
Eulerian rates of elastic incompatibilities applied to sizedependent hardening in finite torsion M.B. Rubin Faculty of Mechanical Engineering, TechnionIsrael Institute of Technology, 32000 Haifa, Israel Lorenzo Bardella Department of Civil, Environmental, Architectural Engineering and Mathematics, University of Brescia, Via Branze, 43 25123, Brescia, Italy Abstract Measures of rates of elastic incompatibilities are developed within an Eulerian framework for finitedeformation response of anisotropic elasticinelastic materials. Such framework relies on the evolution of microstructural vectors. It is emphasized that the rates of incompatibilities, here denoted as R_{ij}, depend on the constitutive equation for the rate of inelasticity. For small strains and rotations, R_{ij} are equal to the negative of the components of the rate of NyeKroner's dislocation density tensor. In contrast to these small strain components, each R_{ij} is invariant under superposed rigid body motions such that it can be used independently in the constitutive equations to describe the material behavior. Specifically, in this work, R_{ij} provide a sizedependent enhancement to hardening that can increase or decrease during loading history, modeling the generation and annihilation of densities of geometrically necessary dislocations in metal plasticity. The application to the finitedeformation cyclic torsion of thin wires demonstrates the potential of this approach and the importance of the constitutive equation for the plastic spin rate both on the rotations of the microstructural vectors and on the predicted sizeeffect. Author Keywords: anisotropic elastic response; elastic incompatibility; elasticinelastic; Eulerian formulation; large deformation; smallscale metal plasticity; sizeeffect
