Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"A chain stretch-based gradient-enhanced model for damage and fracture in elastomers","authors":"S. Mohammad Mousavi ,&nbsp;Jason Mulderrig ,&nbsp;Brandon Talamini ,&nbsp;Nikolaos Bouklas","doi":"10.1016/j.cma.2025.118103","DOIUrl":"10.1016/j.cma.2025.118103","url":null,"abstract":"<div><div>Similar to quasi-brittle materials, it has been recently shown that elastomers can exhibit a macroscopically diffuse damage zone that accompanies the fracture process. In this study, we introduce a stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials (e.g., concrete), they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening (de Borst and Verhoosel, 2016). This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz <em>et al.</em>, 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. We discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118103"},"PeriodicalIF":6.9,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263726","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 posteriori algebraic error estimates and nonoverlapping domain decomposition in mixed formulations: energy coarse grid balancing, local mass conservation on each step, and line search","authors":"Manuela Bastidas Olivares ,&nbsp;Akram Beni Hamad ,&nbsp;Martin Vohralík ,&nbsp;Ivan Yotov","doi":"10.1016/j.cma.2025.118090","DOIUrl":"10.1016/j.cma.2025.118090","url":null,"abstract":"<div><div>We consider iterative algebraic solvers for saddle-point mixed finite element discretizations of the model Darcy flow problem. We propose a posteriori error estimators of the algebraic error as well as a nonoverlapping domain decomposition algorithm. The estimators control the algebraic error from above and from below in a guaranteed and fully computable way. The distinctive feature of the domain decomposition algorithm is that it produces a locally mass conservative approximation on each iteration. Both the estimate and the algorithm rely on a coarse grid solver, a subdomain Neumann solver, and a subdomain Dirichlet solver. The algorithm also employs a line search to determine the optimal step size, leading to a Pythagoras formula for the algebraic error decrease in each iteration. We suppose that the fine mesh is a refinement of a coarse mesh, where both meshes need to be formed by simplices or rectangular parallelepipeds. Numerical experiments illustrate the theoretical developments and confirm the efficiency of the algebraic error estimates and of the domain decomposition algorithm.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118090"},"PeriodicalIF":6.9,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263759","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":"Efficient Bayesian updating with single-loop Kriging model for time-dependent model calibration","authors":"Zhao-Hui Lu ,&nbsp;Wan-Ting Pei ,&nbsp;Zhao Zhao ,&nbsp;Zengzhi Qian","doi":"10.1016/j.cma.2025.118150","DOIUrl":"10.1016/j.cma.2025.118150","url":null,"abstract":"<div><div>Bayesian updating, as a useful tool for system identification and model calibration, has gained signification traction in recent years. However, for time-dependent models, the number of observations will increase rapidly with the increase of the number of time nodes, resulting in Bayesian updating problems facing serious challenges. To settle this issue, this paper proposes an efficient Bayesian updating approach for time-dependent model, called Bayesian updating with single-loop Kriging model (BU-SILK). In the proposed method, Bayesian updating problem of time-dependent model is converted into a parallel system reliability problem, where the number of components is equal to that of discrete time nodes. Then, a single-loop Kriging model is constructed for the purpose of this parallel system reliability analysis. By selecting the best training sample and time node, Kriging model is refined adaptively until the specified stopping criterion is satisfied. The proposed Bayesian updating method can infer the posterior distributions of both static and dynamic parameters of time-dependent model. Four numerical examples show that the proposed method significantly improves computational efficiency without sacrificing accuracy.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118150"},"PeriodicalIF":6.9,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263725","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":"Non-intrusive reduced-order modeling for dynamical systems with spatially localized features","authors":"Leonidas Gkimisis ,&nbsp;Nicole Aretz ,&nbsp;Marco Tezzele ,&nbsp;Thomas Richter ,&nbsp;Peter Benner ,&nbsp;Karen E. Willcox","doi":"10.1016/j.cma.2025.118115","DOIUrl":"10.1016/j.cma.2025.118115","url":null,"abstract":"<div><div>This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains that exhibit fast and slow singular value decay. The dynamics of the subdomain exhibiting slow singular value decay are learned with sFOM while the dynamics with intrinsically low dimensionality on the complementary subdomain are learned with OpInf. The resulting, coupled OpInf-sFOM formulation leverages the computational efficiency of OpInf and the high resolution of sFOM, and thus enables fast non-intrusive predictions for conditions beyond those sampled in the training data set. A novel regularization technique with a closed-form solution based on the Gershgorin disk theorem is introduced to promote stable sFOM and OpInf models. We also provide a data-driven indicator for subdomain selection and ensure solution smoothness over the interface via a post-processing interpolation step. We evaluate the efficiency of the approach in terms of offline and online speedup through a quantitative, parametric computational cost analysis. We demonstrate the coupled OpInf-sFOM formulation for two test cases: a one-dimensional Burgers’ model for which accurate predictions beyond the span of the training snapshots are presented, and a two-dimensional parametric model for the Pine Island Glacier ice thickness dynamics, for which the OpInf-sFOM model achieves an average prediction error on the order of 1% with an online speedup factor of approximately <span><math><mrow><mn>8</mn><mo>×</mo></mrow></math></span> compared to the numerical simulation.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118115"},"PeriodicalIF":6.9,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263758","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":"Isogeometric topology optimization of thin-walled structures with complex design domains","authors":"Ji Sheng,&nbsp;Xiaodong Wei","doi":"10.1016/j.cma.2025.118114","DOIUrl":"10.1016/j.cma.2025.118114","url":null,"abstract":"<div><div>In this work, we present a novel isogeometric topology optimization (TO) method for shell structures that involve complex design domains. In particular, analysis-suitable unstructured T-splines (ASUTS) are used to represent complex design domains in a smooth and watertight manner. On top of such domains, minimum compliance is studied as the model problem, where the Kirchhoff–Love shell is used to compute the structural response and a generalized Cahn–Hilliard phase-field model is proposed to perform TO. Since both models are governed by high-order partial differential equations, ASUTS-based isogeometric analysis (IGA) is adopted for the spatial discretization due to its high-order smooth basis functions. Moreover, IGA provides the possibility to seamlessly integrate design, analysis, and optimization. To demonstrate the efficacy of the proposed method, we first perform several benchmark tests to show that the generalized Cahn–Hilliard model can naturally handle complex topological changes without special treatment. In the end, a couple of real-world engineering structures are studied to show the capability of the proposed method dealing with complex design domains.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118114"},"PeriodicalIF":6.9,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254060","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 resolution independent neural operator","authors":"Bahador Bahmani ,&nbsp;Somdatta Goswami ,&nbsp;Ioannis G. Kevrekidis ,&nbsp;Michael D. Shields","doi":"10.1016/j.cma.2025.118113","DOIUrl":"10.1016/j.cma.2025.118113","url":null,"abstract":"<div><div>The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. In this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the <strong>R</strong>esolution <strong>I</strong>ndependent <strong>N</strong>eural <strong>O</strong>perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118113"},"PeriodicalIF":6.9,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144254061","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":"Stabilizing and solving unique continuation problems by parameterizing data and learning finite element solution operators","authors":"Erik Burman ,&nbsp;Mats G. Larson ,&nbsp;Karl Larsson ,&nbsp;Carl Lundholm","doi":"10.1016/j.cma.2025.118111","DOIUrl":"10.1016/j.cma.2025.118111","url":null,"abstract":"<div><div>We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of boundary observations for typical solutions (collective data) and a bulk measurement of a specific realization. To leverage this collective data, we first compress the boundary data using proper orthogonal decomposition (POD) in a linear expansion. Next, we identify a possible nonlinear low-dimensional structure in the expansion coefficients using an autoencoder, which provides a parametrization of the dataset in a lower-dimensional latent space. We then train an operator network to map the expansion coefficients representing the boundary data to the finite element (FE) solution of the PDE. Finally, we connect the autoencoder’s decoder to the operator network which enables us to solve the inverse problem by optimizing a data-fitting term over the latent space. We analyze the underlying stabilized finite element method (FEM) in the linear setting and establish an optimal error estimate in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm. The nonlinear problem is then studied numerically, demonstrating the effectiveness of our approach.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118111"},"PeriodicalIF":6.9,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242845","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":"Tensor-decomposition-based A Priori Surrogate (TAPS) modeling for ultra large-scale simulations","authors":"Jiachen Guo ,&nbsp;Gino Domel ,&nbsp;Chanwook Park ,&nbsp;Hantao Zhang ,&nbsp;Ozgur Can Gumus ,&nbsp;Ye Lu ,&nbsp;Gregory J. Wagner ,&nbsp;Dong Qian ,&nbsp;Jian Cao ,&nbsp;Thomas J.R. Hughes ,&nbsp;Wing Kam Liu","doi":"10.1016/j.cma.2025.118101","DOIUrl":"10.1016/j.cma.2025.118101","url":null,"abstract":"<div><div>A data-free predictive scientific AI model, termed Tensor-decomposition-based A Priori Surrogate (TAPS), is proposed for tackling ultra large-scale engineering simulations with significant speedup, memory savings, and storage gain. TAPS does not require any training data and can effectively obtain surrogate models for high-dimensional parametric problems with equivalently zetta-scale (<span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>21</mn></mrow></msup></mrow></math></span>) degrees of freedom (DoFs) using a single GPU. TAPS achieves this by directly obtaining reduced-order models through solving the weak form of the governing equations with multiple independent variables such as spatial coordinates, parameters, and time. The paper first introduces an AI-enhanced finite element-type interpolation function called convolution hierarchical deep-learning neural network (C-HiDeNN) with tensor decomposition (TD). Subsequently, the generalized space-parameter-time Galerkin weak form and the corresponding matrix form are derived. Through the choice of TAPS hyperparameters, different convergence rates can be achieved. To show the capabilities of this framework, TAPS is then used to simulate a large-scale additive manufacturing process and achieves around 1,370x speedup, 14.8x memory savings, and 955x storage gain compared to the finite difference method with 3.46 billion spatial DoFs. As a result, the TAPS framework opens a new avenue for many challenging ultra large-scale engineering problems, such as additive manufacturing and integrated circuit design, among others.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118101"},"PeriodicalIF":6.9,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242844","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 hybrid phase-field model for dynamic fracture in fiber-reinforced composites considering interfacial debonding","authors":"Nhon Nguyen-Thanh ,&nbsp;Weidong Li ,&nbsp;Qi Zhang ,&nbsp;Kun Zhou","doi":"10.1016/j.cma.2025.118110","DOIUrl":"10.1016/j.cma.2025.118110","url":null,"abstract":"<div><div>In this work, we develop a hybrid phase-field modeling approach, enhanced by a higher-order nonlocal operator method (NOM) to simulate dynamic brittle fracture in fiber-reinforced composites. This approach captures dynamic fracture patterns in composite materials, including matrix cracking, interfacial debonding, and the interaction between these failure modes. A crack surface density function is applied to incorporate the material anisotropy induced by the fibers. Both weak material anisotropy and coefficient-related strong anisotropy are considered. Moreover, the nonlocal integral form of the dynamic phase-field fracture model is derived using a higher-order NOM. The proposed approach eliminates the need to compute derivatives of the moment matrix. To improve computational accuracy and stability, a nonlocal differential operator derived from the reproducing kernel particle method is employed. The implicit Newmark integration scheme is used for the time discretization of the phase-field governing equations. Numerical examples demonstrate that the proposed method effectively captures the initiation, propagation, and interaction of bulk dynamic fractures and interface cracks, while accurately representing the anisotropic behavior of composite materials.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118110"},"PeriodicalIF":6.9,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144230618","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 porosity-based mechanics model for studying crack evolution from ITZ to mortar matrix in concrete","authors":"Zesen Peng ,&nbsp;Qing-xiang Xiong ,&nbsp;Xiangming Zhou ,&nbsp;Xuan Gao ,&nbsp;Xin-Yu Zhao ,&nbsp;Zhaozheng Meng ,&nbsp;Qing-feng Liu","doi":"10.1016/j.cma.2025.118085","DOIUrl":"10.1016/j.cma.2025.118085","url":null,"abstract":"<div><div>This study proposes a novel porosity-based mechanics model for investigating the crack evolution in concrete under uniaxial compression. This model accounts for the porosity gradient and heterogeneous mechanical properties within the concrete’s interfacial transition zone (ITZ). Validation against experimental results from the literature and international standards demonstrates the model’s accuracy in modeling both the global mechanical performance and crack evolution in concrete. Based on the proposed porosity-based mechanics model, a series of systematic studies are conducted to investigate the potential influence of ITZ mechanical properties, ITZ overlap effects induced by various aggregate volume fractions, and global tensile strength on the cracking mechanisms of concrete. Modeling results indicate that the crack evolution from ITZ to mortar matrix is significantly impacted by the ratio of ITZ to mortar mechanical parameters, and a correlation exists between the cracking proportions of the ITZ and the surrounding mortar. The ITZ overlap effect resulting from closely adjacent aggregates increases the susceptibility of the local mortar matrix to cracking. Increasing the overall tensile strength can reduce the cracking proportion of concrete, but it does not significantly affect crack evolution from ITZ to mortar matrix. Besides, increasing the concrete’s tensile strength significantly reduces tensile cracks in the mortar matrix, while having a limited effect on tensile cracks in the ITZ. Further results and detailed discussions are presented within the main text, hoping to provide new insights into the damage process of concrete under external loading.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118085"},"PeriodicalIF":6.9,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144223573","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}