Pub Date : 2025-12-08DOI: 10.1016/j.cma.2025.118608
Maurice S. Fabien
In this paper we present a cell centered Galerkin (CCG) method applied to miscible displacement problems in heterogeneous porous media. The CCG approach combines concepts from finite volume and discontinuous Galerkin (DG) methods to arrive at an efficient lowest-order approximation (one unknown per cell). We demonstrate that the CCG method can be defined using classical DG weak formulations, only requires one unknown per cell, and is able to deliver comparable accuracy (second-order accuracy for smooth solutions) and improved efficiency over traditional higher-order interior penalty DG methods. In addition, we prove that the CCG method for a model Poisson problem gives rise to a inverse-positive matrix in 1D. A plethora of computational experiments in 2D and 3D showcase the effectiveness of the CCG method for highly heterogeneous flow and transport problems in porous media. Comparisons between CCG and classical DG methods are included.
{"title":"A cell centered galerkin method for miscible displacement in heterogeneous porous media","authors":"Maurice S. Fabien","doi":"10.1016/j.cma.2025.118608","DOIUrl":"10.1016/j.cma.2025.118608","url":null,"abstract":"<div><div>In this paper we present a cell centered Galerkin (CCG) method applied to miscible displacement problems in heterogeneous porous media. The CCG approach combines concepts from finite volume and discontinuous Galerkin (DG) methods to arrive at an efficient lowest-order approximation (one unknown per cell). We demonstrate that the CCG method can be defined using classical DG weak formulations, only requires one unknown per cell, and is able to deliver comparable accuracy (second-order accuracy for smooth solutions) and improved efficiency over traditional higher-order interior penalty DG methods. In addition, we prove that the CCG method for a model Poisson problem gives rise to a inverse-positive matrix in 1D. A plethora of computational experiments in 2D and 3D showcase the effectiveness of the CCG method for highly heterogeneous flow and transport problems in porous media. Comparisons between CCG and classical DG methods are included.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118608"},"PeriodicalIF":7.3,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731153","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}
Pub Date : 2025-12-08DOI: 10.1016/j.cma.2025.118612
Hagen Holthusen , Ellen Kuhl
We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently incorporates anisotropy, and–unlike conventional convex formulations–satisfies the dissipation inequality without requiring convexity.
Our neural network architecture employs invariant-based input representations in terms of mixed elastic, inelastic and structural tensors. It adapts Input Convex Neural Networks, and introduces Input Monotonic Neural Networks to broaden the admissible potential class. To circumvent the use of exponential-map time integration during training–which often leads to numerical instabilities–we employ recurrent Liquid Neural Networks as an auxiliary architecture. During inference, however, the exponential-map update is reinstated to ensure admissibility of the inelastic variables.
The approach is evaluated at both material point and structural scales. We benchmark against recurrent models without physical constraints and validate predictions of deformation and reaction forces for unseen boundary value problems. In all cases, the method delivers accurate and stable performance beyond the training regime. The neural network and finite element implementations are available as open-source and are accessible to the public via Zenodo.org.
{"title":"A complement to neural networks for anisotropic inelasticity at finite strains","authors":"Hagen Holthusen , Ellen Kuhl","doi":"10.1016/j.cma.2025.118612","DOIUrl":"10.1016/j.cma.2025.118612","url":null,"abstract":"<div><div>We propose a complement to constitutive modeling that augments neural networks with material principles to capture anisotropy and inelasticity at finite strains. The key element is a dual potential that governs dissipation, consistently incorporates anisotropy, and–unlike conventional convex formulations–satisfies the dissipation inequality without requiring convexity.</div><div>Our neural network architecture employs invariant-based input representations in terms of mixed elastic, inelastic and structural tensors. It adapts Input Convex Neural Networks, and introduces Input Monotonic Neural Networks to broaden the admissible potential class. To circumvent the use of exponential-map time integration during training–which often leads to numerical instabilities–we employ recurrent Liquid Neural Networks as an auxiliary architecture. During inference, however, the exponential-map update is reinstated to ensure admissibility of the inelastic variables.</div><div>The approach is evaluated at both material point and structural scales. We benchmark against recurrent models without physical constraints and validate predictions of deformation and reaction forces for unseen boundary value problems. In all cases, the method delivers accurate and stable performance beyond the training regime. The neural network and finite element implementations are available as open-source and are accessible to the public via <span><span>Zenodo.org</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118612"},"PeriodicalIF":7.3,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145731154","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}
Pub Date : 2025-12-06DOI: 10.1016/j.cma.2025.118597
Yaohua Zang , Phaedon-Stelios Koutsourelakis
Inverse microstructure design plays a central role in materials discovery, yet remains challenging due to the complexity of structure–property linkages and the scarcity of labeled training data. We propose Design-GenNO, a physics-informed generative neural operator framework that unifies generative modeling with operator learning to address these challenges. In Design-GenNO, microstructures are encoded into a low-dimensional, well-structured latent space, which serves as the generator for both reconstructing microstructures and predicting solution fields of governing PDEs. MultiONet-based decoders enable functional mappings from latent variables to both microstructures and full PDE solution fields, allowing a multitude of design objectives to be addressed without retraining. A normalizing flow prior regularizes the latent space, facilitating efficient sampling and robust gradient-based optimization. A distinctive feature of the framework is its physics-informed training strategy: by embedding PDE residuals directly into the learning objective, Design-GenNO significantly reduces reliance on labeled datasets and can even operate in a self-supervised setting. We validate the method on a suite of inverse design tasks in two-phase materials, including effective property matching, recovery of microstructures from sparse field measurements, and maximization of conductivity ratios. Across all tasks, Design-GenNO achieves high accuracy, generates diverse and physically meaningful designs, and consistently outperforms the state-of-the-art method. Moreover, it demonstrates strong extrapolative capabilities by producing microstructures with effective properties beyond those in the training data. These results establish Design-GenNO as a robust and general framework for physics-informed inverse design, offering a promising pathway toward accelerated materials discovery.
{"title":"Design-GenNO: A physics-informed generative model with neural operators for inverse microstructure design","authors":"Yaohua Zang , Phaedon-Stelios Koutsourelakis","doi":"10.1016/j.cma.2025.118597","DOIUrl":"10.1016/j.cma.2025.118597","url":null,"abstract":"<div><div>Inverse microstructure design plays a central role in materials discovery, yet remains challenging due to the complexity of structure–property linkages and the scarcity of labeled training data. We propose Design-GenNO, a physics-informed generative neural operator framework that unifies generative modeling with operator learning to address these challenges. In Design-GenNO, microstructures are encoded into a low-dimensional, well-structured latent space, which serves as the generator for both reconstructing microstructures and predicting solution fields of governing PDEs. MultiONet-based decoders enable functional mappings from latent variables to both microstructures and full PDE solution fields, allowing a multitude of design objectives to be addressed without retraining. A normalizing flow prior regularizes the latent space, facilitating efficient sampling and robust gradient-based optimization. A distinctive feature of the framework is its physics-informed training strategy: by embedding PDE residuals directly into the learning objective, Design-GenNO significantly reduces reliance on labeled datasets and can even operate in a self-supervised setting. We validate the method on a suite of inverse design tasks in two-phase materials, including effective property matching, recovery of microstructures from sparse field measurements, and maximization of conductivity ratios. Across all tasks, Design-GenNO achieves high accuracy, generates diverse and physically meaningful designs, and consistently outperforms the state-of-the-art method. Moreover, it demonstrates strong extrapolative capabilities by producing microstructures with effective properties beyond those in the training data. These results establish Design-GenNO as a robust and general framework for physics-informed inverse design, offering a promising pathway toward accelerated materials discovery.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118597"},"PeriodicalIF":7.3,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689692","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}
In this work, we present IGrNet, a novel framework that integrates isogeometric analysis (IgA) and graph neural networks (GNNs) to classify non-uniform rational B-spline (NURBS)-based elements by leveraging their intrinsic geometric and connectivity properties. This framework introduces three GNN-based models, GCN-PoolNet, GAT-PoolNet, and SCNN-PoolNet, tailored to predict Gauss quadrature points essential for accurate numerical integration in IgA. Unlike traditional neural network approaches, IGrNet’s graph-based structure captures both node (control points) and edge (geometric relationships) features, allowing for more nuanced representation and localized element refinement. This flexibility enables the model to adapt across elements of varying NURBS orders without the need for separate models, thereby offering an efficient, unified approach. Our proposed architecture benefits from the enriched feature set, including attention mechanisms and spline-based convolutions, which enhances model accuracy even under class imbalance, making it robust for applications in complex mechanics and structural analysis. Also, the saliency map analysis highlights distinct patterns of feature importance across the classes, offering valuable insights into the model’s classification strategy. IGrNet extends beyond quadrature point prediction to provide a general framework for representing and classifying NURBS-based elements. The computational efficiency of the model is demonstrated by first solving a linear elastic problem namely an infinite plate with a hole followed by two benchmark contact problems— Hertz contact, and ironing problem with friction. It significantly reduces the computational cost by adapting the optimal number of Gauss quadrature points while maintaining the desired accuracy.
{"title":"IGrNet: A robust graph neural network framework for classifying NURBS-based elements in isogeometric analysis with application to contact mechanics","authors":"Dipjyoti Nath , Sumit Kumar Das , Debanga Raj Neog , Sachin Singh Gautam","doi":"10.1016/j.cma.2025.118539","DOIUrl":"10.1016/j.cma.2025.118539","url":null,"abstract":"<div><div>In this work, we present IGrNet, a novel framework that integrates isogeometric analysis (IgA) and graph neural networks (GNNs) to classify non-uniform rational B-spline (NURBS)-based elements by leveraging their intrinsic geometric and connectivity properties. This framework introduces three GNN-based models, <em>GCN-PoolNet, GAT-PoolNet</em>, and <em>SCNN-PoolNet</em>, tailored to predict Gauss quadrature points essential for accurate numerical integration in IgA. Unlike traditional neural network approaches, IGrNet’s graph-based structure captures both node (control points) and edge (geometric relationships) features, allowing for more nuanced representation and localized element refinement. This flexibility enables the model to adapt across elements of varying NURBS orders without the need for separate models, thereby offering an efficient, unified approach. Our proposed architecture benefits from the enriched feature set, including attention mechanisms and spline-based convolutions, which enhances model accuracy even under class imbalance, making it robust for applications in complex mechanics and structural analysis. Also, the saliency map analysis highlights distinct patterns of feature importance across the classes, offering valuable insights into the model’s classification strategy. IGrNet extends beyond quadrature point prediction to provide a general framework for representing and classifying NURBS-based elements. The computational efficiency of the model is demonstrated by first solving a linear elastic problem namely an infinite plate with a hole followed by two benchmark contact problems— Hertz contact, and ironing problem with friction. It significantly reduces the computational cost by adapting the optimal number of Gauss quadrature points while maintaining the desired accuracy.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118539"},"PeriodicalIF":7.3,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689693","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}
The cohesive zone model using interface elements is a practical and widely adopted approach for modeling crack initiation and propagation. However, enriching a model with interface elements significantly increases computational costs due to node duplication. To mitigate this, numerous adaptive insertion strategies have been developed to insert interface elements on the fly only when and where needed. Existing strategies rely on stress-based insertion criteria, which often fail to ensure timely and accurate placement of interface elements. Moreover, many existing approaches suffer from a critical limitation: poor configurations of inserted interface elements lead to significant errors in traction computation. In this paper, we investigate the state-of-the-art adaptive insertion methods focusing on the influence of interface elements configurations on traction accuracy. Based upon the findings we propose a novel algorithm that reliably computes the traction of interface elements and serves as a robust and precise insertion criterion, alleviating the limitations of existing techniques. The algorithm leverages the unique formulation of linear interface elements, enabling traction evaluation in an efficient post-processing step without requiring node duplication. Finally, we present a numerical simulation campaign that highlights the error trends inherent to existing adaptive insertion schemes and demonstrates the efficacy of the proposed method.
{"title":"Adaptive insertion of interface elements for fracture analysis:Reliable computation of interface traction","authors":"Koussay Daadouch, Vladislav Gudžulić, Günther Meschke","doi":"10.1016/j.cma.2025.118614","DOIUrl":"10.1016/j.cma.2025.118614","url":null,"abstract":"<div><div>The cohesive zone model using interface elements is a practical and widely adopted approach for modeling crack initiation and propagation. However, enriching a model with interface elements significantly increases computational costs due to node duplication. To mitigate this, numerous adaptive insertion strategies have been developed to insert interface elements on the fly only when and where needed. Existing strategies rely on stress-based insertion criteria, which often fail to ensure timely and accurate placement of interface elements. Moreover, many existing approaches suffer from a critical limitation: poor configurations of inserted interface elements lead to significant errors in traction computation. In this paper, we investigate the state-of-the-art adaptive insertion methods focusing on the influence of interface elements configurations on traction accuracy. Based upon the findings we propose a novel algorithm that reliably computes the traction of interface elements and serves as a robust and precise insertion criterion, alleviating the limitations of existing techniques. The algorithm leverages the unique formulation of linear interface elements, enabling traction evaluation in an efficient post-processing step without requiring node duplication. Finally, we present a numerical simulation campaign that highlights the error trends inherent to existing adaptive insertion schemes and demonstrates the efficacy of the proposed method.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118614"},"PeriodicalIF":7.3,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689695","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}
Pub Date : 2025-12-05DOI: 10.1016/j.cma.2025.118588
K.C. Park , J.A. González , S.J. Shin , S.H. Kang , M.H. Hwang , J.G. Kim , M.F. Baqir , J.H. Han , R.W. Hagos , S.C. Lee , Y.H. Park , H.J. Kim , K.K. Maute , C.A. Felippa
The present paper is a compendium of recent advances by seven research teams who have applied the PartStiff and PartFlex methods in solving seven distinctly different problems. Each of the research teams exploited the key feature of the PartStiff and PartFlex methods: partitioned (unassembled) FEM models without Lagrange multipliers. The unassembled PartStiff equation is given by where () are the partitioned block diagonal mass and block diagonal stiffness matrices and the applied force, acceleration and displacement vectors, and the projection operator which accomplishes the necessary coupling among the partitions. The paper presents applications of both the PartStiff and PartFlex methods: high-fidelity parallel solvers for heterogeneous problems; an element-by-element implicit-explicit transient algorithm; reduced-order modeling (ROM) with a practical model-order reduction criterion; component mode synthesis guided by a rational mode selection guide, identification of damage locations and damage levels via experimentally identified models and/or data-driven digital-twin models; and, topology optimization, among others.
{"title":"Solving FEM models without assembly: Its promise and challenge","authors":"K.C. Park , J.A. González , S.J. Shin , S.H. Kang , M.H. Hwang , J.G. Kim , M.F. Baqir , J.H. Han , R.W. Hagos , S.C. Lee , Y.H. Park , H.J. Kim , K.K. Maute , C.A. Felippa","doi":"10.1016/j.cma.2025.118588","DOIUrl":"10.1016/j.cma.2025.118588","url":null,"abstract":"<div><div>The present paper is a compendium of recent advances by seven research teams who have applied the PartStiff and PartFlex methods in solving seven distinctly different problems. Each of the research teams exploited the key feature of the PartStiff and PartFlex methods: partitioned (unassembled) FEM models without Lagrange multipliers. The unassembled PartStiff equation is given by <span><math><mrow><mi>M</mi><mover><mi>d</mi><mo>¨</mo></mover><mo>=</mo><msub><mi>P</mi><mi>d</mi></msub><mrow><mo>(</mo><mi>f</mi><mo>−</mo><mi>K</mi><mi>d</mi><mo>)</mo></mrow></mrow></math></span> where (<span><math><mrow><mi>M</mi><mo>,</mo><mi>K</mi><mo>,</mo><mi>f</mi><mo>,</mo><mover><mi>d</mi><mo>¨</mo></mover><mo>,</mo><mi>d</mi><mo>,</mo><msub><mi>P</mi><mi>d</mi></msub></mrow></math></span>) are the partitioned block diagonal mass and block diagonal stiffness matrices and the applied force, acceleration and displacement vectors, and the projection operator <span><math><msub><mi>P</mi><mi>d</mi></msub></math></span> which accomplishes the necessary coupling among the partitions. The paper presents applications of both the PartStiff and PartFlex methods: high-fidelity parallel solvers for heterogeneous problems; an element-by-element implicit-explicit transient algorithm; reduced-order modeling (ROM) with a practical model-order reduction criterion; component mode synthesis guided by a rational mode selection guide, identification of damage locations and damage levels via experimentally identified models and/or data-driven digital-twin models; and, topology optimization, among others.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118588"},"PeriodicalIF":7.3,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689699","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}
Pub Date : 2025-12-05DOI: 10.1016/j.cma.2025.118637
Marco Paggi
A theory for simulating nonlocal damage in 2D lattice structures discretized by Euler-Bernoulli beam finite elements is herein proposed. A phase field approach to damage, projected onto the discretized nodes via the graph Laplacian matrix, is formulated to simulate damage evolution by solving a Helmholtz differential equation on the graph. Damage is introduced in the constitutive equations under the assumption of a bilateral damage evolution in tension and in compression, or a monolateral damage only in tension. Both formulations have been enhanced by a threshold driving force to better capture the onset of damage in polymers due to crazing. The staggered coupling scheme alternates between solving mechanical equilibrium and phase field equations, and it has been validated in relation to experiments on unnotched beams made of ABS subject to three-point bending. The approach is then applied to preliminary investigate the response of a complex network material in the nonlinear regime, contributing to understanding how graph-based topologies influence the load-bearing capacity of the material. The method bridges the gap between statistical physics of complex networks and nonlinear mechanics of materials and is expected to have an impact on the design of robust random metamaterials featuring nodes with large connectivities.
{"title":"Mechanics of complex network materials: A formulation based on phase field damage evolution on graphs","authors":"Marco Paggi","doi":"10.1016/j.cma.2025.118637","DOIUrl":"10.1016/j.cma.2025.118637","url":null,"abstract":"<div><div>A theory for simulating nonlocal damage in 2D lattice structures discretized by Euler-Bernoulli beam finite elements is herein proposed. A phase field approach to damage, projected onto the discretized nodes via the graph Laplacian matrix, is formulated to simulate damage evolution by solving a Helmholtz differential equation on the graph. Damage is introduced in the constitutive equations under the assumption of a bilateral damage evolution in tension and in compression, or a monolateral damage only in tension. Both formulations have been enhanced by a threshold driving force to better capture the onset of damage in polymers due to crazing. The staggered coupling scheme alternates between solving mechanical equilibrium and phase field equations, and it has been validated in relation to experiments on unnotched beams made of ABS subject to three-point bending. The approach is then applied to preliminary investigate the response of a complex network material in the nonlinear regime, contributing to understanding how graph-based topologies influence the load-bearing capacity of the material. The method bridges the gap between statistical physics of complex networks and nonlinear mechanics of materials and is expected to have an impact on the design of robust random metamaterials featuring nodes with large connectivities.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118637"},"PeriodicalIF":7.3,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689703","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}
Pub Date : 2025-12-04DOI: 10.1016/j.cma.2025.118594
Giang D. Huynh , Poh Leong Hien , Reza Abedi
Elliptic phase field (EPF) models are successfully used for many quasi-static fracture problems. However, they suffer from high computational costs due to demanding mesh size constraints in the fracturing regions. Advanced solvers are required to handle the resulting large system of equations and damage irreversibility conditions. For dynamic fracture, they tend to overestimate the crack velocity and predict nonphysical fracture patterns. We present a hyperbolic phase field cohesive zone model (HPF-CZM) that addresses these limitations. Using a thermodynamically consistent framework, we systematically incorporate micro-inertia and viscous damping terms that are absent in EPF models. A pseudo-dissipative potential quantifies the rate of energy loss, effectively separating micro- and macro-stresses into elastic and dissipative components. The hyperbolic form of the evolution equation, combined with elastodynamics, results in a fully explicit time integration scheme. This eliminates the need for advanced solvers and provides a local solution scheme with linear scaling, versus the number of elements. A test problem shows an almost perfect strong parallel scaling for the HPF model, whereas the strong scaling of the EPF model quickly degrades beyond 32 processors. An adaptive mesh refinement strategy is also developed to further improve efficiency by automatically refining the mesh as cracks evolve. Finally, by referring to experimental fracture results for polymethyl methacrylate (PMMA) and adjusting the PF wave speed, the HPF model is shown to capture the correct crack speed and fracture pattern. Moreover, a newly proposed energy factor is shown to alleviate incomplete damage regions that tend to occur in high-loading-rate applications.
{"title":"An explicit mesh adaptive parallel hyperbolic phase field-cohesive zone model based on generalized standard materials","authors":"Giang D. Huynh , Poh Leong Hien , Reza Abedi","doi":"10.1016/j.cma.2025.118594","DOIUrl":"10.1016/j.cma.2025.118594","url":null,"abstract":"<div><div>Elliptic phase field (EPF) models are successfully used for many quasi-static fracture problems. However, they suffer from high computational costs due to demanding mesh size constraints in the fracturing regions. Advanced solvers are required to handle the resulting large system of equations and damage irreversibility conditions. For dynamic fracture, they tend to overestimate the crack velocity and predict nonphysical fracture patterns. We present a hyperbolic phase field cohesive zone model (HPF-CZM) that addresses these limitations. Using a thermodynamically consistent framework, we systematically incorporate micro-inertia and viscous damping terms that are absent in EPF models. A pseudo-dissipative potential quantifies the rate of energy loss, effectively separating micro- and macro-stresses into elastic and dissipative components. The hyperbolic form of the evolution equation, combined with elastodynamics, results in a fully explicit time integration scheme. This eliminates the need for advanced solvers and provides a local solution scheme with linear scaling, versus the number of elements. A test problem shows an almost perfect strong parallel scaling for the HPF model, whereas the strong scaling of the EPF model quickly degrades beyond 32 processors. An adaptive mesh refinement strategy is also developed to further improve efficiency by automatically refining the mesh as cracks evolve. Finally, by referring to experimental fracture results for polymethyl methacrylate (PMMA) and adjusting the PF wave speed, the HPF model is shown to capture the correct crack speed and fracture pattern. Moreover, a newly proposed energy factor is shown to alleviate incomplete damage regions that tend to occur in high-loading-rate applications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118594"},"PeriodicalIF":7.3,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689705","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}
Pub Date : 2025-12-04DOI: 10.1016/j.cma.2025.118586
Diab W. Abueidda , Mbebo Nonna , Panos Pantidis , Mostafa E. Mobasher
Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of sequence-to-sequence (seq2seq) RNN architectures, while neural-ODE surrogates cannot incorporate new inputs after initialization. We introduce NCDE-DeepONet, a continuous-time operator network that embeds a Neural Controlled Differential Equation (NCDE) in the branch and augments the trunk with explicit space–time coordinates. The NCDE encodes an entire load history as the solution of a controlled ODE driven by a spline-interpolated input path, making the representation input-resolution-independent: it encodes different input signal discretizations of the observed samples. The trunk then probes this latent path at arbitrary spatial locations and times, rendering the overall map output-resolution independent: predictions can be queried on meshes and time steps unseen during training without retraining or interpolation. Benchmarks on transient Poisson, elastodynamic, and thermoelastic problems confirm the robustness and accuracy of the framework, achieving almost instant solution prediction. These findings suggest that controlled dynamics provide a principled and efficient foundation for high-fidelity operator learning in transient mechanics.
{"title":"Time resolution independent operator learning","authors":"Diab W. Abueidda , Mbebo Nonna , Panos Pantidis , Mostafa E. Mobasher","doi":"10.1016/j.cma.2025.118586","DOIUrl":"10.1016/j.cma.2025.118586","url":null,"abstract":"<div><div>Accurately learning solution operators for time-dependent partial differential equations (PDEs) from sparse and irregular data remains a challenging task. Recurrent DeepONet extensions inherit the discrete-time limitations of sequence-to-sequence (seq2seq) RNN architectures, while neural-ODE surrogates cannot incorporate new inputs after initialization. We introduce <em>NCDE-DeepONet</em>, a continuous-time operator network that embeds a Neural Controlled Differential Equation (NCDE) in the branch and augments the trunk with explicit space–time coordinates. The NCDE encodes an entire load history as the solution of a controlled ODE driven by a spline-interpolated input path, making the representation <em>input-resolution-independent</em>: it encodes different input signal discretizations of the observed samples. The trunk then probes this latent path at arbitrary spatial locations and times, rendering the overall map <em>output-resolution independent</em>: predictions can be queried on meshes and time steps unseen during training without retraining or interpolation. Benchmarks on transient Poisson, elastodynamic, and thermoelastic problems confirm the robustness and accuracy of the framework, achieving almost instant solution prediction. These findings suggest that controlled dynamics provide a principled and efficient foundation for high-fidelity operator learning in transient mechanics.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"450 ","pages":"Article 118586"},"PeriodicalIF":7.3,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145689709","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}
Pub Date : 2025-12-04DOI: 10.1016/j.cma.2025.118620
Eugenio Oñate , Juan M. Gimenez , Francisco Zarate , Sergio R. Idelsohn
We present a fast semi- explicit time integration scheme for solving transient Stokes flow problems via standard numerical methods in space using regular and irregular grids, such as unstructured meshes in the finite element method (FEM), or grids containing cells of very different sizes in the finite volume method (FVM). The new semi-explicit time integration scheme, termed EFT12 scheme, extends one of the explicit FIC-Time (EFT) integration methods for parabolic problems derived by the authors in [24] that allow considerable larger time steps than the forward Euler (FE) scheme. The EFT12 scheme also provides a faster convergence to the steady-state solution than using the FE scheme. The advantages of the EFT12 scheme for the fast and accurate solution of transient Stokes flow problems are shown in one- and two- dimensional problems using the FEM and the FVM with regular and irregular grids.
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