Abstract 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 on‐the‐fly generation of physical models : 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.
Abstract 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.
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 FE 2 $$ {\mathrm{FE}}^2 $$ -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 FE 2 $$ {\mathrm{FE}}^2 $$ -method. The proposed method is demonstrated for two examples, a simpler tensile experiment for testing purposes and a simplified, idealized deep drawing process.
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.
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.
