Three-dimensional simulation of finite-strain debonding using immersed meshes

We propose a method for modeling interfacial damage and debonding under quasi-static loads using immersed meshes in 3D at finite strains. This is an extension of our previous work on an immersed variational multiscale discontinuous Galerkin (VMDG) method in 2D. The variational approach remains the same, but transitioning from 2D to 3D introduces significant complications in the computational geometry aspects. The immersed VMDG method is a stabilized interface formulation derived using variational multiscale (VMS) ideas to apply discontinuous Galerkin (DG) treatment to the interface while employing a continuous Galerkin (CG) approximation elsewhere. Key benefits of VMDG are the variationally derived stabilization terms that evolve during deformation and are free of user-defined parameters. Also, the transition from perfect bond to damage behavior at the interface is handled naturally by incorporating an interfacial gap variable governed by a yield criterion and a flow rule. To support 3D simulations, we introduce algorithms for integrating cut elements, forming interface segments, and computing the VMDG stabilization tensor. Cut-element integration is performed using voxel-based moment-fitting integration to avoid the robustness issues associated with using mesh Booleans and tetrahedral integration cells. A simplification of the stabilization tensor is also proposed to reduce the computational cost while retaining the variational character of the stabilization. Several numerical examples are presented to demonstrate the robustness, efficiency, and range of applicability of the method.