A meshless grain element for micromechanical analysis

This study concerns the development of a 2-D meshless grain element for elastic deformation and intergranular damage initiation and propagation in polycrystalline fee metals under static loading. A nonlinear constitutive model known as the cohesive zone model is employed to represent the inelastic interaction between the grain boundaries; thus permitting grain boundary opening and sliding. The cohesive model describes the deformation characteristics of the grain boundaries through a nonlinear relation between the effective grain boundary tractions and displacements. Because of the presence of nonlinear behavior along the cohesive grain boundaries, the method utilizes the principle of virtual work in conjunction with the meshless formulation in the derivation of the system of nonlinear incremental equilibrium equations. The solution is obtained via an incremental procedure based on the Taylor series expansion about the current equilibrium configuration. The fidelity of the present approach is verified by considering simple polycrystalline metals of only a few grains.