A non-local constitutive model for the Mullins effect in filled elastomers

TL;DR

This paper extends a local constitutive model for filled elastomers to a non-local framework to address mesh dependence, introducing two approaches and providing implementation details and code.

Contribution

It develops two non-local formulations for the Mullins effect in filled elastomers, with numerical implementation and code provided.

Findings

Two different non-local models yield distinct results.

Implementation uses Abaqus with an analogy to the heat equation.

Code for the models is made available.

Abstract

Filled rubber-like materials are widely used in engineering applications and are well known to exhibit the Mullins effect. In this work, an established local constitutive model from the literature is extended to a non-local setting to resolve the mesh dependence inherent to the local approach. Non-local effects are incorporated using two separate approaches: (i) a Helmholtz-type equation governing a non-local soft volume fraction, and (ii) a Laplacian term introduced directly into the soft volume fraction local evolution law. In both formulations, an additional governing partial differential equation arises and is solved numerically in Abaqus using an analogy with the heat equation. The two approaches yield different results, leaving the choice between them to be guided by experimental findings. The details of the implementation, along with the code developed in this work are also provided.