A Shifted Cohesive-Zone Method for Non-Interface-Fitted Meshes with Applications to Crystal Plasticity

TL;DR

The paper introduces the Shifted Cohesive Zone Method (SCZM), enabling accurate interface mechanics simulations on complex microstructures without interface-fitted meshes by shifting enforcement to a surrogate interface.

Contribution

It extends the shifted boundary method to cohesive zones, providing a simple implementation for non-interface-fitted meshes in crystal plasticity simulations.

Findings

SCZM achieves first-order convergence in non-interface-fitted problems.

It closely matches interface-fitted solutions in reaction forces and deformation.

The method is efficiently implemented in the open-source MOOSE framework.

Abstract

The accurate simulation of interface-dominated solid mechanics problems on complex microstructures remains challenging, particularly when interface-fitted quadrilateral or hexahedral meshes are difficult to generate. We extend the shifted boundary method (SBM) to cohesive-zone formulations and introduce the Shifted Cohesive Zone Method (SCZM), with applications to crystal plasticity on non-interface-fitted meshes. By shifting the enforcement of traction-separation laws from the true interface to a nearby surrogate interface, SCZM enables the use of standard finite element spaces while avoiding the meshing burden associated with interface-conformal discretizations. We present a simplified SCZM weak form defined on the surrogate interface, leading to a straightforward implementation of the nonlinear residual and consistent tangent matrix. The method is implemented in the open-source MOOSE framework and coupled with constitutive models from NEML2, enabling simulations with linear elasticity, multiple traction-separation laws, and history-dependent crystal plasticity. We further develop a geometry-aware, PCA-enhanced point classification algorithm to accelerate surrogate-domain construction. Verification and benchmark studies in two and three dimensions demonstrate that SCZM achieves first-order convergence for non-interface-fitted interface problems and closely matches interface-fitted reference solutions in terms of reaction forces, surface energy release, deformation, stress fields, and damage evolution. These results indicate that SCZM provides an accurate and efficient framework for modeling interface mechanics in complex microstructures without requiring interface-fitted meshes.