A Differentiable GPU-Accelerated Finite Element Framework for Inverse Characterization of Finite-Strain Anisotropic Plasticity

2026-06-15

AI Summary

This study addresses the challenge of efficiently and accurately inverting finite-strain anisotropic elastoplastic constitutive models in high-dimensional parameter spaces. To this end, we propose a JAX-based differentiable, GPU-accelerated finite element framework that tightly integrates automatic differentiation with finite element computations, eliminating the need for manual gradient derivation and enabling PDE-constrained inverse parameter identification. By leveraging heterogeneous specimen geometries inspired by topology optimization and full-field displacement measurements, the approach substantially reduces experimental dependency. Implemented on a single H100 GPU, the framework achieves up to 9.4× speedup over an Abaqus implementation running on a 24-core CPU and successfully recovers both homogeneous and spatially varying anisotropic yield and hardening parameters, demonstrating its efficiency and feasibility for high-dimensional inverse problems.

Abstract

We present a fully differentiable, GPU-accelerated finite element framework for forward simulation and inverse characterization of finite-strain anisotropic elastoplastic materials. Built on JAX, the framework exploits modern accelerator architectures by parallelizing the three major computational bottlenecks in nonlinear FEM: elemental weak-form and tangent-stiffness evaluation, global sparse matrix assembly, and sparse linear solution. For a large-scale forward problem with 3 million degrees of freedom, JAX-FEM on a single NVIDIA H100 GPU achieves up to 9.4$\times$ speed-up over a 24-core CPU Abaqus baseline. Automatic differentiation is applied through the constitutive update and solver workflow, providing consistent Jacobians for complex constitutive models without manual derivation and accurate gradients for PDE-constrained inverse analysis. Compared with finite differences, the JAX-AD gradients avoid step-size sensitivity and provide the required sensitivities at substantially lower computational cost. For inverse characterization, we combine information-rich, topology-optimized heterogeneous specimen geometries with full-field displacement data to identify complex constitutive models with many parameters that would otherwise require many conventional experiments to characterize. We demonstrate accurate recovery of anisotropic yield and hardening parameters in progressively challenging settings, including uniform and spatially varying material properties. The resulting AD-based formulation enables efficient optimization in high-dimensional parameter spaces where finite-difference approaches are computationally infeasible. These results establish differentiable, GPU-accelerated FEM as a practical high-throughput engine for simulation, characterization, and optimization workflows in advanced manufacturing.

Problem

• inverse characterization
• finite-strain anisotropic plasticity
• constitutive modeling
• parameter identification
• PDE-constrained optimization

Innovation

• differentiable FEM
• GPU acceleration
• automatic differentiation
• inverse characterization
• anisotropic plasticity