A model for the interaction of dislocations with planar defects based on Allen–Cahn type microstructure evolution coupled to strain gradient elasticity

In classical elasticity theory the stress-field of a dislocation is characterized by $1/r$-type singularity. When such considered together with an Allen-Cahn-type phase-field description for microstructure evolution this leads to singular driving forces order parameter, resulting in non-physical (and discretization-dependent) predictions interaction between dislocations and phase-, twin- or grain-boundaries. We introduce framework based on first strain gradient regularize core. It shown that use energy density quadratic elastic deformation results non-singular stresses but may result forces, whereas energy, which full tensor, regularizes both parameter therefore suitable choice. The applicability demonstrated using comprehensive example.