlining key components of solving algorithms and screening mathematical benchmark functions, all while ensuring sufficient accuracy for overall predictions. Additionally, this study identifies research gaps, suggests future directions, and describes the applications of the proposed solutions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117508"},"PeriodicalIF":6.9,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573205","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":"Finite element-integrated neural network framework for elastic and elastoplastic solids","authors":"Ning Zhang ,&nbsp;Kunpeng Xu ,&nbsp;Zhen Yu Yin ,&nbsp;Kai-Qi Li ,&nbsp;Yin-Fu Jin","doi":"10.1016/j.cma.2024.117474","DOIUrl":"10.1016/j.cma.2024.117474","url":null,"abstract":"<div><div>The Physics-informed neural network method (PINN) has shown promise in resolving unknown physical fields in solid mechanics, owing to its success in solving various partial differential equations. Nonetheless, effectively solving engineering-scale boundary value problems, particularly heterogeneity and path-dependent elastoplasticity, remains challenging for PINN. To address these issues, this study proposes a hybrid computational framework integrating finite element method (FEM) with PINN, known as FEINN. This framework employs finite elements for domain discretization instead of collocation points and utilizes the Gaussian integration scheme and strain-displacement matrix to establish the weak-form governing equation instead of the automatic differentiation operator. By harnessing the strengths of FEM and PINN, this framework exhibits inherent advantages in handling complex boundary conditions with heterogeneous materials. For addressing path-dependent elastoplasticity in material nonlinear boundary value problems, an incremental scheme is developed to accurately compute the stress. To validate the effectiveness of FEINN, five types of numerical experiments are conducted, involving homogenous and heterogeneous problems with various boundaries such as concentrated force, distributed force, and distributed displacement. Both linear elastic and elastoplastic (modified cam-clay) models are employed and evaluated. Using the solutions obtained from FEM as a reference, FEINN demonstrates exceptional accuracy and convergence rate in all experiments compared with previous PINNs. The mean absolute percentage errors between FEINN and FEM are consistently below 1%, and FEINN exhibits notably faster convergence rates than PINNs, highlighting its computational efficiency. Moreover, this study discusses the biases observed in regions of low stress and displacement, factors influencing FEINN's performance, and the potential applications of the FEINN framework.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117474"},"PeriodicalIF":6.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572625","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":"Homogenized models of mechanical metamaterials","authors":"J. Ulloa ,&nbsp;M.P. Ariza ,&nbsp;J.E. Andrade ,&nbsp;M. Ortiz","doi":"10.1016/j.cma.2024.117454","DOIUrl":"10.1016/j.cma.2024.117454","url":null,"abstract":"<div><div>Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the computational modeling of metastructures at macroscopic scales. In the present work, we assess the continuum limit of mechanical metamaterials via homogenized models derived rigorously from variational methods. It is shown through multiple examples that micropolar-type effective energies, derived naturally from analysis, properly capture the kinematics of discrete lattices in two and three dimensions. Moreover, the convergence of the discrete energy to the continuum limit is shown numerically. We provide open-source computational implementations for all examples, including both discrete and homogenized models.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117454"},"PeriodicalIF":6.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572622","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":"An all Mach number semi-implicit hybrid Finite Volume/Virtual Element method for compressible viscous flows on Voronoi meshes","authors":"Walter Boscheri ,&nbsp;Saray Busto ,&nbsp;Michael Dumbser","doi":"10.1016/j.cma.2024.117502","DOIUrl":"10.1016/j.cma.2024.117502","url":null,"abstract":"<div><div>We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the operator splitting of the compressible Navier–Stokes equations into three sub-systems: a convective sub-system solved explicitly using a finite volume (FV) scheme, and the viscous and pressure sub-systems which are discretized implicitly with the aid of a virtual element method (VEM). Consequently, the time step restriction of the overall algorithm depends only on the mean flow velocity and not on the fast pressure waves nor on the viscous eigenvalues. As such, the proposed methodology is well suited for the solution of low Mach number flows at all Reynolds numbers. Moreover, the scheme is proven to be globally energy conserving so that shock capturing properties are retrieved in high Mach number flows while being only linearly implicit in time. To reach high order of accuracy in time and space, an IMEX Runge–Kutta time stepping strategy is employed together with high order spatial reconstructions in terms of CWENO polynomials and virtual element space basis functions. The chosen discretization techniques allow the use of general polygonal grids, a useful tool when dealing with complex domain configurations. The new scheme is carefully validated in both the incompressible limit and the high Mach number regime through a large set of classical benchmarks for fluid dynamics, assessing robustness and accuracy.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"433 ","pages":"Article 117502"},"PeriodicalIF":6.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572623","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}