Two configurational approaches on the modelling of continuum dislocation inelasticity

Abstract

The main focus of this contribution consists in the elaboration of a continuum modelling approach accounting for dislocation-based quantities. Related deformation dependent history-variables are attached to individual material points and, moreover, are extended by means of gradients thereof so that so-called weak non-localities are captured. These gradients of internal variables may be further specified and in this regard are here reduced to particular representations of dislocation density tensors. While in this work we will make use of the concept of a material isomorphism—similarly present in the kinematic framework denoted as multiplicative decomposition—the approach itself can also be generalised, for instance with application to micromorphic continua. Apart from the non-simple kinematic framework, special emphasis is placed on the configurational mechanics perspective of the problem at hand. First, a variational strategy is discussed in detail, whereby the underlying stored energy density is assumed as an isotropic function in terms of its arguments. Later on, the configurational framework derived is compared with the configurational balance of linear momentum as based on straightforward transformation relations of its standard spatial representation. As a result, similar forms of the configurational Eshelby stresses are obtained for the two different approaches, and the related volume forces additionally incorporate contributions related to the material’s hereogeneities and inhomogeneities.