What is the `Correct' Form of the Defect Energy Function in Gurtin's Strain Gradient Theory?

Lucia Nicola and Erik van der Giessen
University of Groningen
Netherlands Institute for Metals Research

Gurtin has recently proposed a strain-gradient theory for crystal plasticity where the gradient effect originates from a defect energy expressing the effect of elastic energy stored due to the presence of a net Burgers vector. The form of this energy function, however, is not pre-determined, nor are there many guiding principles.

In this contribution we explore a number of different possibilities for simple two-dimensional crystals and compare the results with those of discrete dislocation simulations of, for example, stress relaxation in thin films. The objective is to explore which functional dependencies are capable of capturing the size-dependent response of such systems for different crystal orientations. The findings will aid the further development of this theory.

This work is part of an on-going collaboration with Gurtin.