An alternative way to describe thermodynamically-consistent higher-order dissipation within strain gradient plasticity

Abstract

In the context of strain gradient plasticity (SGP), description of higher-order dissipation is the subject of extensive on-going discussions. In most existing SGP theories including thermodynamically-consistent higher-order dissipation, higher-order dissipative processes are described based on the decomposition of the higher-order stresses into recoverable and unrecoverable parts. This higher-order stress decomposition represents the basis of the so-called non-incremental (Gurtin-type) SGP theories, which are the most commonly used in the literature. As formulated, these theories satisfy the thermodynamic requirement of non-negative dissipation. However, they generally lead to unusual effects for some boundary value problems, such as the occurrence of elastic gaps under non-proportional loading conditions. The present work proposes an alternative way to describe higher-order dissipative effects, with an illustration within strain gradient crystal plasticity (SGCP) framework. Inspired by rheological models in series like Maxwell model, the higher-order stress decomposition is replaced by a decomposition of the plastic slip gradients into recoverable and unrecoverable parts. Effects of this decomposition technique are studied and compared with those obtained using higher-order stress decomposition. Capabilities of such a technique to deal with elastic gaps are also investigated.