Modeling plasticity of cubic crystals using a nonlocal lattice particle method

In this paper, a novel nonlocal crystal plasticity lattice particle method (CPLPM) is proposed and verified for modeling plasticity of cubic crystals. The proposed CPLPM is fundamentally different from the classical crystal plasticity finite element method, in which the underlying lattice structures are explicitly incorporated in the model formulation and lattice rotation is used to represent the material anisotropy of crystals. As a first attempt to develop a comprehensive CPLPM framework, constitutive relations based on the Schmid's law and rate-dependent crystal plasticity for infinitesimal deformations are formulated for single crystals of face-centered and body-centered cubic lattice structures. Slip-system-dependent plastic deformation is automatically handled using the underlying crystal topology incorporated in LPM. Numerical solution algorithms for global iteration and plasticity state variables update are discussed in detail. The validity and prediction accuracy of CPLPM are established using several numerical examples, e.g., perfectly plastic deformation of single crystals, plastic slip near crack tip, and the calibration and prediction of experimental results. The performance of the CPLPM algorithm is also discussed considering different viscous properties.