Recovering Mullins damage hyperelastic behaviour with physics augmented neural networks

TL;DR

This paper develops a physics-informed neural network model to accurately simulate Mullins damage in hyperelastic materials, ensuring physical constraints and enabling integration into standard simulation tools.

Contribution

It introduces a compact neural network architecture that incorporates physical restrictions to model Mullins damage in hyperelastic materials, trained on artificial data.

Findings

Accurately captures energy and stress responses.

Successfully models damage evolution.

Compatible with Abaqus simulation software.

Abstract

The aim of this work is to develop a neural network for modelling incompressible hyperelastic behaviour with isotropic damage, the so-called Mullins effect. This is obtained through the use of feed-forward neural networks with special attention to the architecture of the network in order to fulfil several physical restrictions such as objectivity, polyconvexity, non-negativity, material symmetry and thermodynamic consistency. The result is a compact neural network with few parameters that is able to reconstruct the hyperelastic behaviour with Mullinstype damage. The network is trained with artificially generated plane stress data and even correctly captures the full 3D behaviour with much more complex loading conditions. The energy and stress responses are correctly captured, as well as the evolution of the damage. The resulting neural network can be seamlessly implemented in widely used simulation software. Implementation details are provided and all numerical examples are performed in Abaqus.