Implementation of Hyperelastic Physics-Augmented Neural Networks in the Explicit Finite Element Codes Simcenter Radioss and OpenRadioss with Applications to Impact Events

2026-06-29

AI Summary

This study addresses the challenge of accurately capturing the highly nonlinear response of hyperelastic materials under large-deformation impact, which traditional constitutive models struggle to represent. The authors integrate physics-augmented neural networks (PANNs) into industrial-scale explicit finite element solvers—Simcenter Radioss and OpenRadioss—by automatically generating Fortran user material subroutines for data-driven constitutive modeling. Key contributions include the first deployment of PANNs within industrial explicit solvers, the introduction of a computationally more efficient SQuarePlus activation function as a replacement for SoftPlus, and an open-source, automated toolchain enabling end-to-end subroutine generation. Experimental results demonstrate that the proposed approach achieves high accuracy while significantly reducing neural network evaluation overhead, offering an efficient and practical machine learning–based constitutive modeling paradigm for impact simulations.

Abstract

Data-driven material modeling techniques have gained significant attention due to their ability to capture complex constitutive behaviors beyond the limitations of classical material models. Physics-augmented neural networks (PANNs), which embed physical constraints directly into their architecture, combine the flexibility of machine learning with the reliability required for engineering simulations. This work presents an approach to integrate such network architectures into the explicit finite element solvers Simcenter Radioss and OpenRadioss (Siemens). A framework for transferring pretrained network architectures and their parameters to a standalone user material routine is developed. Networks are trained using PyTorch, though the procedure can be adapted to other frameworks such as TensorFlow, enabling the use of PANNs within existing finite element technology without requiring specialized solvers. Particular emphasis is placed on computational efficiency. The influence of network architecture on simulation performance is investigated, and strategies for reducing evaluation costs while preserving accuracy are discussed. Specifically, replacing the SoftPlus activation function with SQuarePlus is shown to reduce computational cost. A publicly available GitHub repository automates the generation of Fortran user material routines, requiring only the specification of the network architecture and trained parameters. An example impact simulation demonstrates that the generated PANN user material reproduces the nonlinear behavior characteristic of hyperelastic materials under large strains, providing a practical route toward machine-learning-based constitutive models in explicit finite element simulations.

Problem

• hyperelasticity
• physics-augmented neural networks
• explicit finite element simulation
• constitutive modeling
• impact events

Innovation

• Physics-augmented neural networks
• Explicit finite element method
• Hyperelastic material modeling
• User material subroutine
• Computational efficiency