Guangjin Mou | Searcharxiv

arXiv2026

On Exotic Materials in 3D Linear Elasticity with High Symmetry Classes

An anisotropic elastic material is referred to as exotic when, under specific loadings, its mechanical response exhibits a higher degree of symmetry than that prescribed by its intrinsic material symmetry. Such materials, which may be regarded as lying, conceptually and functionally, between two distinct symmetry classes, are of significant practical relevance. They enable the tailored design of metamaterials capable of reconciling otherwise incompatible mechanical requirements; for example, achieving directional isotropy of the Young's modulus in an intrinsically anisotropic medium. This work focuses on the systematic classification of exotic structures within the framework of three-dimensional linear elasticity. An exhaustive classification is carried out, leading to the enumeration of 18 exotic structures corresponding to symmetry classes higher than orthotropy. Representative examples of exotic elastic behaviours are analysed in detail.

math-ph↗

arXiv2026

Style-constrained inverse design of microstructures with tailored mechanical properties using unconditional diffusion models

Deep generative models, particularly denoising diffusion models, have achieved remarkable success in high-fidelity generation of architected microstructures with desired properties and styles. Nevertheless, these recent methods typically rely on conditional training mechanisms and demand substantial computational effort to prepare the labeled training dataset, which makes them inflexible since any change in the governing equations or boundary conditions requires a complete retraining process. In this study, we propose a new inverse design framework that integrates unconditional denoising diffusion models with differentiable programming techniques for architected microstructure generation. Our approach eliminates the need for expensive labeled dataset preparation and retraining for different problem settings. By reinterpreting the noise input to the diffusion model as an optimizable design variable, we formulate the design task as an optimization problem over the noise input, enabling control over the reverse denoising trajectory to guide the generated microstructure toward the desired mechanical properties while preserving the stylistic constraints encoded in the training dataset. A unified differentiation pipeline via vector-Jacobian product concatenations is developed to enable end-to-end gradient evaluation through backpropagation. Several numerical examples, ranging from the design of microstructures with specified homogenized properties to those with targeted hyperelastic and elasto-plastic behaviors, showcase the effectiveness of the framework and its potential for advanced design tasks involving diverse performance and style requirements.

cs.CE↗