arXiv subjects

Amirhossein Amiri-Hezaveh

Publications and source records attributed to Amirhossein Amiri-Hezaveh.

3 recordsLinked to original sources

arXiv2026

A Differentiable Framework for Gradient Enhanced Damage with Physics-Augmented Neural Networks in JAX-FEM

Soft materials such as rubbers, hydrogels, and biological tissues undergo damage in the form of stiffness degradation without apparent changes in their stress-free geometry. Accurate simulation of this behavior is critical in applications ranging from soft robotics to the design of medical devices, yet two persistent challenges are the difficulty of constructing flexible, thermodynamically consistent constitutive models, and the mesh dependence of finite element solutions caused by strain softening. Here we address both challenges simultaneously by combining physics-augmented neural network constitutive models with a gradient-enhanced damage formulation implemented within the differentiable finite element framework JAX-FEM. The elastic strain energy and the damage yield function are each parameterized by input-convex neural networks (ICNNs), which enforce polyconvexity and satisfaction of the Clausius--Duhem inequality by design. The gradient-enhanced formulation introduces a non-local damage field governed by an additional partial differential equation, regularizing the spatial distribution of damage and eliminating mesh dependence. The implementation is validated through local stress-strain fits, single-element parametric studies, a mesh and solution strategy study for a uniform deformation case, and a notched plate simulation. The results demonstrate that the proposed framework enables flexible, data-driven, mesh-independent damage simulation for a broad class of soft materials. We anticipate that the open-source implementation will lower the barrier to adopting physics-augmented neural network constitutive models.

cs.CE↗

arXiv2025

Fully data-driven inverse hyperelasticity with hyper-network neural ODE fields

We propose a new framework for identifying mechanical properties of heterogeneous materials without a closed-form constitutive equation. Given a full-field measurement of the displacement field, for instance as obtained from digital image correlation (DIC), a continuous approximation of the strain field is obtained by training a neural network that incorporates Fourier features to effectively capture sharp gradients in the data. A physics-based data-driven method built upon ordinary neural differential equations (NODEs) is employed to discover constitutive equations. The NODE framework can represent arbitrary materials while satisfying constraints in the theory of constitutive equations by default. To account for heterogeneity, a hyper-network is defined, where the input is the material coordinate system, and the output is the NODE-based constitutive equation. The parameters of the hyper-network are optimized by minimizing a multi-objective loss function that includes penalty terms for violations of the strong form of the equilibrium equations of elasticity and the associated Neumann boundary conditions. We showcase the framework with several numerical examples, including heterogeneity arising from variations in material parameters, spatial transitions from isotropy to anisotropy, material identification in the presence of noise, and, ultimately, application to experimental data. As the numerical results suggest, the proposed approach is robust and general in identifying the mechanical properties of heterogeneous materials with very few assumptions, making it a suitable alternative to classical inverse methods.

cs.LG↗

arXiv2025

A Physics-Augmented Machine Learning Constitutive Model for Damage in Solids

We propose a data-driven constitutive framework for anisotropic damage mechanics based on the second-order damage tensor approach for both compressible and incompressible materials. The formulation is thermodynamically consistent and satisfies the Clausius-Duhem inequality. The strain energy density potentials are expressed as isotropic functions of the right Cauchy-Green deformation tensor, along with structural tensors that encode anisotropy either present in the virgin material or resulting from damage. To guarantee the polyconvexity condition, non-decreasing convex neural networks with inputs that ensure polyconvexity are used to parameterize the strain energy density potentials. The model vanishes in the undeformed state, fulfilling the normality condition. In contrast to classical [1-d] damage models, the expressiveness of the new data-driven model is enhanced by employing a family of nonlinear, convex, decreasing functions to capture the effect of damage. Damage evolution is governed through a damage potential, where the corresponding threshold is defined in terms of the damage conjugate forces. As a special case of the general formulation, a new anisotropic generic format is introduced to predict constitutive responses under damage-induced anisotropy in initially isotropic materials. To reduce the computational burden during training, a decoupled training scheme is introduced, and its accuracy is demonstrated in all numerical examples. These include benchmarks for incompressible isotropic, transversely isotropic, and compressible orthotropic materials. The framework is also validated against experimental data capturing anisotropic Mullins-type damage.

physics.app-ph↗