The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place on Wednesday from 9:00 in lecture room K3. The talk will be given by Vít Průša and Karel Tůma. Please see the details below.
Speaker: Vít Průša and Karel Tůma
Title: A Thermodynamic Framework for Non-Isothermal Phenomenological Models for Mullins Effect
Abstract: The Mullins effect is a common name for a family of intriguing inelastic responses of various solid materials, in particular filled rubbers. Given the importance of the Mullins effect, there have been many attempts to develop mathematical models describing the effect. However, most of available models focus exclusively on the mechanical response, and are restricted to the idealised isothermal setting. We lift the restriction to isothermal processes, and we propose a full thermodynamic framework for a class of phenomenological models of Mullins effect. In particular, we identify energy storage mechanisms (Helmholtz free energy) and entropy production mechanisms that on the level of stress–strain relation lead to the idealised Mullins effect or to the Mullins effect with permanent strain. The models constructed within the proposed framework can be used in modelling of fully coupled thermo-mechanical processes, and the models are guaranteed to be consistent with the laws of thermodynamics.
Next, the system of governing equations, that are derived in the Eulerian setting, are transformed to the Lagrangian setting and used for simulations of several different problems such as the investigation of the interplay between the Mullins effect and the Gough-Joule effect or the study of the Mullins effect for a cylinder subjected to combined extension and torsion. The model is implemented in FEniCS finite element.