Computer Methods in Applied Mechanics and Engineering最新文献_第6页

Stabilization-free virtual element method for 2D third medium contact 二维第三介质接触的无稳定虚元法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-12 DOI: 10.1016/j.cma.2025.118611

Bing-Bing Xu, Peter Wriggers

The third medium contact (TMC) has been proven to be an effective approach for simulating contact problems involving large deformations. Unlike traditional contact algorithms, this methodology introduces a third medium between two contacting bodies, thereby avoiding the complex treatment of the contact constraints. The approach has been successfully applied for different problems in the framework of the finite element method (FEM). As a generalization of the finite element method, the virtual element method (VEM) can handle arbitrary polygonal elements, providing greater flexibility for modeling third medium contact. However, due to the introduction of the projection operator, VEM requires additional stabilization terms to control the rank of the stiffness matrix. Moreover, the regularization term in the third medium contact formulation requires a second-order numerical scheme, which further complicates the application of classical virtual element schemes to such problems. In this work, the stabilization-free virtual element method (SFVEM) is adopted to TMC and applied to solve contact problems undergoing large deformations. Different from the traditional VEM, SFVEM does not require additional stabilization terms, which simplifies the construction of necessary regularization terms in third medium contact. Building upon the traditional second-order FEM framework, we present the specific format of SFVEM for solving third medium contact, including the construction of high-order projection operator and the tangent stiffness matrix. Numerical examples are provided to demonstrate the effectiveness and applicability of SFVEM in solving complex 2D contact problems with the TMC approach.

第三介质接触（TMC）已被证明是模拟大变形接触问题的有效方法。与传统的接触算法不同，该方法在两个接触体之间引入了第三种介质，从而避免了接触约束的复杂处理。该方法已成功地应用于有限元框架下的不同问题。虚拟元法作为有限元方法的推广，可以处理任意多边形单元，为第三介质接触建模提供了更大的灵活性。然而，由于引入了投影算子，VEM需要额外的稳定项来控制刚度矩阵的秩。此外，第三介质接触公式中的正则化项需要二阶数值格式，这进一步使经典虚元格式在此类问题中的应用复杂化。本文将无稳定虚元法（SFVEM）应用于TMC，并将其应用于大变形接触问题的求解。与传统VEM不同，SFVEM不需要附加稳定化项，简化了第三次介质接触中必要正则化项的构造。在传统二阶有限元框架的基础上，提出了求解三次介质接触的SFVEM的具体格式，包括构造高阶投影算子和切向刚度矩阵。通过数值算例验证了该方法在求解复杂二维接触问题时的有效性和适用性。

{"title":"Stabilization-free virtual element method for 2D third medium contact","authors":"Bing-Bing Xu, Peter Wriggers","doi":"10.1016/j.cma.2025.118611","DOIUrl":"10.1016/j.cma.2025.118611","url":null,"abstract":"<div><div>The third medium contact (TMC) has been proven to be an effective approach for simulating contact problems involving large deformations. Unlike traditional contact algorithms, this methodology introduces a third medium between two contacting bodies, thereby avoiding the complex treatment of the contact constraints. The approach has been successfully applied for different problems in the framework of the finite element method (FEM). As a generalization of the finite element method, the virtual element method (VEM) can handle arbitrary polygonal elements, providing greater flexibility for modeling third medium contact. However, due to the introduction of the projection operator, VEM requires additional stabilization terms to control the rank of the stiffness matrix. Moreover, the regularization term in the third medium contact formulation requires a second-order numerical scheme, which further complicates the application of classical virtual element schemes to such problems. In this work, the stabilization-free virtual element method (SFVEM) is adopted to TMC and applied to solve contact problems undergoing large deformations. Different from the traditional VEM, SFVEM does not require additional stabilization terms, which simplifies the construction of necessary regularization terms in third medium contact. Building upon the traditional second-order FEM framework, we present the specific format of SFVEM for solving third medium contact, including the construction of high-order projection operator and the tangent stiffness matrix. Numerical examples are provided to demonstrate the effectiveness and applicability of SFVEM in solving complex 2D contact problems with the TMC approach.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118611"},"PeriodicalIF":7.3,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731145","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}

引用次数: 0

An implicit RKPM formulation for large deformations in elastoplastic micropolar media: Framework, stabilization and assessment 弹塑性微极介质中大变形的隐式RKPM公式：框架、稳定和评估

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-11 DOI: 10.1016/j.cma.2025.118582

T. Mader , A. Dummer , P. Gamnitzer , H. Gimperlein , M. Neuner

Lagrangian finite element methods (FEM) can suffer from excessive mesh distortion or entanglements in simulations involving large deformations, which become critical in the modeling of quasi-brittle materials characterized by failure mechanisms involving highly localized deformations such as shear bands. To overcome these limitations, we present an implicit numerical framework based on the Reproducing Kernel Particle Method (RKPM) for the micropolar continuum. The latter provides an effective framework to mitigate pathological mesh dependencies in shear-dominated failure and allows to consider size effects due to its intrinsic length scale. The RK shape functions are formulated in a semi-Lagrangian description based on B-Spline kernel functions. The weak form of the governing equations of the micropolar continuum is then derived and discretized within the RKPM framework. For implicit time integration, algorithmic tangent operators are derived to obtain quadratic convergence within the Newton-Raphson solution procedure. Several stabilization techniques are adopted for the proposed framework. First, stabilized nodal integration (SNI) is employed. In this context, a novel quasi-conforming update scheme for the smoothing domains is proposed, leveraging the full deformation gradient. Second, Naturally Stabilized Nodal Integration (NSNI) is applied by expanding the internal virtual work contributions for both linear and angular momentum into linear Taylor series. As an alternative to NSNI, a sub-domain integration (SDI) is presented, where each smoothing domain is partitioned into smaller sub-domains to improve integration accuracy and stability. Finally, to achieve variationally consistent integration (VCI), a Petrov-Galerkin correction is applied to the gradients of the test functions. The performance of the method is demonstrated by 2D benchmark simulations of Cook’s membrane using an elastic Neo-Hookean micropolar material. In addition, simulations of a plane strain compression test considering perfect plasticity using a Drucker-Prager-based micropolar model are performed. The capabilities of the formulation are assessed by comparing the results with those obtained with the FEM and the Material Point Method (MPM), highlighting its potential for modeling large deformations in quasi-brittle materials.

拉格朗日有限元方法（FEM）在涉及大变形的模拟中可能遭受过度的网格畸变或纠缠，这对于以涉及高度局部变形（如剪切带）的破坏机制为特征的准脆性材料的建模至关重要。为了克服这些限制，我们提出了一个基于再现核粒子法（RKPM）的隐式数值框架。后者提供了一个有效的框架，以减轻剪切主导破坏中的病态网格依赖，并允许考虑由于其固有长度尺度而产生的尺寸效应。RK形状函数是基于b样条核函数的半拉格朗日描述。然后导出微极连续统控制方程的弱形式，并在RKPM框架内进行离散化。对于隐式时间积分，导出了切线算子算法，在Newton-Raphson解过程中获得二次收敛。该框架采用了几种稳定技术。首先，采用稳定节点集成（SNI）。在此背景下，提出了一种利用全变形梯度的光滑域准一致性更新方案。其次，通过将线性动量和角动量的内部虚功贡献扩展为线性泰勒级数，应用自然稳定节点积分（NSNI）。作为NSNI的替代方案，提出了子域集成（SDI），其中每个平滑域被划分为更小的子域，以提高集成精度和稳定性。最后，为了实现变相一致积分（VCI），对测试函数的梯度进行Petrov-Galerkin校正。采用弹性Neo-Hookean微极性材料对Cook膜进行了二维基准模拟，证明了该方法的性能。此外，采用基于drucker - prager的微极模型对考虑完美塑性的平面应变压缩试验进行了模拟。通过将结果与FEM和材料点法（MPM）的结果进行比较，评估了该公式的能力，突出了其在准脆性材料中模拟大变形的潜力。

{"title":"An implicit RKPM formulation for large deformations in elastoplastic micropolar media: Framework, stabilization and assessment","authors":"T. Mader , A. Dummer , P. Gamnitzer , H. Gimperlein , M. Neuner","doi":"10.1016/j.cma.2025.118582","DOIUrl":"10.1016/j.cma.2025.118582","url":null,"abstract":"<div><div>Lagrangian finite element methods (FEM) can suffer from excessive mesh distortion or entanglements in simulations involving large deformations, which become critical in the modeling of quasi-brittle materials characterized by failure mechanisms involving highly localized deformations such as shear bands. To overcome these limitations, we present an implicit numerical framework based on the Reproducing Kernel Particle Method (RKPM) for the micropolar continuum. The latter provides an effective framework to mitigate pathological mesh dependencies in shear-dominated failure and allows to consider size effects due to its intrinsic length scale. The RK shape functions are formulated in a semi-Lagrangian description based on B-Spline kernel functions. The weak form of the governing equations of the micropolar continuum is then derived and discretized within the RKPM framework. For implicit time integration, algorithmic tangent operators are derived to obtain quadratic convergence within the Newton-Raphson solution procedure. Several stabilization techniques are adopted for the proposed framework. First, stabilized nodal integration (SNI) is employed. In this context, a novel quasi-conforming update scheme for the smoothing domains is proposed, leveraging the full deformation gradient. Second, Naturally Stabilized Nodal Integration (NSNI) is applied by expanding the internal virtual work contributions for both linear and angular momentum into linear Taylor series. As an alternative to NSNI, a sub-domain integration (SDI) is presented, where each smoothing domain is partitioned into smaller sub-domains to improve integration accuracy and stability. Finally, to achieve variationally consistent integration (VCI), a Petrov-Galerkin correction is applied to the gradients of the test functions. The performance of the method is demonstrated by 2D benchmark simulations of Cook’s membrane using an elastic Neo-Hookean micropolar material. In addition, simulations of a plane strain compression test considering perfect plasticity using a Drucker-Prager-based micropolar model are performed. The capabilities of the formulation are assessed by comparing the results with those obtained with the FEM and the Material Point Method (MPM), highlighting its potential for modeling large deformations in quasi-brittle materials.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118582"},"PeriodicalIF":7.3,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731766","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}

引用次数: 0

Design of stiff elasto-plastic structures 刚性弹塑性结构设计

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-11 DOI: 10.1016/j.cma.2025.118622

Gunnar Granlund, Mathias Wallin

This study investigates “stiffness” optimization of path-dependent elasto-plastic structures by comparing the traditional secant stiffness formulation with a novel tangent stiffness formulation. Design updates are generated using the gradient-based Method of Moving Asymptotes (MMA), and the material behavior is modeled and limited to small-strain elasto-plasticity and isotropic hardening. Numerical examples compare and analyze the two stiffness definitions, revealing that they produce different designs and structural responses. Cross validation and comparison reveals that the secant stiffness optimized designs may have very low end tangent stiffness, and that the end tangent stiffness optimized designs may have very low secant stiffness, showing that the two formulations can contradict each other for elasto-plastic structures.

通过比较传统的割线刚度公式和新的切线刚度公式，研究了路径相关弹塑性结构的“刚度”优化问题。设计更新使用基于梯度的移动渐近线方法（MMA）生成，材料行为建模并仅限于小应变弹塑性和各向同性硬化。数值算例对两种刚度定义进行了比较和分析，揭示了它们产生不同的设计和结构响应。交叉验证和比较表明，割线刚度优化设计可能具有非常低的端切刚度，而端切刚度优化设计可能具有非常低的割线刚度，这表明两种公式对于弹塑性结构可能相互矛盾。

引用次数: 0

An efficient level set-based mesh adaptation for the particle finite element method 基于水平集的粒子有限元网格自适应方法

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-11 DOI: 10.1016/j.cma.2025.118644

Martin Lacroix, Eduardo Fernández, Simon Février, Luc Papeleux, Romain Boman, Jean-Philippe Ponthot

The Particle Finite Element Method (PFEM) is a discretization technique that combines the flexibility of particle-based methods with the precision of finite elements, using a Lagrangian approach to naturally track evolving interfaces and automatic remeshing to prevent mesh distortion. Historically, the PFEM has relied on the extraction of an α-shape from a Delaunay triangulation of the cloud of nodes forming fluid domain during the remeshing process. This approach helps to maintain good quality elements throughout the simulation, but introduces shortcomings that demand geometrical treatments tailored to each problem. In order to improve the remeshing process in PFEM, Falla et al. (2023) proposed a 2D mesh adaptation technique based on the edge splitting, showing promising results in terms of mass conservation and mesh quality. In parallel, Fernández et al. (2023) proposed the use of a level set (LS) function instead of the α-shape criterion, demonstrating improved mass conservation and free surface smoothness compared to standard approaches. While both innovative and foundational, these approaches have been limited to 2D applications, and the computation of the LS adds significant execution time to the PFEM. In this work, we propose a new remeshing algorithm, building upon the advances achieved by Falla and Fernández, designed to deliver good performance while extending the capability to handle 3D scenarios effectively. The interest of the LS lies in its ability to consider the overall fluid volume rather than focusing on the shape of individual elements as in the classical α-shape. Consequently, the LS allows for a better control over the connecting elements that are created during the fluid/fluid or fluid/solid contact, which helps to reduce spurious mass creation when merging free surfaces. The methodology is presented and validated using free surface flow problems in 2D and 3D. Finally, an overview of computation times is provided.

粒子有限元法（PFEM）是一种离散化技术，它结合了基于粒子的方法的灵活性和有限元的精度，使用拉格朗日方法自然地跟踪不断变化的界面和自动重划分以防止网格变形。历史上，PFEM依赖于重网格过程中形成流体域的节点云的Delaunay三角剖分提取α-形状。这种方法有助于在整个模拟过程中保持高质量的元素，但也引入了需要针对每个问题进行几何处理的缺点。为了改进PFEM中的网格重划分过程，Falla et al.（2023）提出了一种基于边缘分裂的二维网格自适应技术，在质量守恒和网格质量方面都取得了良好的效果。与此同时，Fernández等人（2023）提出使用水平集（LS）函数代替α-形状准则，与标准方法相比，证明了质量守恒和自由表面光滑性的改进。虽然这些方法都是创新和基础的，但它们仅限于2D应用，并且LS的计算增加了PFEM的执行时间。在这项工作中，我们提出了一种新的重网格算法，建立在Falla和Fernández取得的进步的基础上，旨在提供良好的性能，同时扩展有效处理3D场景的能力。LS的有趣之处在于它能够考虑整体流体体积，而不是像经典的α-形状那样专注于单个元素的形状。因此，LS可以更好地控制流体/流体或流体/固体接触过程中产生的连接元件，这有助于减少合并自由表面时产生的虚假质量。在二维和三维自由表面流动问题中提出并验证了该方法。最后，概述了计算时间。

{"title":"An efficient level set-based mesh adaptation for the particle finite element method","authors":"Martin Lacroix, Eduardo Fernández, Simon Février, Luc Papeleux, Romain Boman, Jean-Philippe Ponthot","doi":"10.1016/j.cma.2025.118644","DOIUrl":"10.1016/j.cma.2025.118644","url":null,"abstract":"<div><div>The Particle Finite Element Method (PFEM) is a discretization technique that combines the flexibility of particle-based methods with the precision of finite elements, using a Lagrangian approach to naturally track evolving interfaces and automatic remeshing to prevent mesh distortion. Historically, the PFEM has relied on the extraction of an <em>α</em>-shape from a Delaunay triangulation of the cloud of nodes forming fluid domain during the remeshing process. This approach helps to maintain good quality elements throughout the simulation, but introduces shortcomings that demand geometrical treatments tailored to each problem. In order to improve the remeshing process in PFEM, Falla et al. (2023) proposed a 2D mesh adaptation technique based on the edge splitting, showing promising results in terms of mass conservation and mesh quality. In parallel, Fernández et al. (2023) proposed the use of a level set (LS) function instead of the <em>α</em>-shape criterion, demonstrating improved mass conservation and free surface smoothness compared to standard approaches. While both innovative and foundational, these approaches have been limited to 2D applications, and the computation of the LS adds significant execution time to the PFEM. In this work, we propose a new remeshing algorithm, building upon the advances achieved by Falla and Fernández, designed to deliver good performance while extending the capability to handle 3D scenarios effectively. The interest of the LS lies in its ability to consider the overall fluid volume rather than focusing on the shape of individual elements as in the classical <em>α</em>-shape. Consequently, the LS allows for a better control over the connecting elements that are created during the fluid/fluid or fluid/solid contact, which helps to reduce spurious mass creation when merging free surfaces. The methodology is presented and validated using free surface flow problems in 2D and 3D. Finally, an overview of computation times is provided.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118644"},"PeriodicalIF":7.3,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731765","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}

引用次数: 0

Efficient bound-preserving numerical schemes for a phase-Field model of tumor growth with extracellular matrix degradation 具有细胞外基质降解的肿瘤生长相场模型的有效保界数值格式

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-10 DOI: 10.1016/j.cma.2025.118621

Qiumei Huang , Zhonghua Qiao , Cheng Wang , Huiting Yang

In cancer research, the role of the extracellular matrix (ECM) and its associated matrix-degrading enzyme (MDE) has been a significant area of focus. This study presents a numerical algorithm designed to simulate a previously established tumor model that incorporates various biological factors, including tumor cells, viable cells, necrotic cells, and the dynamics of MDE and ECM. The model consists of a system that includes a phase-field equation, two reaction-diffusion equations, and two ordinary differential equations (ODEs). We employ the fast exponential time differencing Runge-Kutta (ETDRK) method with stabilizing terms to solve this system, resulting in a decoupled, explicit, linear numerical algorithm. The objective of this algorithm is to preserve the physical properties of the model variables, including the maximum bound principle (MBP) for nutrient concentration and MDE volume fraction, as well as bound preserving for ECM density and tumor volume fraction. We perform simulations of 2D and 3D tumor models and discuss how different biological components impact growth dynamics. These simulations may help predict tumor evolution trends, offer insights for related biological and medical research, potentially reduce the number and cost of experiments, and improve research efficiency.

在癌症研究中，细胞外基质（ECM）及其相关基质降解酶（MDE）的作用一直是一个重要的关注领域。本研究提出了一种数值算法，旨在模拟先前建立的肿瘤模型，该模型包含各种生物因素，包括肿瘤细胞、活细胞、坏死细胞以及MDE和ECM的动态。该模型由一个相场方程、两个反应扩散方程和两个常微分方程组成。采用带稳定项的快速指数差分龙格-库塔（ETDRK）方法求解该系统，得到解耦、显式、线性的数值算法。该算法的目标是保留模型变量的物理性质，包括营养物质浓度和MDE体积分数的最大结合原理（MBP），以及ECM密度和肿瘤体积分数的结合保存。我们进行了二维和三维肿瘤模型的模拟，并讨论了不同的生物成分如何影响生长动力学。这些模拟可能有助于预测肿瘤的进化趋势，为相关的生物学和医学研究提供见解，有可能减少实验的数量和成本，并提高研究效率。

{"title":"Efficient bound-preserving numerical schemes for a phase-Field model of tumor growth with extracellular matrix degradation","authors":"Qiumei Huang , Zhonghua Qiao , Cheng Wang , Huiting Yang","doi":"10.1016/j.cma.2025.118621","DOIUrl":"10.1016/j.cma.2025.118621","url":null,"abstract":"<div><div>In cancer research, the role of the extracellular matrix (ECM) and its associated matrix-degrading enzyme (MDE) has been a significant area of focus. This study presents a numerical algorithm designed to simulate a previously established tumor model that incorporates various biological factors, including tumor cells, viable cells, necrotic cells, and the dynamics of MDE and ECM. The model consists of a system that includes a phase-field equation, two reaction-diffusion equations, and two ordinary differential equations (ODEs). We employ the fast exponential time differencing Runge-Kutta (ETDRK) method with stabilizing terms to solve this system, resulting in a decoupled, explicit, linear numerical algorithm. The objective of this algorithm is to preserve the physical properties of the model variables, including the maximum bound principle (MBP) for nutrient concentration and MDE volume fraction, as well as bound preserving for ECM density and tumor volume fraction. We perform simulations of 2D and 3D tumor models and discuss how different biological components impact growth dynamics. These simulations may help predict tumor evolution trends, offer insights for related biological and medical research, potentially reduce the number and cost of experiments, and improve research efficiency.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118621"},"PeriodicalIF":7.3,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145732428","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}

引用次数: 0

On the role of locking mitigation in phase-field modelling of ductile fracture 塑性断裂相场模拟中锁紧减缓的作用

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-10 DOI: 10.1016/j.cma.2025.118607

A. Quintanas-Corominas , P. Olivares-Rodríguez , J. Reinoso , I.G. García

The development of nonlocal fracture models based on the phase-field fracture approach has been a subject of intensive research in recent years. This work focuses on the analysis of shear band localisation in ductile fracture through the application of well-established numerical techniques to mitigate volumetric locking. In particular, the corresponding performance of the B-Bar and the enhanced assumed strain formulations is examined, alongside a detailed energy-based analysis of ductile fracture models employing damage activation thresholds within the phase-field fracture framework. The standard von Mises (J2) plasticity model is used to describe the mechanical response at the material point level, which is coupled with the phase-field. Several representative benchmark problems are addressed, with special attention given to the discrepancies observed in shear band formation and the resulting failure patterns when locking alleviation techniques are applied. The present results demonstrate the efficiency and applicability of these formulations for predicting shear band localisation.

基于相场裂缝方法的非局部裂缝模型的发展是近年来研究的热点。这项工作的重点是通过应用成熟的数值技术来减轻体积锁定，分析韧性断裂中的剪切带局部化。特别地，研究了B-Bar的相应性能和增强的假设应变公式，以及在相场断裂框架内采用损伤激活阈值的韧性断裂模型的详细能量分析。采用标准的von Mises （J2）塑性模型来描述与相场耦合的材料点水平的力学响应。讨论了几个代表性的基准问题，特别注意在应用锁定缓解技术时观察到的剪切带形成和由此产生的破坏模式的差异。目前的结果证明了这些公式在预测剪切带局部化方面的有效性和适用性。

{"title":"On the role of locking mitigation in phase-field modelling of ductile fracture","authors":"A. Quintanas-Corominas , P. Olivares-Rodríguez , J. Reinoso , I.G. García","doi":"10.1016/j.cma.2025.118607","DOIUrl":"10.1016/j.cma.2025.118607","url":null,"abstract":"<div><div>The development of nonlocal fracture models based on the phase-field fracture approach has been a subject of intensive research in recent years. This work focuses on the analysis of shear band localisation in ductile fracture through the application of well-established numerical techniques to mitigate volumetric locking. In particular, the corresponding performance of the B-Bar and the enhanced assumed strain formulations is examined, alongside a detailed energy-based analysis of ductile fracture models employing damage activation thresholds within the phase-field fracture framework. The standard von Mises (J2) plasticity model is used to describe the mechanical response at the material point level, which is coupled with the phase-field. Several representative benchmark problems are addressed, with special attention given to the discrepancies observed in shear band formation and the resulting failure patterns when locking alleviation techniques are applied. The present results demonstrate the efficiency and applicability of these formulations for predicting shear band localisation.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118607"},"PeriodicalIF":7.3,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731151","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}

引用次数: 0

A novel shape transformation method via the nonlocal modified Allen-Cahn model: Analysis and numerical simulations* 一种基于非局部修正Allen-Cahn模型的形状变换新方法：分析与数值模拟*

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-10 DOI: 10.1016/j.cma.2025.118639

Zhifeng Weng , Shuying Zhai , Junseok Kim

In this study, we develop and analyze a new shape transformation method using a nonlocal modified Allen-Cahn (MAC) model, in which a fidelity term is incorporated to refine the phase-field value ensuring its convergence towards target position within the desired region, while simultaneously reducing its influence beyond the target area. The developed transformation method is fast, explicit, spectral accurate in space and second-order accurate in time. At each time step, it only requires solving several decoupled closed-form solutions. The unconditional maximum-bound-preservation and energy dissipation as well as the sharp convergence for the fully discrete scheme are established. Notably, the modified energy functional is close to the classical energy up to O(τ), where τ is the splitting step. This appears to be the first energy dissipation study for second-order three-operator splitting method. Extensive numerical experiments on complex shape transformations are performed to validate the theoretical analysis and the efficiency of the present method. It is observed that the nonlocal MAC model can provide much better results than the local model, especially in shape transformations involving corners or discontinuities.

在本研究中，我们开发并分析了一种新的形状变换方法，该方法使用非局部修正的Allen-Cahn （MAC）模型，其中加入保真度项来改进相场值，以确保其在期望区域内向目标位置收敛，同时减少其在目标区域以外的影响。所提出的变换方法具有快速、显式、空间谱精度和时间二阶精度的特点。在每个时间步，它只需要求解几个解耦的封闭解。建立了完全离散格式的无条件最大界保持性、能量耗散性和锐收敛性。值得注意的是，修正的能量泛函接近于O（τ）的经典能量，其中τ为分裂步长。这似乎是二阶三算子分裂法的首次能量耗散研究。对复杂形状变换进行了大量的数值实验，验证了理论分析和方法的有效性。结果表明，非局部MAC模型能提供比局部模型更好的结果，特别是在涉及角点或不连续点的形状变换中。

{"title":"A novel shape transformation method via the nonlocal modified Allen-Cahn model: Analysis and numerical simulations*","authors":"Zhifeng Weng , Shuying Zhai , Junseok Kim","doi":"10.1016/j.cma.2025.118639","DOIUrl":"10.1016/j.cma.2025.118639","url":null,"abstract":"<div><div>In this study, we develop and analyze a new shape transformation method using a nonlocal modified Allen-Cahn (MAC) model, in which a fidelity term is incorporated to refine the phase-field value ensuring its convergence towards target position within the desired region, while simultaneously reducing its influence beyond the target area. The developed transformation method is fast, explicit, spectral accurate in space and second-order accurate in time. At each time step, it only requires solving several decoupled closed-form solutions. The unconditional maximum-bound-preservation and energy dissipation as well as the sharp convergence for the fully discrete scheme are established. Notably, the modified energy functional is close to the classical energy up to <em>O</em>(<em>τ</em>), where <em>τ</em> is the splitting step. This appears to be the first energy dissipation study for second-order three-operator splitting method. Extensive numerical experiments on complex shape transformations are performed to validate the theoretical analysis and the efficiency of the present method. It is observed that the nonlocal MAC model can provide much better results than the local model, especially in shape transformations involving corners or discontinuities.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118639"},"PeriodicalIF":7.3,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145732429","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}

引用次数: 0

Machine learning-based moment closure model for the linear Boltzmann equation with uncertainties 不确定线性Boltzmann方程的基于机器学习的矩闭模型

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-10 DOI: 10.1016/j.cma.2025.118569

Juntao Huang , Liu Liu , Kunlun Qi , Jiayu Wan

The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving closed macroscopic moment systems from the Boltzmann equation remains a long-standing challenge due to the intrinsic non-closure of the moment hierarchy. In this paper, we propose a machine learning (ML)-based moment closure model for the linear Boltzmann equation, addressing both the deterministic and stochastic settings. Our approach leverages neural networks to learn the spatial gradient of the unclosed highest-order moment, enabling effective training through natural output normalization. For the deterministic problem, to ensure global hyperbolicity and stability, we derive and apply the constraints that enforce symmetrizable hyperbolicity of the system. For the stochastic problem, we adopt the generalized polynomial chaos (gPC)-based stochastic Galerkin method to discretize the random variables, resulting in a system for which the approach in the deterministic case can be used similarly. Several numerical experiments are shown to demonstrate the effectiveness and accuracy of our ML-based moment closure model for the linear Boltzmann equation with or without uncertainties.

玻尔兹曼方程是动力学理论中的一个基本方程，是连接微观粒子动力学和宏观连续介质力学的桥梁。然而，从玻尔兹曼方程推导出封闭的宏观力矩系统仍然是一个长期的挑战，因为力矩层次的内在非闭性。在本文中，我们提出了一个基于机器学习（ML）的线性玻尔兹曼方程的矩闭模型，解决了确定性和随机设置。我们的方法利用神经网络来学习非封闭最高阶矩的空间梯度，通过自然输出归一化实现有效的训练。对于确定性问题，为了保证系统的全局双曲性和稳定性，我们推导并应用了强制系统具有对称双曲性的约束。对于随机问题，我们采用基于广义多项式混沌（gPC）的随机伽辽金方法对随机变量进行离散化，从而得到一个系统，该方法在确定性情况下可以类似地使用。几个数值实验表明，我们的基于ml的矩闭模型对线性玻尔兹曼方程具有或不具有不确定性的有效性和准确性。

{"title":"Machine learning-based moment closure model for the linear Boltzmann equation with uncertainties","authors":"Juntao Huang , Liu Liu , Kunlun Qi , Jiayu Wan","doi":"10.1016/j.cma.2025.118569","DOIUrl":"10.1016/j.cma.2025.118569","url":null,"abstract":"<div><div>The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving closed macroscopic moment systems from the Boltzmann equation remains a long-standing challenge due to the intrinsic non-closure of the moment hierarchy. In this paper, we propose a machine learning (ML)-based moment closure model for the linear Boltzmann equation, addressing both the deterministic and stochastic settings. Our approach leverages neural networks to learn the spatial gradient of the unclosed highest-order moment, enabling effective training through natural output normalization. For the deterministic problem, to ensure global hyperbolicity and stability, we derive and apply the constraints that enforce symmetrizable hyperbolicity of the system. For the stochastic problem, we adopt the generalized polynomial chaos (gPC)-based stochastic Galerkin method to discretize the random variables, resulting in a system for which the approach in the deterministic case can be used similarly. Several numerical experiments are shown to demonstrate the effectiveness and accuracy of our ML-based moment closure model for the linear Boltzmann equation with or without uncertainties.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118569"},"PeriodicalIF":7.3,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731152","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}

引用次数: 0

Adaptive Bayesian support vector regression with advanced simulation and dimension reduction for efficient reliability analysis 自适应贝叶斯支持向量回归与先进的模拟和降维，有效的可靠性分析

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-10 DOI: 10.1016/j.cma.2025.118606

Jinsheng Wang , Guoji Xu , Stergios-Aristoteles Mitoulis , Jamie F. Townsend , Chenfeng Li , Ahsan Kareem

Reliability analysis of engineering structures with varying complexities presents significant challenges, particularly in achieving a balance between accuracy and computational efficiency. This study proposes a novel active learning framework for structural reliability analysis, integrating Bayesian support vector regression as a surrogate model to accurately approximate complex performance functions. A key innovation lies in the construction of a quasi-optimal importance sampling density, derived via subset simulation and kernel density estimation, and further enhanced by Markov Chain Monte Carlo (MCMC) sampling in intermediate failure regions. To mitigate the curse of dimensionality commonly associated with surrogate-based methods, a dimension reduction strategy based on the first-order reliability method is adopted to differentiate between critical and non-critical random variables. Additional contributions include an error-based learning function allocation scheme, a hierarchical stopping criterion, and an efficient sampling strategy that leverages failure samples in the design of experiments whenever possible to initiate the MCMC process. The effectiveness of the proposed method is demonstrated through six benchmark problems exhibiting diverse characteristics, including multiple failure regions, high-dimensional parameter spaces, rare failure events, and computationally demanding engineering cases. Results confirm the robustness and efficiency of the approach, offering a promising and adaptable tool for reliability analysis in complex engineering applications.

不同复杂性的工程结构的可靠性分析提出了重大的挑战，特别是在实现精度和计算效率之间的平衡。本研究提出了一种新的主动学习框架，用于结构可靠性分析，将贝叶斯支持向量回归作为代理模型来精确逼近复杂的性能函数。一个关键的创新在于构建了准最优重要采样密度，该密度通过子集模拟和核密度估计得到，并通过中间失效区域的马尔可夫链蒙特卡罗（MCMC）采样进一步增强。为了减轻基于代理的方法通常存在的维数问题，采用基于一阶可靠性方法的降维策略来区分关键和非关键随机变量。其他贡献包括基于错误的学习函数分配方案，分层停止准则，以及有效的采样策略，该策略在实验设计中尽可能地利用失败样本来启动MCMC过程。通过六个具有不同特征的基准问题，包括多失效区域、高维参数空间、罕见失效事件和计算量高的工程实例，验证了该方法的有效性。结果证实了该方法的鲁棒性和有效性，为复杂工程应用中的可靠性分析提供了一种有前途的、适应性强的工具。

{"title":"Adaptive Bayesian support vector regression with advanced simulation and dimension reduction for efficient reliability analysis","authors":"Jinsheng Wang , Guoji Xu , Stergios-Aristoteles Mitoulis , Jamie F. Townsend , Chenfeng Li , Ahsan Kareem","doi":"10.1016/j.cma.2025.118606","DOIUrl":"10.1016/j.cma.2025.118606","url":null,"abstract":"<div><div>Reliability analysis of engineering structures with varying complexities presents significant challenges, particularly in achieving a balance between accuracy and computational efficiency. This study proposes a novel active learning framework for structural reliability analysis, integrating Bayesian support vector regression as a surrogate model to accurately approximate complex performance functions. A key innovation lies in the construction of a quasi-optimal importance sampling density, derived via subset simulation and kernel density estimation, and further enhanced by Markov Chain Monte Carlo (MCMC) sampling in intermediate failure regions. To mitigate the curse of dimensionality commonly associated with surrogate-based methods, a dimension reduction strategy based on the first-order reliability method is adopted to differentiate between critical and non-critical random variables. Additional contributions include an error-based learning function allocation scheme, a hierarchical stopping criterion, and an efficient sampling strategy that leverages failure samples in the design of experiments whenever possible to initiate the MCMC process. The effectiveness of the proposed method is demonstrated through six benchmark problems exhibiting diverse characteristics, including multiple failure regions, high-dimensional parameter spaces, rare failure events, and computationally demanding engineering cases. Results confirm the robustness and efficiency of the approach, offering a promising and adaptable tool for reliability analysis in complex engineering applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118606"},"PeriodicalIF":7.3,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731702","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}

引用次数: 0

Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs 用于时间相关参数偏微分方程实时预测的物理信息潜在神经算子

IF 7.3 1区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Computer Methods in Applied Mechanics and Engineering

Pub Date : 2025-12-09 DOI: 10.1016/j.cma.2025.118599

Sharmila Karumuri, Lori Graham-Brady, Somdatta Goswami

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. In this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.

深度算子网络（DeepONet）作为由偏微分方程（PDEs）控制的系统的替代模型，在无限维函数空间之间实现精确映射，显示出了巨大的前景。然而，当应用于具有由大量空间和时间搭配点产生的高维输入输出映射的系统时，这些模型通常需要严重的过度参数化网络，从而导致较长的训练时间。Latent DeepONet通过引入两步方法来解决这些挑战：首先使用单独的模型学习减少的潜在空间，然后在该潜在空间内进行算子学习。虽然有效，但这种方法本质上是数据驱动的，缺乏纳入物理定律的机制，限制了其在数据稀缺环境中的稳健性和通用性。在这项工作中，我们提出了PI-Latent-NO，这是一个物理信息的潜在神经算子框架，将控制物理直接集成到学习过程中。我们的架构具有两个端到端训练的耦合deeponet：一个学习解决方案的低维表示的latent - deeponet，以及一个将这种潜在表示映射回物理空间的Reconstruction-DeepONet。通过自动分化将PDE约束嵌入到训练中，我们的方法消除了对标记训练数据的需求，并确保了物理一致的预测。所提出的框架既具有内存效率，又具有计算效率，随着问题的大小显示出近乎恒定的缩放，并且比传统的物理信息算子模型显示出显著的速度提升。我们在一系列参数化偏微分方程上验证了我们的方法，展示了它的准确性、可扩展性和对复杂物理系统实时预测的适用性。

{"title":"Physics-informed latent neural operator for real-time predictions of time-dependent parametric PDEs","authors":"Sharmila Karumuri, Lori Graham-Brady, Somdatta Goswami","doi":"10.1016/j.cma.2025.118599","DOIUrl":"10.1016/j.cma.2025.118599","url":null,"abstract":"<div><div>Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied to systems with high-dimensional input-output mappings arising from large numbers of spatial and temporal collocation points, these models often require heavily overparameterized networks, leading to long training times. Latent DeepONet addresses some of these challenges by introducing a two-step approach: first learning a reduced latent space using a separate model, followed by operator learning within this latent space. While efficient, this method is inherently data-driven and lacks mechanisms for incorporating physical laws, limiting its robustness and generalizability in data-scarce settings. In this work, we propose PI-Latent-NO, a physics-informed latent neural operator framework that integrates governing physics directly into the learning process. Our architecture features two coupled DeepONets trained end-to-end: a Latent-DeepONet that learns a low-dimensional representation of the solution, and a Reconstruction-DeepONet that maps this latent representation back to the physical space. By embedding PDE constraints into the training via automatic differentiation, our method eliminates the need for labeled training data and ensures physics-consistent predictions. The proposed framework is both memory and compute-efficient, exhibiting near-constant scaling with problem size and demonstrating significant speedups over traditional physics-informed operator models. We validate our approach on a range of parametric PDEs, showcasing its accuracy, scalability, and suitability for real-time prediction in complex physical systems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118599"},"PeriodicalIF":7.3,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731155","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}

引用次数: 0