An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact

Abstract

We propose an enriched finite element formulation to address the computational modeling of contact problems and the coupling of non-conforming discretizations in the small deformation setting. The displacement field is augmented by enriched terms that are associated with generalized degrees of freedom collocated along non-conforming interfaces or contact surfaces. The enrichment strategy effectively produces an enriched node-to-node discretization that can be used with any constraint enforcement criterion; this is demonstrated with both multi-point constraints and Lagrange multipliers, the latter in a generalized Newton implementation where both primal and Lagrange multiplier fields are updated simultaneously. We show that the node-to-node enrichment ensures continuity of the displacement field—without locking—in mesh coupling problems, and that tractions are transferred accurately at contact interfaces without the need for stabilization. We also show the formulation is stable with respect to the condition number of the stiffness matrix by using a simple Jacobi-like diagonal preconditioner.

An object‐oriented geometric engine design for discontinuities in unfitted/immersed/enriched finite element methods

“…The method can seamlessly resolve boundaries so it can be used to solve immersed boundary (fictitious domain) problems—and with smooth reactive tractions in Dirichlet boundaries 36,37 . In addition, IGFEM has been used to prescribe Bloch‐Floquet periodic boundary conditions in the analysis of phononic crystals, 38 and for coupling non‐conforming meshes and highly nonlinear contact problems 39 . In the context of topology optimization, IGFEM has been used for compliance minimization, 33 and for tailoring the fracture resistance in brittle structures 40 .…”

“…36,37 In addition, IGFEM has been used to prescribe Bloch-Floquet periodic boundary conditions in the analysis of phononic crystals, 38 and for coupling non-conforming meshes and highly nonlinear contact problems. 39 In the context of topology optimization, IGFEM has been used for compliance minimization, 33 and for tailoring the fracture resistance in brittle structures. 40 Finally, IGFEM has also been generalized for the unified treatment of both weak and strong discontinuities in the Discontinuity-Enriched Finite Element Method (DE-FEM).…”

A multi-point constraint unfitted finite element method

“…In each of these methods (GFEM, XFEM and Cut-FEM), the enrichments are associated with element nodes. An alternative approach is to associate the enrichments directly with the discontinuity itself, as seen in the discontinuity enriched (DEFEM) [29,30] (see also the interface enriched method [31,32]) and the element enriched finite element method (EFEM) [33][34][35][36][37][38][39].…”