Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"Self-stabilized virtual element modeling of 2D mixed-mode cohesive crack propagation in isotropic elastic solids","authors":"Y. Chen ,&nbsp;D. Sun ,&nbsp;Q. Li ,&nbsp;U. Perego","doi":"10.1016/j.cma.2025.117880","DOIUrl":"10.1016/j.cma.2025.117880","url":null,"abstract":"<div><div>A comprehensive strategy for the simulation of mixed-mode cohesive crack propagation in a mesh of originally self-stabilized Virtual Elements (VEs) is proposed. Exploiting the VEs substantial insensitivity to mesh distortion, the propagating cohesive crack is accommodated within existing self-stabilized first-order quadrilateral VEs by simply adding new edges separated by a cohesive interface. The added edges make however the VE unstable and a new procedure for the stabilization of initially stable VE is developed. The method is formulated within a recently proposed Hu–Washizu variational framework, allowing for a higher order, independent modeling of stresses. In this way, a more accurate estimate of the stress at the tip of the cohesive process zone can be achieved allowing for a more accurate assessment of crack propagation conditions and direction. The proposed method is validated by application to several benchmark problems.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117880"},"PeriodicalIF":6.9,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Similarity equivariant graph neural networks for homogenization of metamaterials","authors":"Fleur Hendriks ,&nbsp;Vlado Menkovski ,&nbsp;Martin Doškář ,&nbsp;Marc G.D. Geers ,&nbsp;Ondřej Rokoš","doi":"10.1016/j.cma.2025.117867","DOIUrl":"10.1016/j.cma.2025.117867","url":null,"abstract":"<div><div>Soft, porous mechanical metamaterials exhibit pattern transformations that may have important applications in soft robotics, sound reduction and biomedicine. To design these innovative materials, it is important to be able to simulate them accurately and quickly, in order to tune their mechanical properties. Since conventional simulations using the finite element method entail a high computational cost, in this article we aim to develop a machine learning-based approach that scales favorably to serve as a surrogate model. To ensure that the model is also able to handle various microstructures, including those not encountered during training, we include the microstructure as part of the network input. Therefore, we introduce a graph neural network that predicts global quantities (energy, stress, stiffness) as well as the pattern transformations that occur (the kinematics) in hyperelastic, two-dimensional, microporous materials. Predicting these pattern transformations means predicting the displacement field. To make our model as accurate and data-efficient as possible, various symmetries are incorporated into the model. The starting point is an <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span>-equivariant graph neural network (which respects translation, rotation and reflection) that has periodic boundary conditions (i.e., it is in-/equivariant with respect to the choice of RVE), is scale in-/equivariant, can simulate large deformations, and can predict scalars, vectors as well as second and fourth order tensors (specifically energy, stress and stiffness). The incorporation of scale equivariance makes the model equivariant with respect to the similarities group, of which the Euclidean group <span><math><mrow><mi>E</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></math></span> is a subgroup. We show that this network is more accurate and data-efficient than graph neural networks with fewer symmetries. To create an efficient graph representation of the finite element discretization, we use only the internal geometrical hole boundaries from the finite element mesh to achieve a better speed-up and scaling with the mesh size.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117867"},"PeriodicalIF":6.9,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143593811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive multi-patch isogeometric analysis for heat transfer in three-dimensional solid","authors":"Lin Wang ,&nbsp;Tiantang Yu ,&nbsp;Sundararajan Natarajan ,&nbsp;Weihua Fang ,&nbsp;Zhiwei Zhou","doi":"10.1016/j.cma.2025.117895","DOIUrl":"10.1016/j.cma.2025.117895","url":null,"abstract":"<div><div>This paper presents an adaptive multi-patch isogeometric framework for modeling heat conduction in isotropic/orthotropic media. The proposed adaptive scheme is a novel combination of local mesh refinement and adaptive time-stepping to improve the calculation efficiency and reduce meshing burden. The local adaptive refinement is driven by a recovery-based error estimator. Truncated hierarchical NURBS (TH-NURBS) are utilized for local adaptive mesh refinement due to their excellent properties, such as linear independence, partition-of-unity, and exact description of complex geometry. Multi-patch technique is applied to model complex structures, with Nitsche’s method as the coupling strategy. The computational accuracy of the proposed model is verified through several 3D numerical examples. The high efficiency of the adaptive scheme is demonstrated by comparing with uniform refinement method and fixed time-stepping method separately.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117895"},"PeriodicalIF":6.9,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"FCA method for predicting effective viscosity of particle reinforced thermoplastic melt and a metric for measuring clusters","authors":"Zheng Li,&nbsp;Yinghao Nie,&nbsp;Gengdong Cheng","doi":"10.1016/j.cma.2025.117899","DOIUrl":"10.1016/j.cma.2025.117899","url":null,"abstract":"<div><div>The effective viscosity of particle reinforced thermoplastic melt shows strongly anisotropic behavior and is also shear rate-dependent. The traditional homogenization method may face challenge due to extremely expensive computational cost, when the non-linear effective viscosities on all the directions of Particle Reinforced Thermoplastics (PRT) are demanded. This paper approaches this challenge with the FEM-Cluster based reduced order Analysis (FCA) method [1]. The governing equations are solved by minimizing a cluster-based dual formulation of the dissipating energy, where the cluster-wise Admissible Shear Stress (ASS) set is obtained by FCA together with a Spectrum Analysis Algorithm (SAA). In addition, considering the fact that there is a lack of effective method for determining the proper number of clusters, a cluster metric is developed, which relates the given number of clusters and the prediction accuracy of FCA method. This metric can be easily used in the offline stage to pre-estimate the applicability of the obtained clusters on the given loading conditions with a small amount of additional computation.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117899"},"PeriodicalIF":6.9,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear dynamic substructuring in the frequency domain","authors":"Hossein Soleimani,&nbsp;Niels Aage","doi":"10.1016/j.cma.2025.117882","DOIUrl":"10.1016/j.cma.2025.117882","url":null,"abstract":"<div><div>In this paper, we introduce a nonlinear dynamic substructuring technique to efficiently evaluate nonlinear systems with localized nonlinearities in the frequency domain. A closed-form equation is derived from coupling the dynamics of substructures and nonlinear connections. The method requires the linear frequency response functions of the substructures, which can be calculated independently using reduced-order methods. Increasing the number of linear bases in the reduction method for substructures does not affect the number of nonlinear equations, unlike in component mode synthesis techniques. The performance of the method is evaluated through three case studies: a lumped parameter system with cubic nonlinearity, bars with a small gap (normal contact), and a plate with a couple of nonlinear energy sinks. The results demonstrate promising accuracy with significantly reduced computational cost.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117882"},"PeriodicalIF":6.9,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On efficient simulation of self-assembling diblock copolymers using a peridynamic-enhanced Fourier spectral method","authors":"Farshid Mossaiby ,&nbsp;Gregor Häfner ,&nbsp;Arman Shojaei ,&nbsp;Alexander Hermann ,&nbsp;Christian Cyron ,&nbsp;Marcus Müller ,&nbsp;Stewart Silling","doi":"10.1016/j.cma.2025.117878","DOIUrl":"10.1016/j.cma.2025.117878","url":null,"abstract":"<div><div>This study introduces a computational framework for simulating the self-assembly of diblock copolymers using a novel peridynamic (PD)-enhanced Fourier spectral method (FSM). Diblock copolymers, composed of two distinct polymer blocks, are capable of forming nanostructured domains with applications in nanoelectronics, photonics, and advanced membranes. Current simulation techniques face challenges in capturing the multiscale dynamics of polymer systems and are often limited by computational inefficiencies. Our approach combines a phase-field model with FSM for spatial discretization and leverages a PD-based diffusion operator to overcome the stability restrictions of explicit time-stepping schemes. This integration allows for larger time steps, ensuring both stability and computational efficiency. The method’s scalability is enhanced through parallel implementation using C++ and OpenMP, optimized for multi-core CPUs. Validation through phase diagrams of copolymer melts and simulations of evaporation-induced self-assembly (EISA) processes demonstrates the capability of the proposed method to accurately capture large-scale, dynamic morphologies. Our approach provides a versatile framework and was found in certain examples to improve computational efficiency by more than a factor of 6 compared to forward-Euler FSM approach.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117878"},"PeriodicalIF":6.9,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143580587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Assessing the Capriccio method via one-dimensional systems for coupled continuum-particle simulations in various uniaxial load cases using a novel interdimensional comparison approach","authors":"Lukas Laubert ,&nbsp;Felix Weber ,&nbsp;Sebastian Pfaller","doi":"10.1016/j.cma.2025.117817","DOIUrl":"10.1016/j.cma.2025.117817","url":null,"abstract":"<div><div>This contribution investigates sources of insufficiencies observed with the Capriccio method for concurrent continuum-particle coupling using a novel comparison technique. This approach maps the deformation states of three-dimensional (3D) coupled domains into a concise one-dimensional (1D) representation, which allows for a separate evaluation of the domain strains in a unified representation, enabling facile comparisons of the domain states during deformation. For the investigation, we employ both a 1D coupled system resembling the most relevant features of the full 3D Capriccio method as well as a corresponding 3D setup. Our analysis explores interactions between different material models in finite element (FE) and molecular dynamics (MD) domains. Based on various load cases studied in the 1D setup, we identify a resistance of the coupling region to spatial movement as the fundamental cause of strain convergence problems when applying the staggered solution scheme. Using the developed mapping approach, examination of the corresponding 3D setup reveals that these strain inconsistencies are even exacerbated by adverse relaxation effects in viscous MD models, particularly when coupled to a corresponding viscoelastic–viscoplastic FE model, leading to divergence from optimal strain. Our findings confirm that smaller strain increments in combination with larger load step numbers significantly improve strain convergence in all domains. Overall, this indicates the need for detailed sensitivity analysis of coupling parameter influences to reduce the identified motion resistance of the coupling region. Based on promising results in 1D, we further recommend exploring monolithic solving schemes for 3D systems to achieve optimal strain convergence for all types of Capriccio-based coupled particle and continuum material models. Moreover, our systematic approach of system definition and interdimensional comparison may serve as a model to assess other domain-decomposition coupling techniques.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117817"},"PeriodicalIF":6.9,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic particle packing to generate complex geometries","authors":"Muhammad Sameer ,&nbsp;C. Fred Higgs III","doi":"10.1016/j.cma.2025.117802","DOIUrl":"10.1016/j.cma.2025.117802","url":null,"abstract":"<div><div>Analyzing the discrete nature of solid structures is crucial, particularly in situations where system behavior relies on material discontinuities, such as fracture and wear, along with their subsequent effects. It is not only essential to investigate when failure or discontinuity occurs within a material, but also how it unfolds and impacts its surroundings. While numerical methods serve as effective tools for analyzing structural behavior, continuum-based approaches may not provide a comprehensive view when dealing with discontinuities in a material. Discrete models provide the capability to simulate these discontinuities by bonding discrete elements (particles) together, thereby also simulating continuum behavior. However, the challenge lies in packing these particles within a complex-shaped structure. The dynamic packing approach excels in generating a tightly packed, randomly arranged bonded-particle structure with consistent mechanical behavior. However, it struggles when it comes to generating complex geometries. Conversely, the geometric approach is proficient at generating complex structures but lacks the reliability needed to simulate engineering materials. The method outlined in this paper represents the first attempt to dynamically pack particles within a complex geometry while maintaining all the necessary mechanical properties to accurately model isotropic engineering materials. Such precision in structure and methodology is vital for calibrating the bonds, ensuring that the bonded-particle structure behaves similarly to real materials. As an example, several bonded-particle structures are generated and tested to demonstrate the complexity of their shapes and their realistic mechanical behavior.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117802"},"PeriodicalIF":6.9,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Three-dimensional varying-order NURBS discretization method for enhanced IGA of large deformation frictional contact problems","authors":"Vishal Agrawal","doi":"10.1016/j.cma.2025.117853","DOIUrl":"10.1016/j.cma.2025.117853","url":null,"abstract":"<div><div>In this contribution, we introduce a varying-order (VO) NURBS discretization method to enhance the performance of the isogeometric analysis (IGA) technique for solving three-dimensional (3D) large deformation frictional contact problems involving two deformable bodies. Building on the promising results obtained from the previous work on the 2D isogeometric contact analysis (Agrawal and Gautam, 2020), this work extends the method’s capability for tri-variate NURBS-based discretization. The proposed method allows for independent, user-defined application of higher-order NURBS functions to discretize the contact surface while employing the minimum order NURBS for the remaining volume of the elastic solid. This flexible strategy enables the possibility to refine a NURBS-constructed solid at a fixed mesh with the controllable order elevation-based approach while preserving the original volume parametrization. The advantages of the method are twofold. First, employing higher-order NURBS for contact integral evaluations considerably enhances the accuracy of the contact responses at a fixed mesh, fully exploiting the advantage of higher-order NURBS specifically for contact computations. Second, the minimum order NURBS for the computations in the remaining bulk volume substantially reduces the computational cost inherently associated with the standard uniform order NURBS-based isogeometric contact analyses.</div><div>The capabilities of the proposed method are demonstrated using various contact problems between elastic solids with or without considering friction. The results with the standard uniform order of tri-variate NURBS-based discretizations are also included to provide a comprehensive comparative assessment. We show that to attain results of similar accuracy, the varying-order NURBS discretization uses a much coarser mesh resolution than the standard uniform-order NURBS-based discretization, hence leading to a major gain in computational efficiency for isogeometric contact analysis. The convergence study demonstrates the consistent performance of the method for efficient IGA of 3D frictional contact problems. Furthermore, the simplicity of the method facilitates its direct integration into the existing 3D NURBS-based IGA framework with only a few minor modifications.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117853"},"PeriodicalIF":6.9,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143548986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Region-optimal Gaussian process surrogate model via Dirichlet process for cold-flow and combustion emulations","authors":"Mingshuo Zhou ,&nbsp;Ruiye Zuo ,&nbsp;Chih-Li Sung ,&nbsp;Yanjie Tong ,&nbsp;Xingjian Wang","doi":"10.1016/j.cma.2025.117894","DOIUrl":"10.1016/j.cma.2025.117894","url":null,"abstract":"<div><div>Surrogate modeling plays an increasingly important role in engineering design. The present work develops a novel surrogate model, region-optimal Gaussian process (roGP), to accurately emulate cold-flow and combustion fields in a significantly short time period. The model leverages an advanced statistical approach, Dirichlet process (DP) mixture model, to partition the entire spatial domain of concern into discrete subregions in a physics-informed manner. Each subregion contains the common features embedded in the collected dataset and is modeled by a Gaussian process (GP) with shared hyperparameters. Additionally, an active learning strategy iteratively refines the training dataset by prioritizing high-uncertainty regions, further enhancing predictive accuracy. The roGP model is evaluated on three representative cases of increasing complexity, consistently outperforming conventional GP-based surrogates. Results show that roGP effectively mitigates overfitting in independent GP models and reduces information loss in proper-orthogonal-decomposition GP models. In all test cases, roGP achieves superior spatial prediction accuracy, with relative root mean square errors below 5.5 %. A unique characteristic of the roGP model is that the DP-optimized subregions of roGP connect physics-alike coordinates among sampling design points. The entire pressure field in cold-flow case is effectively described by five subregions, while physical fields in two combustion cases require the elevated number of subregions due to their increased complexity. roGP achieves substantial acceleration in prediction time, up to eight orders of magnitude faster than numerical simulations. The developed surrogate model can be implemented to emulate a range of high-dimensional engineering applications with high accuracy and efficiency.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"439 ","pages":"Article 117894"},"PeriodicalIF":6.9,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143548984","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}