A reduced basis method for frictional contact problems formulated with Nitsche's method

TL;DR

This paper introduces an efficient reduced basis method for frictional contact problems using Nitsche's formulation, employing Empirical Interpolation to handle nonlinearity, demonstrated on Hertz contact problems with parameter-dependent geometries.

Contribution

The paper presents a novel reduced basis approach combined with Empirical Interpolation for nonlinear frictional contact problems formulated via Nitsche's method.

Findings

Significant reduction in computational cost for contact problems.

Effective handling of nonlinearity through Empirical Interpolation.

Improved performance over traditional mixed formulations.

Abstract

We develop an efficient reduced basis method for the frictional contact problem formulated using Nitsche's method. We focus on the regime of small deformations and on Tresca friction. The key idea ensuring the computational efficiency of the method is to treat the nonlinearity resulting from the contact and friction conditions by means of the Empirical Interpolation Method. The proposed algorithm is applied to the Hertz contact problem between two half-disks with parameter-dependent radius. We also highlight the benefits of the present approach with respect to the mixed (primal-dual) formulation.