Computer Methods in Applied Mechanics and Engineering最新文献

{"title":"T-splines-based panel method for aerodynamic topology optimization of engineering shell structures using isogeometric analysis","authors":"Xiao Zhang ,&nbsp;Liang Gao ,&nbsp;Mi Xiao ,&nbsp;Jie Gao","doi":"10.1016/j.cma.2025.118154","DOIUrl":"10.1016/j.cma.2025.118154","url":null,"abstract":"<div><div>Engineering shell structures have been extensively used in aerospace, automotive and other fields, whose aerodynamic performance is significant in structural design. In the current work, the primary intention is to propose an aerodynamic topology optimization design framework for arbitrary engineering shell structures using the T-splines-based panel method and isogeometric analysis. Firstly, the T-splines-based isogeometric analysis formulation is developed for arbitrary shell structures using Bézier extraction, which can maintain the consistency of geometric model in an accurate representation and numerical model of shells. Secondly, a higher-order panel method is developed for calculating aerodynamic solutions with unidirectional effects using T-splines, where Neumann boundary conditions are imposed using the collocation method. Moreover, the source density distributions of engineering shells are solved numerically with T-spline blending function, and Bézier basis functions are applied to describe the velocity potential distributions, achieving an efficient solution of 3D potential flow problem and ensuring the stability and efficiency of aerodynamic computation. Thirdly, the mathematical formulation is developed for implementing aerodynamic topology optimization designs of engineering shells, in which an efficient T-splines-based topology description model using Bézier elements is developed and the sensitivity analysis is derived in detail. Finally, several engineering thin shells are studied to demonstrate the effectiveness of the proposed aerodynamic topology design framework, and the related numerical results also reveal the optimized shell topologies that perfectly cater for aerodynamic pressure distributions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118154"},"PeriodicalIF":6.9,"publicationDate":"2025-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144307151","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":"Adaptive deep physics-informed neural network with dual-nested activation for solving complex partial differential equations","authors":"Tianhao Wang ,&nbsp;Guirong Liu ,&nbsp;Eric Li ,&nbsp;Xu Xu","doi":"10.1016/j.cma.2025.118125","DOIUrl":"10.1016/j.cma.2025.118125","url":null,"abstract":"<div><div>Physics-informed neural networks (PINNs) hold promise for solving partial differential equations (PDEs), but they often face challenges in achieving high accuracy, especially in complex, real-world scenarios. This paper presents an adaptive deep PINN (ad-PINN) framework designed to enhance the efficiency of both activation and loss functions. The proposed ad-PINN introduces two main innovations: (1) an adaptive activation function with dual-nested mechanism, called the <em>dual-tanh</em> function, which dynamically adjusts its <em>slope</em> and <em>shape</em> to optimize learning capacity beyond traditional activations; and (2) an adaptive Huber loss function, which automatically adjusts its parameters, eliminating the need for manual tuning. This dual adaptability in activation and loss functions improves the model’s flexibility and performance. Theoretically, we demonstrate that with proper initialization and learning rates, a gradient descent algorithm minimizing the loss function avoids convergence to suboptimal points or local minima. The effectiveness of ad-PINN is showcased through real-world applications, including shockwave propagation and reflection, incompressible solid mechanics, bi-material problems, and fluid dynamics. Comparative experiments reveal that ad-PINN achieves significantly higher accuracy than some existing PINNs, highlighting its capability to tackle complex problems with high-gradient solutions, capture hidden incompressibility, handle displacement discontinuities, manage high-dimensional systems with complex geometric and physical features, and address systems governed by partially known physical laws.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118125"},"PeriodicalIF":6.9,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144299012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A coupled mathematical and numerical model for protein spreading and tissue atrophy applied to Alzheimer’s disease","authors":"Valentina Pederzoli ,&nbsp;Mattia Corti ,&nbsp;Davide Riccobelli ,&nbsp;Paola F. Antonietti","doi":"10.1016/j.cma.2025.118118","DOIUrl":"10.1016/j.cma.2025.118118","url":null,"abstract":"<div><div>The aim of this paper is to introduce, analyze and test in practice a new mathematical model describing the interplay between biological tissue atrophy driven by the diffusion of a biological agent, with applications to neurodegenerative disorders. This study introduces a novel mathematical and computational model comprising a Fisher–Kolmogorov equation for species diffusion coupled with an elasticity equation governing mass loss. These equations intertwine through a logistic law dictating the reduction of the medium’s mass. This model is applied to the onset and development of Alzheimer’s disease. Here, the equations describe the propagation of misfolded <span><math><mi>τ</mi></math></span>-proteins and the ensuing brain atrophy characteristic of the disease. To address numerically the inherited complexities, we propose a Discontinuous Galerkin method for spatial discretization, while time integration relies on the Crank–Nicolson method. We present the mathematical model, explore its characteristics, and present the proposed discretization. Furthermore, convergence results are presented to verify the model’s implementation, accompanied by simulations illustrating the application scenario of the onset of Alzheimer’s disease.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118118"},"PeriodicalIF":6.9,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144299011","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":"Robust trimmed multipatch IGA with singular maps","authors":"Tobias Jonsson,&nbsp;Mats G. Larson,&nbsp;Karl Larsson","doi":"10.1016/j.cma.2025.118124","DOIUrl":"10.1016/j.cma.2025.118124","url":null,"abstract":"<div><div>We consider elliptic problems in multipatch isogeometric analysis (IGA) where the patch parameterizations may be singular. Specifically, we address cases where certain dimensions of the parametric geometry diminish as the singularity is approached — for example, a curve collapsing into a point (in 2D), or a surface collapsing into a point or a curve (in 3D). To deal with this issue, we develop a robust weak formulation for the second-order Laplace equation that allows trimmed (cut) elements, enforces interface and Dirichlet conditions weakly, and does not depend on specially constructed approximation spaces. Our technique for dealing with the singular maps is based on the regularization of the Riemannian metric tensor, and we detail how to implement this robustly. We investigate the method’s behavior when applied to a square-to-cusp parameterization that allows us to vary the singular behavior’s aggressiveness in how quickly the measure tends to zero when the singularity is approached. We propose a scaling of the regularization parameter to obtain optimal order approximation. Our numerical experiments indicate that the method is robust also for quite aggressive singular parameterizations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118124"},"PeriodicalIF":6.9,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144299013","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":"Multiscale topology optimization of architected fiber reinforced composites considering manufacturability","authors":"Arijit Pradhan,&nbsp;Narasimha Boddeti","doi":"10.1016/j.cma.2025.118121","DOIUrl":"10.1016/j.cma.2025.118121","url":null,"abstract":"<div><div>Advances in additive manufacturing and tow-steered processes are now enabling the fabrication of fiber-reinforced composites (FRCs) with architected microstructures, via complex curvilinear fiber paths/layouts, for desired structural response at the macroscale. Engineers can leverage these advances, via multiscale topology optimization (MTO), to design structures with optimized macro and microstructures, and realize what we term as architected fiber-reinforced composites (AFRCs). However, a majority of MTO approaches do not consider manufacturability and lead to a significantly different manufactured structure than the optimized design. The most critical manufacturability considerations for AFRCs are no gaps or overlaps between adjacent fiber paths and no singularities, i.e., points where the local fiber orientation vector is not well-defined. To address these considerations, we devised an easy to implement MTO framework that innovatively employs both level set and density-based parametrizations, unlike other approaches in the literature. Specifically, we use a level set function to parametrize the fibrous microstructure while using fictitious densities for the macrostructure following the widely used density-based topology optimization. Gaps and overlaps between fiber paths are prevented by restricting the level set function to a distance field, while singularities are mitigated by penalizing the material stiffness tensor. The restriction to a distance field is achieved by minimizing the residual of the eikonal equation along with the principal objective of the design problem. The effectiveness of the proposed method is demonstrated by two-scale (i.e., macro and microstructures) and single-scale (microstructure-only) optimization of planar FRC structures with either continuous or discontinuous reinforcement.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118121"},"PeriodicalIF":6.9,"publicationDate":"2025-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291582","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":"On shells of revolution with random profiles","authors":"Stefano Giani ,&nbsp;Harri Hakula ,&nbsp;Duc Khuat","doi":"10.1016/j.cma.2025.118081","DOIUrl":"10.1016/j.cma.2025.118081","url":null,"abstract":"<div><div>Thin structures and shells in particular are well-known to be highly sensitive to manufacturing imperfections such as perturbations on the profile of a shell of revolution. The main result of this study is that one cannot expect to apply standard models for perturbations, such as Karhunen–Loève expansions, without careful consideration on how the applied model depends on the regularity of the random field. Through theoretical analysis and numerical experiments it is demonstrated that the chosen model does impose restrictions on the types of imperfections one can study. If the conditions are satisfied, the standard computational techniques such as stochastic collocation are applicable also in this problem domain. The efficacy of the simple approach is shown in the special case of symmetric concentrated loads. All classes of shell geometries have been considered in both clamped and sensitive configurations.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118081"},"PeriodicalIF":6.9,"publicationDate":"2025-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144279374","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":"Surrogate models of stress for triply periodic minimal surface lattices","authors":"Sy Nguyen-Van ,&nbsp;Guha Manogharan ,&nbsp;Lan-Hsuan Huang ,&nbsp;Julián A. Norato","doi":"10.1016/j.cma.2025.118119","DOIUrl":"10.1016/j.cma.2025.118119","url":null,"abstract":"<div><div>This work formulates compact and efficient surrogates of the stress field for sheet-network, triply periodic minimal surface (TPMS) lattices, which have been gaining popularity due to advancements in additive manufacturing methods. The proposed surrogates can be employed to determine, for example, the largest von Mises or principal stresses in a TPMS lattice as a function of the wall thickness, base material properties, and applied tractions. Therefore, they can be used for the multi-scale analysis and design of porous macro structures made of TPMS lattices with regard to stress-driven criteria. The surrogates circumvent the need to mesh the lattice surface and instead allow the mechanical analysis of the macro structure to be performed using solid finite elements. The construction of the stress surrogates exploits the geometric structure of the TPMS, namely the fact that the unit cell consists of geometric transformations of a single fundamental unit. It is proven that it is only necessary to obtain surrogates for one fundamental unit to compute the stress field for the entire unit cell. Surrogates are developed for multiple types of TPMS lattices. A comparison of the stresses obtained using the surrogates with those obtained using a body-fitted mesh of a compression test specimen made of a TPMS and to published values of strength is presented for validation. To demonstrate the usefulness of the proposed surrogates, they are applied to the stress prediction of a cantilever beam made of a uniform-thickness TPMS and a simply supported beam made of a variable-thickness TPMS. An open-source code that implements the surrogates is made publicly available.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118119"},"PeriodicalIF":6.9,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144279373","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":"Quasi-static loading of granular media as a linear complementarity problem","authors":"Matthew R. Kuhn","doi":"10.1016/j.cma.2025.118117","DOIUrl":"10.1016/j.cma.2025.118117","url":null,"abstract":"<div><div>The discrete quasi-static response of rate-independent dissipative granular media is addressed. Granular systems are conventionally simulated with methods that are intrinsically dynamic, such as the discrete element (DEM) and discontinuous deformation (DDA) methods, with the particles’ accelerations and damping being essential aspects. In contrast, quasi-static methods derive from the static stiffness relationships among the particles. With frictional contacts, an assembly’s stiffness is incrementally non-linear and dependent on the direction of loading. The paper resolves this difficulty by casting the response as a linear complementarity problem (LCP). The approach benefits from a foundation of past research on existence, uniqueness, and stability of LCP solutions. Results of this research are expounded in a concise set of rules. The LCP of a granular system is derived, accounting for geometric effects that arise from curvatures of particles at their contacts, frictional contact stiffnesses, and displacement constraints on the particles. A Bott–Duffin generalized inverse is used for resolving the displacement constraints. The paper describes eight aberrant conditions (pathologies) of granular systems, in the forms of various bifurcations and instabilities. When placed in the context of an LCP, the eight conditions are unambiguously defined. These pathologies include three types of bifurcation: discrete, continuous-bounded (not yet reported in the literature), and continuous-unbounded. Another pathology, not yet reported in the literature, is an abrupt discontinuous change in movements upon a continuous change of the data. Methods and results are illustrated with examples of granular systems. Results show that instability and bifurcation are pervasive conditions near failure; that failure and softening are sensitive to the geometric contours of the particles at contacts; and that quasi-static systems can encounter states that require a dynamic transition to resolve a lack of paths consistent with further loading.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118117"},"PeriodicalIF":6.9,"publicationDate":"2025-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144271058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A chain stretch-based gradient-enhanced model for damage and fracture in elastomers","authors":"S. Mohammad Mousavi ,&nbsp;Jason Mulderrig ,&nbsp;Brandon Talamini ,&nbsp;Nikolaos Bouklas","doi":"10.1016/j.cma.2025.118103","DOIUrl":"10.1016/j.cma.2025.118103","url":null,"abstract":"<div><div>Similar to quasi-brittle materials, it has been recently shown that elastomers can exhibit a macroscopically diffuse damage zone that accompanies the fracture process. In this study, we introduce a stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials (e.g., concrete), they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening (de Borst and Verhoosel, 2016). This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz <em>et al.</em>, 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. We discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118103"},"PeriodicalIF":6.9,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A posteriori algebraic error estimates and nonoverlapping domain decomposition in mixed formulations: energy coarse grid balancing, local mass conservation on each step, and line search","authors":"Manuela Bastidas Olivares ,&nbsp;Akram Beni Hamad ,&nbsp;Martin Vohralík ,&nbsp;Ivan Yotov","doi":"10.1016/j.cma.2025.118090","DOIUrl":"10.1016/j.cma.2025.118090","url":null,"abstract":"<div><div>We consider iterative algebraic solvers for saddle-point mixed finite element discretizations of the model Darcy flow problem. We propose a posteriori error estimators of the algebraic error as well as a nonoverlapping domain decomposition algorithm. The estimators control the algebraic error from above and from below in a guaranteed and fully computable way. The distinctive feature of the domain decomposition algorithm is that it produces a locally mass conservative approximation on each iteration. Both the estimate and the algorithm rely on a coarse grid solver, a subdomain Neumann solver, and a subdomain Dirichlet solver. The algorithm also employs a line search to determine the optimal step size, leading to a Pythagoras formula for the algebraic error decrease in each iteration. We suppose that the fine mesh is a refinement of a coarse mesh, where both meshes need to be formed by simplices or rectangular parallelepipeds. Numerical experiments illustrate the theoretical developments and confirm the efficiency of the algebraic error estimates and of the domain decomposition algorithm.</div></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":"444 ","pages":"Article 118090"},"PeriodicalIF":6.9,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144263759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}