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

summary

The gist

The gist: This work presents an approach to integrate physics-augmented neural networks into explicit finite element solvers SIMCENTER RADIOSS and OPENRADIOSS by developing a framework for

In short

This work integrates Physics-Augmented Neural Networks (PANNs) into explicit finite element solvers like Simcenter Radioss and OpenRadioss. A framework allows transferring pre-trained network architectures and parameters to create standalone user material routines. By replacing the SoftPlus activation with SQuarePlus, the method achieves a practical route for using machine learning models in engineering simulations while maintaining computational efficiency.

Key concepts

Physics-Augmented Neural Networks (PANNs): These are neural networks designed to embed physical constraints directly into their structure. Instead of just learning data patterns, they are architected to ensure the resulting model adheres to known physical laws, making them reliable for engineering simulations.
Scalar Strain-Energy Density Function ($\psi$): This function mathematically describes the material's behavior under deformation. The paper uses this function instead of predicting stress directly; stresses and stiffness are derived by differentiating this potential using automatic differentiation methods embedded in the network.
SQuarePlus Activation Function: This is a specific mathematical activation function used within the neural network. It was chosen to replace SoftPlus because it reduces the computational cost when calculating material responses, offering a practical way to speed up simulations without losing accuracy.

Terminology used across episodes

Reinforcement Learning (RL) — explained in 25 episodes
Sample Complexity — explained in 18 episodes
Federated Learning — explained in 17 episodes
Quantum Fisher Information (QFI) — explained in 16 episodes
Retrieval-Augmented Generation (RAG) — explained in 16 episodes
Interpretability — explained in 15 episodes

This episode discusses

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

The paper

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

L. Maurer, S. Eisenträger, D. Juhre, M. Bulla

Institute of Materials, Technologies and Mechanics at Otto von Guericke University Magdeburg · Siemens Digital Industries

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.

DOI: 10.1002/nme.70439

Transcript

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: I'm Tom.

Jane: And I'm Jane, here with Lu, Meng and our in-house large language model, Lalam.

Tom: Today's paper: "Implementation of Hyperelastic Physics-Augmented Neural Networks in the Explicit Finite Element Codes Simcenter Radioss and OpenRadioss with Applications to Impact Events".

Jane: The gist:

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So to recap this paper, it’s about integrating physics-augmented neural networks into explicit finite element codes like Simcenter Radioss and OpenRadioss. The core thesis is that PANNs combine machine learning flexibility with the reliability needed for engineering simulations by embedding physical constraints directly into their architecture one <ref:2606.29874#pg2>.

Jane: And they achieve this by focusing on isotropic hyperelastic materials, using a strain-energy density function psi that depends only on the deformation state, and then using automatic differentiation to derive stresses from that potential.

Lu: They are showing an approach to transfer pretrained network architectures and their corresponding parameters into a standalone user material routine.

Meng: This is important because it means you don't need a specialized solver for the neural network part; you can use existing finite element technology without needing extra tools just for the model itself.

Tom: And they also show how to make this practical by automating the generation of Fortran user material routines using a script, which requires just specifying the architecture and parameters.

Jane: This approach is particularly interesting because it shows how you can use PyTorch for training but generate code that runs in a language like Fortran, which is what these solvers use.

Lu: It addresses the need to simplify material behavior in a controlled manner while still enabling reliable predictions of stresses and strains, which is a central task of material modeling one <ref:2606.29874#pg2,while still enabling reliable predictions of stresses and strains>.

Meng: So, it’s about taking complex material behavior and making it accessible inside existing explicit dynamics software. That’s what I care about for deployment.

Tom: And they also touched on computational efficiency by showing that replacing the SoftPlus activation function with SQuarePlus can reduce the computational cost of the PANN routine.

Jane: It’s a small saving, but it shows that you can optimize these models to run faster in practice, which is something every engineer wants to see.

Lu: The results show that this optimization leads to a net time saving for the one-hidden-layer network compared to the Carroll model when using SQuarePlus one <ref:2606.29874#pg2>.

Meng: So it's not just about getting a model that works; it's about making sure the runtime is low enough for real-world simulations.

Conclusion: Tom: So, wrapping up this talk on "Implementation of Hyperelastic Physics-Augmented Neural Networks in the Explicit Finite Element Codes Simcenter Radioss and OpenRadioss with Applications to Impact Events". The paper presents a framework for integrating these PANNs into explicit finite element solvers.

Jane: It essentially shows that physics-augmented neural networks can be incorporated into established explicit finite element workflows with manageable computational overhead.

Lu: The code-generation approach provides a practical step toward using machine-learning-based constitutive models in engineering simulations.

Meng: I think the real value is taking this from a concept and making it something deployable that engineers can actually use on their machines without needing to write complex solver integrations themselves.

Tom: And the authors are Maurer, Eisenträger, and Juhre from the Institute of Materials, Technologies and Mechanics at Otto von Guericke University Magdeburg. The implication is that this technique is a practical step toward incorporating AI into material modeling in explicit dynamics simulations one <ref:2606.29874#pg2>.

Jane: It means that instead of just relying on classical models for everything, you have a way to use these learned behaviors when you need them in high-speed impact events.

Lu: Future work should focus on generalizing the code-generation procedure to broader PANN architectures and incorporating the computation of consistent tangent stiffness matrices into that framework one <ref:2606.29874#pg2>.

Meng: Right, so the immediate path is getting a deployable tool that engineers can actually use for modeling large strains efficiently.

Tom: That seems like a solid summary of what this paper is about.

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