On the thermodynamics of pseudo-elastic material models to reproduce the Mullins effect

TL;DR

This paper analyzes the thermodynamics of pseudo-elastic models for the Mullins effect, derives their properties, and proposes a generalized approach to incorporate softening effects in thermomechanical models.

Contribution

It provides a theoretical analysis of existing models and introduces a new thermodynamically consistent method to extend models with softening effects.

Findings

Thermomechanical properties of two pseudo-elastic models are derived.

A new approach to model softening effects via free energy is proposed.

Thermodynamic consistency of the generalized models is demonstrated.

Abstract

This work focuses on the thermodynamics of pseudo-elastic models which represent the Mullins effect. Two established models are analyzed theoretically, their thermomechanical properties are derived, and certain critical points are identified. These findings are used to deduce an alternative approach to deviate pseudo-elasticity. This is achieved by defining a suitable free energy which imposes conditions on the stress tensor and the dissipation using the Clausius-Duhem inequality. The concept of pseudo-elasticity is then generalized to extend arbitrary thermomechanical, even inelastic, material models to allow for softening effects. Under weak assumptions on the softening function the thermomechanical consistency is shown.