[Paper Review] MorteX method for contact along real and embedded surfaces: coupling X-FEM with the Mortar method

Basava Raju Akula, Julien Vignollet+1 more|arXiv (Cornell University)|Feb 3, 2019

Numerical methods in engineering33 references4 citations

TL;DR

This paper introduces the MorteX method, a novel X-FEM and mortar method coupling for frictional contact along real and embedded surfaces in 2D finite element analysis. It addresses mesh locking and spurious stress oscillations via coarse-graining of Lagrange multipliers, achieving accuracy comparable to classical mortar methods even under high material and mesh density contrasts.

ABSTRACT

A method to treat frictional contact problems along embedded surfaces in the finite element framework is developed. Arbitrarily shaped embedded surfaces, cutting through finite element meshes, are handled by the X-FEM. The frictional contact problem is solved using the monolithic augmented Lagrangian method within the mortar framework which was adapted for handling embedded surfaces. We report that the resulting mixed formulation is prone to mesh locking in case of high elastic and mesh density contrasts across the contact interface. The mesh locking manifests itself in spurious stress oscillations in the vicinity of the contact interface. We demonstrate that in the classical patch test, these oscillations can be removed simply by using triangular blending elements. In a more general case, the triangulation is shown inefficient, therefore stabilization of the problem is achieved by adopting a recently proposed coarse-graining interpolation of Lagrange multipliers. Moreover, we demonstrate that the coarse-graining is also beneficial for the classical mortar method to avoid spurious oscillations for contact interfaces with high elastic contrast. The performance of this novel method, called MorteX, is demonstrated on several examples which show as accurate treatment of frictional contact along embedded surfaces as the classical mortar method along boundary fitted surfaces.

Motivation & Objective

• To develop a unified framework for frictional contact between boundary-fitted and embedded (intra-mesh) surfaces in finite element analysis.
• To overcome the challenge of mesh locking and spurious stress oscillations arising from high elastic and mesh density contrasts across contact interfaces.
• To extend the monolithic augmented Lagrangian method within the mortar framework to handle embedded surfaces via X-FEM.
• To demonstrate that coarse-graining of Lagrange multipliers effectively stabilizes the formulation in both embedded and classical mortar contact problems.
• To validate the method on benchmark and realistic contact problems, showing accuracy comparable to classical mortar methods.

Proposed method

• Combines X-FEM with the mortar method to model contact between a real surface (boundary-fitted) and an embedded virtual surface (non-conforming to mesh).
• Employs the monolithic augmented Lagrangian method to enforce contact constraints, avoiding active-set strategies and ensuring robust convergence.
• Applies a mixed finite element formulation with Lagrange multipliers to enforce contact constraints weakly across non-matching interfaces.
• Introduces coarse-graining of Lagrange multipliers by assigning them only to selected master nodes and interpolating values to slave nodes via shape functions.
• Uses a subsampling strategy for Lagrange multipliers based on the local ratio of mortar nodes to blending elements, governed by mesh and material contrasts.
• Adapts the coarse-graining technique from prior work to stabilize both embedded surface (MorteX) and classical mortar contact formulations.

Experimental results

Research questions

• RQ1 Can a monolithic augmented Lagrangian approach with mortar method be effectively extended to handle frictional contact between real and embedded surfaces?
• RQ2 Why does the mixed formulation exhibit mesh locking and spurious stress oscillations under high material and mesh density contrasts?
• RQ3 Can triangular blending elements eliminate oscillations in the classical patch test, and is this sufficient for general contact problems?
• RQ4 Does coarse-graining of Lagrange multipliers significantly reduce spurious oscillations in both embedded and classical mortar contact scenarios?
• RQ5 Can the MorteX method achieve accuracy comparable to classical mortar methods while enabling efficient simulation of evolving interfaces like in wear?

Key findings

• The MorteX method successfully couples X-FEM and mortar methods to treat frictional contact along embedded surfaces with high accuracy.
• Spurious stress oscillations due to mesh locking are eliminated in the classical patch test using triangular blending elements.
• For general cases, triangular meshing alone is insufficient to prevent oscillations, necessitating stabilization via coarse-graining of Lagrange multipliers.
• Coarse-graining reduces the amplitude of spurious oscillations by more than two orders of magnitude under extreme contrasts (Young’s modulus ratio 1000, node-to-element ratio 10).
• The coarse-graining technique is also effective for classical mortar methods, stabilizing contact problems with high material and mesh density contrasts.
• The MorteX method produces accurate results free of oscillations for complex problems such as frictional contact between two cylinders and shallow ironing simulations.