Fluid Model of Crystal Plasticity: Numerical Simulations of 2-turn Equal Channel Angular Extrusion

Considering severe plastic deformation experiments as a motivation, the plastic behaviour of crystalline solids is treated as a flow of a highly viscous, compressible material. Starting from classical single crystal hypothesis we present a purely Eulerian set of equations describing flow of a plastic material. Moreover, we provide a thermodynamic justification of the evolution of the Cauchy stress based on the Gibbs potential. Numerical simulations for a 2-turn equal channel angular extrusion are reported

Transport of congestion in two-phase compressible/incompressible flows

We study the existence of weak solutions to the two-phase fluid model with congestion constraint. The model encompasses the flow in the uncongested regime (compressible) and the congested one (incompressible) with the free boundary separating the two phases. The congested regime appears when the density in the uncongested regime achieves a threshold value that describes the comfort zone of individuals. This quantity is prescribed initially and transported along with the flow. We prove that this system can be approximated by the fully compressible Navier–Stokes system with a singular pressure, supplemented with transport equation for the congestion density. We also present the application of this approximation for the purposes of numerical simulations in the one-dimensional domain