A note on the physical meaning of gradient constitutive relations

TL;DR

This paper discusses the physical interpretation of gradient constitutive relations in gradient plasticity theory, aiming to clarify open questions and provide insights into size effect phenomena in heterogeneous materials.

Contribution

It offers a new interpretation of gradient terms, enhancing understanding of size effects and material instabilities in gradient plasticity.

Findings

Provides a new physical interpretation of gradient terms.

Clarifies the role of gradient plasticity in size effects.

Addresses open questions in the theory's application.

Abstract

Gradient plasticity theory proposed initially by Aifantis and co-workers has proven very useful in problems dealing with material heterogeneity and material instabilities. Although it has been used successfully in many applications by many authors, still some open questions remain unanswered. The modest goal of the present short note is to provide some thoughts on these open questions, providing a new interpretation of the gradient terms leading to a successful interpretation of both extrinsic and intrinsic size effect phenomena.