Pub Date : 2026-01-17DOI: 10.1016/j.cma.2026.118727
Tim Bürchner , Lars Radtke , Sascha Eisenträger , Alexander Düster , Ernst Rank , Stefan Kollmannsberger , Philipp Kopp
Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass matrices of cut elements to cure their adverse impact on the critical time step size of the global system. We use spectral basis functions, specifically C0 continuous Lagrangian interpolation polynomials defined on Gauss-Lobatto-Legendre (GLL) points, which, in combination with its associated GLL quadrature rule, yield high-order convergent diagonal mass matrices for uncut elements. Moreover, considering cut elements, we combine the proposed GEVS approach with the finite cell method to guarantee definiteness of the system matrices. However, the proposed GEVS stabilization can directly be applied to other immersed boundary finite element methods. Numerical experiments demonstrate that the stabilization strategy achieves optimal convergence rates and recovers critical time step sizes of equivalent boundary-conforming discretizations. This also holds in the presence of weakly enforced Dirichlet boundary conditions using either Nitsche’s method or penalty formulations.
{"title":"Generalized Eigenvalue stabilization for immersed explicit dynamics","authors":"Tim Bürchner , Lars Radtke , Sascha Eisenträger , Alexander Düster , Ernst Rank , Stefan Kollmannsberger , Philipp Kopp","doi":"10.1016/j.cma.2026.118727","DOIUrl":"10.1016/j.cma.2026.118727","url":null,"abstract":"<div><div>Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass matrices of cut elements to cure their adverse impact on the critical time step size of the global system. We use spectral basis functions, specifically <em>C</em><sup>0</sup> continuous Lagrangian interpolation polynomials defined on Gauss-Lobatto-Legendre (GLL) points, which, in combination with its associated GLL quadrature rule, yield high-order convergent diagonal mass matrices for uncut elements. Moreover, considering cut elements, we combine the proposed GEVS approach with the finite cell method to guarantee definiteness of the system matrices. However, the proposed GEVS stabilization can directly be applied to other immersed boundary finite element methods. Numerical experiments demonstrate that the stabilization strategy achieves optimal convergence rates and recovers critical time step sizes of equivalent boundary-conforming discretizations. This also holds in the presence of weakly enforced Dirichlet boundary conditions using either Nitsche’s method or penalty formulations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118727"},"PeriodicalIF":7.3,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995462","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 : 2026-01-17DOI: 10.1016/j.cma.2025.118646
Carsten Carstensen , Asha K. Dond , Ruma R. Maity , Neela Nataraj , Lara Théallier
The Landau-de Gennes model for nematic liquid crystals provides the computational challenges of a second-order elliptic boundary value problem with reduced regularity in non-convex domains as well as exciting topological singularities called vortices for certain Dirichlet data of non-zero winding number for larger order parameter ℓ (named after Ginzburg). In two dimensions it simplifies to a Ginzburg-Landau model. The energy landscape in this non-convex minimisation problem is unexpectedly rich with many stationary points of the energy functional and the local solve faces severe difficulties. The nonconforming Crouzeix-Raviart finite elements have recently been shown to allow the computation of a guaranteed lower bound of the energy for sufficiently small meshes. We present an explicit residual-based a posteriori error estimate under the assumption that the discrete solution is sufficiently close to an isolated solution u. Our adaptive algorithm relies on a rigorous mathematical a posteriori error analysis for an asymptotic regime in the semi-linear problem and very small initial mesh-sizes that resolve the various stationary points of the energy. The emphasis is on the numerical verification of optimal convergence rates in computational benchmarks for the non-conforming Crouzeix-Raviart finite element method with lower-energy bounds. The validation of a physical model gives new insight into the energies of the two known global minimisers and four other local minimisers. The vortex localisation with adaptive mesh design is studied in a third example of winding number two. In all numerical experiments, the novel adaptive algorithm recovers optimal convergence rates.
{"title":"Adaptive Crouzeix-Raviart finite elements for a non-convex Ginzburg-Landau model for nematic liquid crystals","authors":"Carsten Carstensen , Asha K. Dond , Ruma R. Maity , Neela Nataraj , Lara Théallier","doi":"10.1016/j.cma.2025.118646","DOIUrl":"10.1016/j.cma.2025.118646","url":null,"abstract":"<div><div>The Landau-de Gennes model for nematic liquid crystals provides the computational challenges of a second-order elliptic boundary value problem with reduced regularity in non-convex domains as well as exciting topological singularities called vortices for certain Dirichlet data of non-zero winding number for larger order parameter ℓ (named after Ginzburg). In two dimensions it simplifies to a Ginzburg-Landau model. The energy landscape in this non-convex minimisation problem is unexpectedly rich with many stationary points of the energy functional and the local solve faces severe difficulties. The nonconforming Crouzeix-Raviart finite elements have recently been shown to allow the computation of a guaranteed lower bound of the energy for sufficiently small meshes. We present an explicit residual-based a posteriori error estimate under the assumption that the discrete solution is sufficiently close to an isolated solution <em>u</em>. Our adaptive algorithm relies on a rigorous mathematical a posteriori error analysis for an asymptotic regime in the semi-linear problem and very small initial mesh-sizes that resolve the various stationary points of the energy. The emphasis is on the numerical verification of optimal convergence rates in computational benchmarks for the non-conforming Crouzeix-Raviart finite element method with lower-energy bounds. The validation of a physical model gives new insight into the energies of the two known global minimisers and four other local minimisers. The vortex localisation with adaptive mesh design is studied in a third example of winding number two. In all numerical experiments, the novel adaptive algorithm recovers optimal convergence rates.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118646"},"PeriodicalIF":7.3,"publicationDate":"2026-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145995463","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 : 2026-01-16DOI: 10.1016/j.cma.2026.118749
Sunwoo Kim , Suyeong Jin , Jung-Wuk Hong
Simulating heat conduction has been studied using approaches including peridynamics. However, accurately capturing heat transfer across discontinuities such as cracks and material interfaces remains a major challenge. This study presents a computational framework for heat transfer that utilizes a peridynamic differential operator approach to offer a unified modeling approach for both continuous and discontinuous media. The classical heat conduction equation is computed by using peridynamic differential operators, enabling natural treatment of discontinuities. A bond-wise function is defined by the interaction state between nodes, enabling a consistent representation of heat transfer for both intact and broken bonds. For broken bonds, thermal contact conductance is incorporated into the bond-wise function to capture heat transfer across partial discontinuities. The framework is verified through numerical analyses of a two-panel contact problem and a three-dimensional L-shaped bimaterial panel. The results demonstrate accurate prediction of interfacial phenomena, including temperature drops and localized heat flux concentration. The analyses further show that the bond-wise function successfully captures the influence of the thermal contact conductance on both the degree of heat transfer across crack interfaces and the resulting alteration of singularity characteristics. Overall, the framework provides a general and computationally efficient tool for simulating heat conduction in heterogeneous systems with partial discontinuities and establishes a basis for fully coupled thermomechanical analyses.
{"title":"Numerical simulation of heat transfer across partial discontinuities using the peridynamic differential operator","authors":"Sunwoo Kim , Suyeong Jin , Jung-Wuk Hong","doi":"10.1016/j.cma.2026.118749","DOIUrl":"10.1016/j.cma.2026.118749","url":null,"abstract":"<div><div>Simulating heat conduction has been studied using approaches including peridynamics. However, accurately capturing heat transfer across discontinuities such as cracks and material interfaces remains a major challenge. This study presents a computational framework for heat transfer that utilizes a peridynamic differential operator approach to offer a unified modeling approach for both continuous and discontinuous media. The classical heat conduction equation is computed by using peridynamic differential operators, enabling natural treatment of discontinuities. A bond-wise function is defined by the interaction state between nodes, enabling a consistent representation of heat transfer for both intact and broken bonds. For broken bonds, thermal contact conductance is incorporated into the bond-wise function to capture heat transfer across partial discontinuities. The framework is verified through numerical analyses of a two-panel contact problem and a three-dimensional L-shaped bimaterial panel. The results demonstrate accurate prediction of interfacial phenomena, including temperature drops and localized heat flux concentration. The analyses further show that the bond-wise function successfully captures the influence of the thermal contact conductance on both the degree of heat transfer across crack interfaces and the resulting alteration of singularity characteristics. Overall, the framework provides a general and computationally efficient tool for simulating heat conduction in heterogeneous systems with partial discontinuities and establishes a basis for fully coupled thermomechanical analyses.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118749"},"PeriodicalIF":7.3,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980093","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 : 2026-01-16DOI: 10.1016/j.cma.2026.118752
Mario Setta, Eddie Wadbro, Grigor Nika
We present homogenization and simulation results for an enhanced heat equation model that captures thermal scale-size effects through higher-gradient corrections involving characteristic internal lengths. The resulting equation is a fourth-order parabolic equation that incorporates thermal scale effects inherent to microstructured materials. We derive effective thermal coefficients for the time-stationary problem using asymptotic homogenization. This enables accurate simulation via a quadratic B-spline-based finite element approach. Our results quantify the influence of microstructure shape and volume fraction on the effective thermal behavior, demonstrating how scale-size-induced phenomena critically affect heat transport in micro- and nanoscale devices.
{"title":"Simulation of effective scale-size dependent heat conduction in rigid microgeometries","authors":"Mario Setta, Eddie Wadbro, Grigor Nika","doi":"10.1016/j.cma.2026.118752","DOIUrl":"10.1016/j.cma.2026.118752","url":null,"abstract":"<div><div>We present homogenization and simulation results for an enhanced heat equation model that captures thermal scale-size effects through higher-gradient corrections involving characteristic internal lengths. The resulting equation is a fourth-order parabolic equation that incorporates thermal scale effects inherent to microstructured materials. We derive effective thermal coefficients for the time-stationary problem using asymptotic homogenization. This enables accurate simulation via a quadratic B-spline-based finite element approach. Our results quantify the influence of microstructure shape and volume fraction on the effective thermal behavior, demonstrating how scale-size-induced phenomena critically affect heat transport in micro- and nanoscale devices.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118752"},"PeriodicalIF":7.3,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980096","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 : 2026-01-16DOI: 10.1016/j.cma.2026.118751
Yehui Cui , Zhilang Zhang
Locking phenomena, including volumetric and shear locking, pose a critical challenge in conventional FE2 modeling frameworks. Their nested solution schemes complicate the incorporation of classical locking-alleviation techniques, as scale-to-scale data transfer and multiscale boundary coupling often destabilize the solution. Their nested solution schemes complicate the incorporation of classical locking-alleviation techniques, as the macro–micro iterations require repeated exchange of strain/stress information and consistent enforcement of RVE boundary conditions, which increases implementation complexity and computational cost, and may hinder convergence for strongly nonlinear RVEs. Accordingly, while the locking mechanisms themselves are not unique to FE2, systematic incorporation and benchmarking of locking remedies within coupled FE2 implementations is less commonly reported. The Direct FE2 (DFE2) method reformulates FE2 into a monolithic solution scheme by employing a constraint matrix that couples macroscopic nodal forces with tractions on RVE boundaries. This structure not only improves computational efficiency but also provides a robust basis for integrating projection-based remedies. Leveraging this framework, this study develops three improved locking-free multiscale formulations: high-order model, stabilized selective relaxation (SSR) model, and enhanced B-bar (EB) model. These approaches systematically integrate projection methods into the concurrent multiscale setting to effectively suppress locking artifacts, thereby significantly improving the accuracy of DFE2. Their performance is thoroughly evaluated against Direct Numerical Simulation (DNS) and fine-mesh DFE2 across several 2D and 3D examples. Results show that the SSR-DFE2 model effectively mitigates shear locking while maintaining the efficiency of the standard DFE2 approach; however, it fails to alleviate volumetric locking, leading to errors in nearly incompressible cases. In contrast, the EB-DFE2 model achieves a superior accuracy–efficiency balance, delivering solutions close to DNS while reducing computational costs by factors of 20–200 relative to DNS, 10–30 versus fine-mesh DFE2 and 5–10 compared to the high-order model.
{"title":"Locking-free monolithic FE2 frameworks for concurrent multiscale modeling","authors":"Yehui Cui , Zhilang Zhang","doi":"10.1016/j.cma.2026.118751","DOIUrl":"10.1016/j.cma.2026.118751","url":null,"abstract":"<div><div>Locking phenomena, including volumetric and shear locking, pose a critical challenge in conventional FE<sup>2</sup> modeling frameworks. Their nested solution schemes complicate the incorporation of classical locking-alleviation techniques, as scale-to-scale data transfer and multiscale boundary coupling often destabilize the solution. Their nested solution schemes complicate the incorporation of classical locking-alleviation techniques, as the macro–micro iterations require repeated exchange of strain/stress information and consistent enforcement of RVE boundary conditions, which increases implementation complexity and computational cost, and may hinder convergence for strongly nonlinear RVEs. Accordingly, while the locking mechanisms themselves are not unique to FE<sup>2</sup>, systematic incorporation and benchmarking of locking remedies within coupled FE<sup>2</sup> implementations is less commonly reported. The Direct FE<sup>2</sup> (DFE<sup>2</sup>) method reformulates FE<sup>2</sup> into a monolithic solution scheme by employing a constraint matrix that couples macroscopic nodal forces with tractions on RVE boundaries. This structure not only improves computational efficiency but also provides a robust basis for integrating projection-based remedies. Leveraging this framework, this study develops three improved locking-free multiscale formulations: high-order model, stabilized selective relaxation (SSR) model, and enhanced B-bar (EB) model. These approaches systematically integrate projection methods into the concurrent multiscale setting to effectively suppress locking artifacts, thereby significantly improving the accuracy of DFE<sup>2</sup>. Their performance is thoroughly evaluated against Direct Numerical Simulation (DNS) and fine-mesh DFE<sup>2</sup> across several 2D and 3D examples. Results show that the SSR-DFE<sup>2</sup> model effectively mitigates shear locking while maintaining the efficiency of the standard DFE<sup>2</sup> approach; however, it fails to alleviate volumetric locking, leading to errors in nearly incompressible cases. In contrast, the EB-DFE<sup>2</sup> model achieves a superior accuracy–efficiency balance, delivering solutions close to DNS while reducing computational costs by factors of 20–200 relative to DNS, 10–30 versus fine-mesh DFE<sup>2</sup> and 5–10 compared to the high-order model.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118751"},"PeriodicalIF":7.3,"publicationDate":"2026-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980095","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 : 2026-01-15DOI: 10.1016/j.cma.2026.118748
Oriol Colomés , Jan Modderman , Guglielmo Scovazzi
Many engineering and scientific problems require the solution of partial differential equations in complex geometries. Often, these problems involve parametrized geometries, e.g. design optimization, or moving domains, e.g. fluid-structure interaction problems. For such cases, traditional methods based on body-fitted grids require time-consuming mesh generation or re-meshing techniques. Unfitted finite element methods, e.g. CutFEM of AgFEM, are appealing techniques that address these challenges. However, they require ad-hoc integration methods and stabilization techniques to prevent instabilities for small cut cells. Recently, the Shifted Boundary Method (SBM), was introduced to prevent integration over cut cells and small cut-cell instabilities. An extension of the SBM was recently introduced, the Weighted Shifted Boundary Method (WSBM), where the variational form is weighted by the elemental active volume fraction, improving discrete mass/momentum conservation properties in simulations with moving domains. In this work we introduce the Generalized Shifted Boundary Method (GSBM), a geometry-agnostic generalization of the SBM and WSBM formulations that avoids the need of redefinition of integration domains and finite element spaces. The GSBM enables a unified formulation for problems with evolving geometries, supports gradient-based optimization of problems with varying geometries including topological changes, and unifies SBM, WSBM, and optimal-surrogate variants within a single framework. In this work we describe the formulation, and corresponding tests, for three model problems, namely: the Poisson problem, linear elasticity and transient Stokes flow.
{"title":"The generalized shifted boundary method for geometry-parametric PDEs and time-dependent domains","authors":"Oriol Colomés , Jan Modderman , Guglielmo Scovazzi","doi":"10.1016/j.cma.2026.118748","DOIUrl":"10.1016/j.cma.2026.118748","url":null,"abstract":"<div><div>Many engineering and scientific problems require the solution of partial differential equations in complex geometries. Often, these problems involve parametrized geometries, e.g. design optimization, or moving domains, e.g. fluid-structure interaction problems. For such cases, traditional methods based on body-fitted grids require time-consuming mesh generation or re-meshing techniques. Unfitted finite element methods, e.g. CutFEM of AgFEM, are appealing techniques that address these challenges. However, they require ad-hoc integration methods and stabilization techniques to prevent instabilities for small cut cells. Recently, the Shifted Boundary Method (SBM), was introduced to prevent integration over cut cells and small cut-cell instabilities. An extension of the SBM was recently introduced, the Weighted Shifted Boundary Method (WSBM), where the variational form is weighted by the elemental active volume fraction, improving discrete mass/momentum conservation properties in simulations with moving domains. In this work we introduce the Generalized Shifted Boundary Method (GSBM), a geometry-agnostic generalization of the SBM and WSBM formulations that avoids the need of redefinition of integration domains and finite element spaces. The GSBM enables a unified formulation for problems with evolving geometries, supports gradient-based optimization of problems with varying geometries including topological changes, and unifies SBM, WSBM, and optimal-surrogate variants within a single framework. In this work we describe the formulation, and corresponding tests, for three model problems, namely: the Poisson problem, linear elasticity and transient Stokes flow.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118748"},"PeriodicalIF":7.3,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980092","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 : 2026-01-15DOI: 10.1016/j.cma.2025.118719
Sarvesh Joshi , S. Mohammad Mousavi , Craig M. Hamel , Stavros Gaitanaros , Prashant K. Purohit , Ryan Alberdi , Nikolaos Bouklas
Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transitions. Their macroscopic response–including energy dissipation during impact, large recoverable deformations, morphing between configurations, and auxetic behavior–remains difficult to capture with conventional continuum models, which often rely on discrete approaches that limit scalability. We propose a nonlocal continuum formulation that captures both stable and unstable responses of elastic architected metamaterials. The framework extends anisotropic hyperelasticity by introducing nonlocal variables and internal length scales reflective of microstructural features. Local polyconvex free-energy models are systematically augmented with two families of non-(poly)convex energies, enabling both metastable and bistable responses. Implementation in a finite element framework enables solution using a hybrid monolithic–staggered strategy. Simulations capture densification fronts, forward and reverse transitions, hysteresis loops, imperfection sensitivity, and globally coordinated auxetic modes. Overall, this framework provides a robust foundation for accelerated modeling of instability-driven phenomena in architected metamaterials, while enabling extensions to anisotropic, dissipative, and active systems as well as integration with data-driven and machine learning approaches.
{"title":"Instabilities and phase transitions in architected metamaterials: a gradient-enhanced continuum approach","authors":"Sarvesh Joshi , S. Mohammad Mousavi , Craig M. Hamel , Stavros Gaitanaros , Prashant K. Purohit , Ryan Alberdi , Nikolaos Bouklas","doi":"10.1016/j.cma.2025.118719","DOIUrl":"10.1016/j.cma.2025.118719","url":null,"abstract":"<div><div>Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transitions. Their macroscopic response–including energy dissipation during impact, large recoverable deformations, morphing between configurations, and auxetic behavior–remains difficult to capture with conventional continuum models, which often rely on discrete approaches that limit scalability. We propose a nonlocal continuum formulation that captures both stable and unstable responses of elastic architected metamaterials. The framework extends anisotropic hyperelasticity by introducing nonlocal variables and internal length scales reflective of microstructural features. Local polyconvex free-energy models are systematically augmented with two families of non-(poly)convex energies, enabling both metastable and bistable responses. Implementation in a finite element framework enables solution using a hybrid monolithic–staggered strategy. Simulations capture densification fronts, forward and reverse transitions, hysteresis loops, imperfection sensitivity, and globally coordinated auxetic modes. Overall, this framework provides a robust foundation for accelerated modeling of instability-driven phenomena in architected metamaterials, while enabling extensions to anisotropic, dissipative, and active systems as well as integration with data-driven and machine learning approaches.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118719"},"PeriodicalIF":7.3,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145980091","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 : 2026-01-14DOI: 10.1016/j.cma.2025.118698
Luis Andres Mollericon Titirico , Sylvain Lefebvre , Ole Sigmund , Jonàs Martínez
We study the structural optimization of a stack of elastic rings subjected to gravity. The aim is to optimize for minimum or maximum volume enclosing structures while preventing their collapse under their own weight. We formulate the problem using a parameterization of the cross-section geometry of the rings and a tailored optimization scheme that considers axisymmetric finite elements. As demonstrated through numerical examples, our method produces structurally sound shapes that can then be fabricated by stacking ring components or through extrusion-based manufacturing.
{"title":"Structural optimization of a stack of elastic rings under gravity","authors":"Luis Andres Mollericon Titirico , Sylvain Lefebvre , Ole Sigmund , Jonàs Martínez","doi":"10.1016/j.cma.2025.118698","DOIUrl":"10.1016/j.cma.2025.118698","url":null,"abstract":"<div><div>We study the structural optimization of a stack of elastic rings subjected to gravity. The aim is to optimize for minimum or maximum volume enclosing structures while preventing their collapse under their own weight. We formulate the problem using a parameterization of the cross-section geometry of the rings and a tailored optimization scheme that considers axisymmetric finite elements. As demonstrated through numerical examples, our method produces structurally sound shapes that can then be fabricated by stacking ring components or through extrusion-based manufacturing.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118698"},"PeriodicalIF":7.3,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145962659","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 : 2026-01-14DOI: 10.1016/j.cma.2026.118731
Yingzhi Qian , Xiaoping Zhang , Yan Zhu , Lili Ju , Jiesheng Huang
Accurately modeling solute transport in porous media is essential for effective agricultural water resource management. However, strong advection or localized sink/source terms often leads to steep local concentration gradients, posing significant challenges for numerical simulation. To address these issues, this paper proposes an efficient algorithm based on the Vertex-Centered Finite Volume Method (VCFVM). In this approach, the primary unknowns are defined at the mesh vertices, and the fluxes across dual edges are computed as weighted combinations of these vertex values. This formulation enables the advection-diffusion equation to be directly solved on arbitrary polygonal meshes-including nonmatching grids-without requiring complex preprocessing. The use of nonmatching grids allows for flexible local refinement, significantly enhancing the method’s ability to capture sharp concentration gradients. The proposed algorithm is particularly well-suited for simulating solute transport characterized by sharp gradients induced by strong advection or localized sink/source terms, and it has been validated through three representative benchmark cases. Numerical results show that the method accurately reproduces solute transport behavior in complex geometries, effectively maintains local Péclet numbers below 4, and successfully reduces numerical oscillations while suppressing excessive diffusion, as well as save about 50% CPU time in field scale simulation. This algorithm can be seamlessly integrated with existing groundwater and soil water flow models, offering a practical solution for managing sharp gradients in both water flow and solute transport.
{"title":"A vertex-centered finite volume method for solute transport in porous media on arbitrary polygonal meshes","authors":"Yingzhi Qian , Xiaoping Zhang , Yan Zhu , Lili Ju , Jiesheng Huang","doi":"10.1016/j.cma.2026.118731","DOIUrl":"10.1016/j.cma.2026.118731","url":null,"abstract":"<div><div>Accurately modeling solute transport in porous media is essential for effective agricultural water resource management. However, strong advection or localized sink/source terms often leads to steep local concentration gradients, posing significant challenges for numerical simulation. To address these issues, this paper proposes an efficient algorithm based on the Vertex-Centered Finite Volume Method (VCFVM). In this approach, the primary unknowns are defined at the mesh vertices, and the fluxes across dual edges are computed as weighted combinations of these vertex values. This formulation enables the advection-diffusion equation to be directly solved on arbitrary polygonal meshes-including nonmatching grids-without requiring complex preprocessing. The use of nonmatching grids allows for flexible local refinement, significantly enhancing the method’s ability to capture sharp concentration gradients. The proposed algorithm is particularly well-suited for simulating solute transport characterized by sharp gradients induced by strong advection or localized sink/source terms, and it has been validated through three representative benchmark cases. Numerical results show that the method accurately reproduces solute transport behavior in complex geometries, effectively maintains local Péclet numbers below 4, and successfully reduces numerical oscillations while suppressing excessive diffusion, as well as save about 50% CPU time in field scale simulation. This algorithm can be seamlessly integrated with existing groundwater and soil water flow models, offering a practical solution for managing sharp gradients in both water flow and solute transport.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"452 ","pages":"Article 118731"},"PeriodicalIF":7.3,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979615","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 : 2026-01-14DOI: 10.1016/j.cma.2026.118728
Benjamin Alheit , Mathias Peirlinck , Siddhant Kumar
Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs), i.e., neural network-based constitutive models, offer a highly expressive and flexible framework for modeling complex material behavior in solid mechanics. However, their practical adoption in large-scale FE simulations remains limited due to significant computational costs, especially in repeatedly evaluating stress and stiffness. NCMs thus represent an extreme case: their large computational graphs make stress and stiffness evaluations prohibitively expensive, restricting their use to small-scale problems. In this work, we introduce COMMET, an open-source FE framework whose architecture has been redesigned from the ground up to accelerate high-cost constitutive updates. Our framework features a novel assembly algorithm that supports batched and vectorized constitutive evaluations, compute-graph-optimized derivatives that replace automatic differentiation, and distributed-memory parallelism via MPI. These advances dramatically reduce runtime, with speed-ups exceeding three orders of magnitude relative to traditional non-vectorized automatic differentiation-based implementations. While we demonstrate these gains primarily for NCMs, the same principles apply broadly wherever for-loop based assembly or constitutive updates limit performance, establishing a new standard for large-scale, high-fidelity simulations in computational mechanics.
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