Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Bayesian neural networks for predicting uncertainty in full-field material response","authors":"","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":null,"pages":null},"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":"","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":null,"pages":null},"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":"","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":null,"pages":null},"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":"","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":null,"pages":null},"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":"","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":null,"pages":null},"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}

{"title":"Uniform multiple laminates interpolation model and design method for double–double laminates based on multi-material topology optimization","authors":"","doi":"10.1016/j.cma.2024.117492","DOIUrl":"10.1016/j.cma.2024.117492","url":null,"abstract":"<div><div>Double–Double (DD) laminates, incorporating a repetition of sub-plies featuring two groups of balanced angles, offer broad design flexibility together with the ease of design and manufacturing. In this work, a novel optimization design method is proposed for DD composite laminates based on multi-material topology optimization. First, the uniform multiple laminates interpolation (UMLI) model is proposed to describe the certainty of the stacking direction in multi-layer composite structures, inspired by the interpolation model in multi-material topology optimization. Specifically, the stiffness matrices of all alternative angle combinations of laminates are interpolated to form virtual laminates. The UMLI model eliminates the need for adding interlayer constraints during the optimization process. Then, the optimization problem is defined to minimize the compliance of the composite structures and is solved using the gradient-based optimization algorithm. Finally, the proposed method is applied to the design of the composite stiffened panel, the composite Unmanned Aerial Vehicle (UAV) wing, and the rear fuselage. The results demonstrate that the UMLI model and proposed optimization method have considerable potential in the angle optimization design of multi-layer structures.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572624","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 geometrically exact thin-walled rod model with warping and stress-resultant-based plasticity obtained with a two-level computational approach","authors":"","doi":"10.1016/j.cma.2024.117497","DOIUrl":"10.1016/j.cma.2024.117497","url":null,"abstract":"<div><div>In this work, we propose an two-level computational approach to enrich a seven degree-of-freedom kinematically exact rod model for thin-walled members, allowing for a simple elastoplastic-hardening constitutive equation. The novelty lies in upper-level description, where the effects of coupled elastoplastic-local geometrical instabilities are characterized in terms of cross-sectional stress resultants and generalized rod strains in a fully 3D context. Torsion-warping degrees of freedom and arbitrary (plastic) failure mode capabilities are present, allowing for the modeling of complex structural behavior in thin-walled members. The lower level is based on a kinematically exact shell or 3D-solid model with usual von Mises plasticity and linear isotropic hardening. At such level, simulations are performed in a pre-process stage, with the resulting equivalent stress-resultant-based hardening plastic parameters directly transferred to the upper-level as input data. No iterative procedure further binding the upper/lower level representations is required. This rather phenomenological approach of incorporating local effects may satisfactorily replicate the overall behavior of thin-walled members consisted of ductile materials, such as, but not only, steel or aluminum beam/column profiles. Numerical solution of the upper-level is carried in the framework of operator split, whereby, the local variables are solved in an element-wise fashion through numerical condensation, thus not adding any extra DOFs to the upper-level. The model is implemented in an in-house finite element program for the analysis of flexible thin structures and is validated against reference solutions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552279","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":"NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements","authors":"","doi":"10.1016/j.cma.2024.117498","DOIUrl":"10.1016/j.cma.2024.117498","url":null,"abstract":"<div><div>Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. This study introduces NeuroSEM, a hybrid framework integrating PINNs with the high-fidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh–Bénard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU–CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552278","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":"Surrogate construction via weight parameterization of residual neural networks","authors":"","doi":"10.1016/j.cma.2024.117468","DOIUrl":"10.1016/j.cma.2024.117468","url":null,"abstract":"<div><div>Surrogate model development is a critical step for uncertainty quantification or other sample-intensive tasks for complex computational models. In this work we develop a multi-output surrogate form using a class of neural networks (NNs) that employ shortcut connections, namely Residual NNs (ResNets). ResNets are known to regularize the surrogate learning problem and improve the efficiency and accuracy of the resulting surrogate. Inspired by the continuous, Neural ODE analogy, we augment ResNets with weight parameterization strategy with respect to ResNet depth. Weight-parameterized ResNets regularize the NN surrogate learning problem and allow better generalization with a drastically reduced number of learnable parameters. We demonstrate that weight-parameterized ResNets are more accurate and efficient than conventional feed-forward multi-layer perceptron networks. We also compare various options for parameterization of the weights as functions of ResNet depth. We demonstrate the results on both synthetic examples and a large scale earth system model of interest.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142550561","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 dual experimental/computational data-driven approach for random field modeling based strength estimation analysis of composite structures","authors":"","doi":"10.1016/j.cma.2024.117476","DOIUrl":"10.1016/j.cma.2024.117476","url":null,"abstract":"<div><div>This paper proposes a dual experimental/computational data-driven analysis framework for apparent strength estimation of composite structures consisting of randomly arranged unidirectional fiber-reinforced plastics. In the proposed framework, multiscale stochastic analysis is performed with random field modeling of local apparent quantities such as apparent elastic modulus or strength. Significant improvements are needed in terms of computational accuracy, uncertainty quantification, random field modeling, and computational efficiency for the quantitative strength estimation by numerical analysis. For this problem, a novel computational framework assisted by the dual data-driven approach is established in this research. In the proposed approach, the accuracy of the strength estimation analysis for deterministic conditions is improved by an experimental data-driven approach based on the in-situ microscopic full-field displacement measurement. A computational data-driven approach based on random field modeling assisted by machine learning is employed for non-deterministic conditions. In this paper, the outline of the proposed dual data-driven multiscale stochastic analysis framework is introduced first. Subsequently, the details of the proposed experimental data-driven approach for determining the microscopic fracture criteria are presented, and the computational data-driven approach for improving the effectiveness and efficiency of the random field modeling-based probabilistic analysis is described. The presented approach is applied to the strength estimation of a randomly arranged unidirectional fiber-reinforced composite plate under transverse tensile loading, and its validity and effectiveness are discussed with comparisons between the experimental and numerical results obtained assuming several computational conditions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142551532","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}