Multiple Time Scale Modeling for Cyclic Deformation with Crystal Plasticity

摘要

In this paper,we propose a multi-time scale modeling technique for analyzing cyclic plastic deformation in crystalline solids subject to periodic loading.An asymptotic expansion of the variables in the time domain,together with homogenization forms the basis of multi-time scaling.In the macroscopic scale analysis,the oscillatory behavior of the load is averaged out and neglected,and the rate of averaged material behavior is quite slow in cyclic deformation.Implicitly,this means that the periodicity of some variables may be assumed for the oscillatory potion of the material behavior may be approximated.In this formulation,the governing equations are divided into two initial-boundary value problems with two different time scale:one is long time scale problem for describing the smooth averaged solution(global problem)and the other is for the remaining oscillatory potion(local problem).For the global problem,long time increments,which are longer than one cycle period,can be used and this multi-time scaling becomes an effective integrator.