GAMM Mitteilungen最新文献

{"title":"Agentic artificial intelligence in mechanics of materials: A review of building tailored models on demand","authors":"Marius Tacke,&nbsp;Matthias Busch,&nbsp;Kevin Linka,&nbsp;Roland Aydin,&nbsp;Christian Cyron","doi":"10.1002/gamm.70016","DOIUrl":"https://doi.org/10.1002/gamm.70016","url":null,"abstract":"<p>In mechanics of materials, many powerful methods are accessible only to experts. Constitutive models, for example, describe the relation between stress and strain in materials and are a core ingredient of simulations from structural engineering to biomechanics. Yet building and using such models requires specialized expertise—a barrier for the many potential users trained in other fields. Artificial intelligence based on foundation models, increasingly organized as agents, is beginning to lower this barrier by allowing users to generate tailored models on demand. The same development is underway in many other fields where specialized tools have long been hand-crafted anew for each task. We call this emerging paradigm the <i>on-the-fly generation of physical models</i>: from a plain request, an agent creates a physical model on demand—from scratch and tailored to the problem. Its appeal is accessibility and flexibility. As a consequence, the lasting artifact is no longer a fixed model but the orchestration and prompting of the agents that produce it. This review surveys the concepts behind the paradigm, within mechanics of materials and in neighboring fields, and examines them through two lenses: effectiveness (the accuracy of the generated models) and trustworthiness (their physical admissibility). Trustworthiness is pursued along two routes: deepening the agent's integration under explicit validation, or restraining its autonomy in favor of trusted components. Given the rapid progress of foundation models, and the bitter lesson that general methods leveraging computation tend to prevail, we call for paradigms designed to scale with this progress rather than to compete with it.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"49 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.70016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149214720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Microscale FFT-based modeling of artificial porous microstructures and analysis of macroscopic models under varying loading scenarios","authors":"Julian Dahler,&nbsp;Sarah Staub,&nbsp;Lisa Scheunemann","doi":"10.1002/gamm.70015","DOIUrl":"https://doi.org/10.1002/gamm.70015","url":null,"abstract":"<p>This article investigates the modeling of metallic isotropic porous materials by evaluating and comparing macroscopic and microstructure-resolved simulation approaches. At the macroscopic level, different variants of the Deshpande-Fleck (DF) model are implemented to describe the elastoplastic behavior of metallic porous materials. Considering the porous microstructure explicitly, FFT-based simulations are performed to compute homogenized responses of synthetically generated microstructures under various loading conditions. Assessing representativeness and morphological variation, different realizations of artificial closed-cell porous microstructures with different relative densities are analyzed. The study systematically compares macroscopic DF model predictions with the results of FFT-based homogenization to assess DF model accuracy and identify limitations in different loading scenarios in a wide range of porosities. The results demonstrate that the original DF model captures key trends in the mechanical response, but needs repeated calibration for varied load paths. Using modified DF models, the identification of varying ellipticity based on uniaxial and hydrostatic compression simulations enables a good representation of multiaxial compression loading. The FFT-based simulations highlight the strong influence of morphological properties, emphasizing the universality of microstructure-based models without the need for recalibration for different loading scenarios, but leading to increased computational effort. The findings provide valuable insights into the capabilities and limitations of the different DF models over a wide range of porosities and demonstrate the universality of microstructure-resolved simulations for reliable prediction of porous material behavior under varying loading conditions.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"49 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.70015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148532976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local continuum consistent peridynamics with bond-associated modeling and dynamic fracture","authors":"Kai Partmann,&nbsp;Robert I. Weinbrenner,&nbsp;Christian Wieners,&nbsp;Kerstin Weinberg","doi":"10.1002/gamm.70014","DOIUrl":"https://doi.org/10.1002/gamm.70014","url":null,"abstract":"<p>This paper explores the theoretical foundations and practical challenges of peridynamics as a nonlocal continuum mechanics method. We establish connections between classical continuum mechanics principles and peridynamics formulations, with a particular focus on understanding how the pairwise force function in peridynamics relates to stress concepts in local theories. The work addresses persistent numerical challenges in peridynamic simulations, including zero-energy modes and instabilities in correspondence-based formulations. We present bond-associated modeling approaches that enhance stability while maintaining computational accuracy. The theoretical discussions are supplemented with discretization methods for spatial and temporal domains. Through illustrative examples of complex fracture phenomena, we demonstrate how these theoretical insights translate to practical applications, providing guidance on selecting appropriate peridynamic formulations for computational mechanics problems. The numerical comparison identifies the bond-associated quadrature point formulation as the most accurate correspondence-class approach in the elastic regime. Under progressive bond deletion, however, the shape tensor, on which this formulation relies, becomes ill-conditioned, and the model loses stability. This necessitates the development of refined damage formulations within the correspondence framework.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"49 1-2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.70014","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148300129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gradient Crystal Plasticity Modeling of Laminate Microstructures","authors":"Claudius Klein,&nbsp;Thomas Böhlke","doi":"10.1002/gamm.70009","DOIUrl":"https://doi.org/10.1002/gamm.70009","url":null,"abstract":"<p>Metallic materials may show an ultra-fine lamellar morphology leading to desirable macroscopic mechanical properties. In this paper, an analytical method for modeling the size-dependent mechanical behavior of material systems with lamellar microstructure is proposed. The main contribution of this manuscript is the combination of the exact elastic localization relations for a periodic laminate having inhomogeneous phases with a gradient plasticity constitutive model. This allows a new formulation of the equations governing the evolution of the plastic deformation as a closed system of equations. The yield functions form a system of integro-differential equations that can be solved analytically. This new framework allows to model the size-dependent mechanical behavior of multiphase lamellar materials where the subdomains are elastoplastic single crystals. This is demonstrated using a two-phase laminate. In addition, bounds for the qualitative distributions of the plastic slip and the back stress are derived using a dimensionless quantity. The kinematic hardening due to the back stress depends on the lamella width and the slip system orientation. The back stress vanishes not only for increasing lamella widths but also in slip systems where the slip plane normal is parallel to the lamination direction.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"48 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.70009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145469993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deformation dependent permeability from variationally consistent homogenization","authors":"David René Rollin,&nbsp;Fredrik Larsson,&nbsp;Kenneth Runesson,&nbsp;Ralf Jänicke","doi":"10.1002/gamm.70010","DOIUrl":"https://doi.org/10.1002/gamm.70010","url":null,"abstract":"<p>In this article, the influence of large deformations on the effective permeability of a bicontinuous porous material is investigated. On the fine-scale, Neo–Hooke hyperelasticity is considered for the solid skeleton. In a third medium approach, we model the pore space as filled with a softer material of the same type. Fluid flow through the deformed pores is expressed in terms of a Stokes' flow model. The influence of the pore pressure on the deformation is neglected, resulting in a one-way coupling which allows for a sequential solution of the two physical problems. The framework of Variationally Consistent Homogenization is used to derive a two-scale formulation based on a Representative Volume Element (RVE) characterizing the microstructure. Finally, a two-step procedure to compute the deformation dependent permeability is established: Firstly, the deformation of the RVE for a given macroscale deformation gradient is computed. Secondly, sensitivities for the fluid flow through the deformed RVE are computed and used to determine the effective permeability tensor. A numerical study is conducted for sets of RVEs with the same material parameters and different porosity. For the case of uniaxial compression, a significant influence of the deformation on the effective permeability is observed: For a macroscale compression of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>20</mn>\u0000 <mo>%</mo>\u0000 </mrow>\u0000 <annotation>$$ 20% $$</annotation>\u0000 </semantics></math>, the effective permeability orthogonal to the compression direction is reduced by almost <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>60</mn>\u0000 <mo>%</mo>\u0000 </mrow>\u0000 <annotation>$$ 60% $$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"48 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.70010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145406763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Data-Driven Inverse Design of Spinodoid Architected Materials","authors":"Alexandra Otto,&nbsp;Max Rosenkranz,&nbsp;Karl A. Kalina,&nbsp;Markus Kästner","doi":"10.1002/gamm.70008","DOIUrl":"https://doi.org/10.1002/gamm.70008","url":null,"abstract":"<p>We present a workflow for the inverse design of architected materials with targeted effective mechanical properties. The approach leverages a low-dimensional descriptor space to represent the topology and morphology of complex mesostructures, enabling efficient navigation within the design space. Data for training is generated through numerical homogenization using a Fast Fourier Transform (FFT)-based solver, providing high-fidelity mappings from structural descriptors on the mesoscale to effective properties. A neural network (NN)-based surrogate model is trained to approximate this mapping. The inverse design task is then formulated as an optimization problem over the descriptor space, where gradient-based optimizers are applied to identify the descriptors, the inputs of the surrogate. We focus on the case of anisotropic linear elasticity and demonstrate the method using spinodoid architected materials, which offer tunable anisotropy and a low-dimensional descriptor space. The framework is validated for the inverse design targeting the anisotropic stiffness of a femoral bone sample. In addition, we propose a method to determine the anisotropy class of a given stiffness tensor. This enables a quantitative evaluation of how closely the bone's anisotropy class can be approximated by spinodoids. We analyze the influence of the optimization loss function on the inverse design outcome by comparing results across different losses. Ultimately, a logarithmic loss function is chosen, as it enables simultaneous optimization of the stiffness and compliance.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"48 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.70008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145297484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantification of microstructure-related uncertainties in structural analysis based on artificial microstructures and the \u0000 \u0000 \u0000 \u0000 \u0000 FE\u0000 \u0000 \u0000 2\u0000 \u0000 \u0000 \u0000 $$ {mathrm{FE}}^2 $$\u0000 -method","authors":"Hendrik Dorn,&nbsp;Niklas Miska,&nbsp;Daniel Balzani","doi":"10.1002/gamm.70007","DOIUrl":"https://doi.org/10.1002/gamm.70007","url":null,"abstract":"<p>The characteristics of microstructure morphology of micro-heterogeneous materials may vary over the macroscopic length scale and thus result in macroscopically distributed, uncertain material properties. Hence, multiscale approaches for the structural analysis of such materials, for example, in terms of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mtext>FE</mtext>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathrm{FE}}^2 $$</annotation>\u0000 </semantics></math>-method, should not be based on a single representative volume element. In this contribution a method is proposed, which considers different, artificial statistically similar volume elements at each macroscopic integration point which mimic the microstructure variability of the real material as a random field. For this purpose, the microstructure variation of the real material is quantified first in terms of the distribution of a scalar measure containing deviations of statistical measures of higher order, and then this distribution is used to construct a set of artificial microstructures to be used as volume elements within the multiscale simulation. To avoid manual discretization of the large amount of statistically similar volume elements, the finite cell method is combined with concurrent computational homogenization following the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mtext>FE</mtext>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathrm{FE}}^2 $$</annotation>\u0000 </semantics></math>-method. The proposed method is demonstrated for two examples, a simpler tensile experiment for testing purposes and a simplified, idealized deep drawing process.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"48 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.70007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145101404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spectral Normalization and Voigt–Reuss net: A universal approach to microstructure-property forecasting with physical guarantees","authors":"Sanath Keshav,&nbsp;Julius Herb,&nbsp;Felix Fritzen","doi":"10.1002/gamm.70005","DOIUrl":"https://doi.org/10.1002/gamm.70005","url":null,"abstract":"<p>Heterogeneous materials are crucial to producing lightweight components, functional components, and structures composed of them. A crucial step in the design process is the rapid evaluation of their effective mechanical, thermal, or, in general, constitutive properties. The established procedure is to use forward models that accept microstructure geometry and local constitutive properties as inputs. The classical simulation-based approach, which uses, for example, finite elements and FFT-based solvers, can require substantial computational resources. At the same time, simulation-based models struggle to provide gradients with respect to the microstructure and the constitutive parameters. Such gradients are, however, of paramount importance for microstructure design and for inverting the microstructure-property mapping. Machine learning surrogates can excel in these situations. However, they can lead to unphysical predictions that violate essential bounds on the constitutive response, such as the upper (Voigt-like) or the lower (Reuss-like) bound in linear elasticity. Therefore, we propose a novel spectral normalization scheme that a priori enforces these bounds. The approach is fully agnostic with respect to the chosen microstructural features and the utilized surrogate model: It can be linked to neural networks, kernel methods, or combined schemes. All of these will automatically and strictly predict outputs that obey the upper and lower bounds by construction. The technique can be used for any constitutive tensor that is symmetric and where upper and lower bounds (in the Löwner sense) exist, that is, for permeability, thermal conductivity, linear elasticity, and many more. We demonstrate the use of spectral normalization in the Voigt–Reuss net using a simple neural network. Numerical examples on truly extensive datasets illustrate the improved accuracy, robustness, and independence of the type of input features in comparison to much-used neural networks.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"48 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.70005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144773864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analytical estimates for elastic properties of composites accounting for canonical interfaces","authors":"Ali Javili","doi":"10.1002/gamm.70006","DOIUrl":"https://doi.org/10.1002/gamm.70006","url":null,"abstract":"<div>\u0000 \u0000 <p>The objective of this contribution is to provide novel analytical estimates for the effective properties of micro-heterogeneous elastic solids accounting for interfacial effects, and to compare the results with computational simulations using the finite element method. The interphase transition zone between different constituents in the microstructure here is replaced by the recently proposed <i>canonical interface model</i>. The canonical interface model encompasses all previous interface models such as the general interface model, the cohesive interface model, and the elastic interface model. This manuscript presents a comprehensive study covering a broad range of interface parameters and stiffness ratios, demonstrating the utility of the proposed solutions in understanding and fine-tuning composites behavior.</p>\u0000 </div>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"48 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A comparison of classical phenomenological, hybrid neural network, and high performance ROM FE2 models for open-cell foams: Efficiency, accuracy, and flexibility","authors":"Nils Lange,&nbsp;Alexander Malik,&nbsp;Martin Abendroth,&nbsp;Geralf Hütter,&nbsp;Bjoern Kiefer","doi":"10.1002/gamm.70004","DOIUrl":"https://doi.org/10.1002/gamm.70004","url":null,"abstract":"<p>Computational homogenization has become an attractive path to determine the macroscopic inelastic behavior of a structure from the knowledge of the behavior of its (usually simpler) constituents, using a Representative Volume Element (RVE) at the microscale. Since the numerical solution of both scales by means of the FE² method is prohibitively expensive, much research effort has been spent on the development of surrogate models, particularly by making use of data-driven machine learning methods. Due to the vast spectrum of proposed surrogate modeling approaches, the decision on the method of choice for potential applicants is difficult. While computational efficiency is usually used as the central performance measure, a careful distinction between on- and offline efforts is important. Moreover, the simulation context should also influence the selection. If, for instance, a thousand simulations are to be carried out for a single microstructure, the choice of approach may be different than if single, or a few, simulations are to be carried out for a thousand different microstructures. In the latter case, the flexibility and adaption effort of the method to new microstructures plays a key role. The present study aims to derive guidelines in this direction, by comparing different such approaches and carefully analyzing their performance in simulating inelastic macroscale behaviors, influenced by the morphology of 3D foam-like microstructures. Four formulations are considered: the Deshpande–Fleck phenomenological macroscale model, a general analytical surrogate model, a hybrid neural network surrogate model, and a hyper-reduced FE² approach. The methods are compared with respect to computational costs and predictive capabilities for two 3D benchmark scenarios.</p>","PeriodicalId":53634,"journal":{"name":"GAMM Mitteilungen","volume":"48 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/gamm.70004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144292863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}