Diffuse-interface polycrystal plasticity: Expressing grain boundaries as geometrically necessary dislocations

*Correspondence: [email protected] 1Materials Science and Engineering Department, University of California Los Angeles, Los Angeles, California, USA 2Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, California, USA Abstract The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in each grain, and imposing suitable traction and slip boundary conditions across grain boundaries. In this fashion, the system is modeled as a collection of boundary-value problems with matching boundary conditions. In this paper, we develop a diffuse-interface crystal plasticity model for polycrystalline materials that results in a single boundary-value problem with a single crystal as the reference configuration. Using a multiplicative decomposition of the deformation gradient into lattice and plastic parts, i.e. F(X , t) = FL(X , t)FP(X , t), an initial stress-free polycrystal is constructed by imposing FL to be a piecewise constant rotation field R0(X), and FP = R0(X)T, thereby having F(X , 0) = I , and zero elastic strain. This model serves as a precursor to higher order crystal plasticity models with grain boundary energy and evolution.