A Counterpoint to Cermelli and Gurtin’s Criteria for Choosing the ‘Correct’ Geometric Dislocation Tensor in Finite Plasticity

Abstract

The criteria in [4] (Cermelli and Gurtin, 2001, J. Mech. Phys. Solids, 49, 1539–1568) for choosing a geometric dislocation tensor in finite plasticity are reconsidered. It is shown that physically reasonable alternate criteria could just as well be put forward to select other measures; overall, the emphasis should be on the connections between various physically meaningful measures as is customary in continuum mechanics and geometry, rather than on criteria to select one or another specific measure. A more important question is how the geometric dislocation tensor should enter a continuum theory and it is shown that the inclusion of the dislocation density tensor in the specific free energy function in addition to the elastic distortion tensor is not consistent with the free energy content of a body as predicated by classical dislocation theory. Even in the case when the specific free energy function is meant to represent some spatial average of the actual microscopic free energy content of the body, a dependence on the average dislocation density tensor cannot be adequate.