On configurational forces in multiplicative elastoplasticity

Abstract

The main goal of this work consists in the elaboration of the material or rather configurational mechanics in the context of multiplicative elastoplasticity. This nowadays well-established approach, which is inherently related to the concept of a material isomorphism or in other words to a local rearrangement, is adopted as a paradigm for the general modelling of finite inelasticity. The overall motion in space is throughout assumed to be compatible and sufficiently smooth. According to the underlying configurations, namely the material and the spatial configuration as well as what we call the intermediate configuration, different representations of balance of linear momentum are set up for the static case. The underlying flux terms are thereby identified as stress tensors of Piola and Cauchy type and are assumed to derive from a free energy density function, thus taking hyperelastic formats. Moreover, the incorporated source terms, namely the configurational volume forces, are identified by comparison arguments. These quantities include gradients of distortions as well as dislocation density tensors. In particular those dislocation density tensors related to the elastic or plastic distortion do not vanish due to the general incompatibility of the intermediate configuration. As a result, configurational volume forces which are settled in the intermediate configuration embody non-vanishing dislocation density tensors while their material counterparts directly incorporate non-vanishing gradients of distortions. This fundamental property enables us to recover the celebrated Peach–Koehler force for finite inelasticity, acting on a single dislocation, from the intermediate configuration volume forces.