Incompressible inelasticity as an essential ingredient for the validity of the kinematic decomposition F = (FFi)-F-e

作者：Reina Celia^*; Conti Sergio

来源：Journal of the Mechanics and Physics of Solids, 2017, 107: 322-342.

DOI：10.1016/j.jmps.2017.07.004

• Crystal plasticity
• Finite deformations
• Growth
• Homogenization

The multiplicative decomposition of the total deformation F = (FFi)-F-e between an elastic (Fe) and an inelastic component (F-i) is standard in the modeling of many irreversible processes such as plasticity, growth, thermoelasticity, viscoelasticty or phase transformations. The heuristic argument for such kinematic assumption is based on the chain rule for the compatible scenario (Curl F-i = 0) where the individual deformation tensors are gradients of deformation mappings, i.e. F = D phi = D(phi(e) omicron phi(i)) = (D phi(e)) omicron phi' (D phi) = (FFi)-F-e. Yet, the conditions for its validity in the general incompatible case (Curl Fi not equal 0) has so far remained uncertain. We show in this paper that det F-i =1 and Curl F-i bounded are necessary and sufficient conditions for the validity of F = (FFi)-F-e for a wide range of inelastic processes. In particular, in the context of crystal plasticity, we demonstrate via rigorous homogenization from discrete dislocations to the continuum level in two dimensions, that the volume preserving property of the mechanistics of dislocation glide, combined with a finite dislocation density, is sufficient to deliver (F) over dot = (FFP)-F-e at the continuum scale. We then generalize this result to general two-dimensional inelastic processes that may be described at a lower dimensional scale via a multiplicative decomposition while exhibiting a finite density of incompatibilities. The necessity of the conditions det F-i = 1 and Curl F-i bounded for such systems is demonstrated via suitable counterexamples.

• 出版日期2017-10