AI summaryⓘ
The authors demonstrate how to use physics-augmented neural networks (PANNs) to improve material modeling in finite element simulations, which are used to predict how materials behave under stress. They developed a method to integrate pretrained neural networks into existing simulation software without needing special solvers, focusing on making the process faster and efficient. The paper also shows that changing a part of the network, the activation function, can reduce computation time while keeping accuracy. Their approach is made user-friendly by providing automated tools to generate code for these neural networks. They tested this method on a simulation of a material stretched a lot and found it matched known complex material behavior well.
Physics-Augmented Neural NetworksFinite Element MethodConstitutive ModelingHyperelasticityActivation FunctionSoftPlusSQuarePlusExplicit Finite Element SolverPyTorchUser Material Routine
Authors
Lukas Maurer, Sascha Eisenträger, Marian Bulla, Daniel Juhre
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.