An energy-based ghost-force-free multivariate coupling scheme for bond-based peridynamics and classical continuum mechanics

In this work, we propose a novel energy-based multivariate coupling method for peridynamics and classical continuum mechanics (CCM) models to fully take advantage of their merits. The peridynamic model, which bypasses the continuity requirement of the displacement field, is applied where crack propagates or damage emerges, while the CCM model is used in the remaining region to save computational cost and enforce boundary conditions. The coupling of the two models is set to pass the energy and force patch tests by using a multivariate coupling parameter and modified elasticity tensor. This fundamentally eliminates the ghost force in a typical energy-based coupling scheme and preserves the energy equivalence. Depending on the existence of a solution to the discretized energy and force patch test equations, the multivariate coupling parameters and modified elasticity tensor are determined through an l(1)-minimization or a least-square technique with l(1)-regularization. Several one and two dimensional numerical examples are presented, which exhibit no ghost force and demonstrate the accuracy and efficiency of the coupling approach.