A priori error for unilateral contact problems with augmented Lagrange multipliers and IsoGeometric Analysis
It provides theoretical error bounds for contact mechanics simulations, which is incremental for computational mechanics researchers.
The paper extends a priori error estimates for unilateral contact problems using an augmented Lagrangian method with IsoGeometric Analysis, providing optimal error estimates validated in 2D and 3D for small and large deformations.
The aim of the present work is to extend the a priori error for contact problems with an augmented Lagrangian method. We focus on unilateral contact problem without friction between an elastic body and a rigid one. We consider the pushforward of a NURBS space of degree $p$ for the displacement and the pushforward of a B-Spline space of degree $p-2$ for the Lagrange multipliers. This specific choice of space is a stable couple of spaces. An optimal a priori error estimate inspired from the Nitsche's method theory is provided and compared to the regularity of the solution. We perform a numerical validation with two- and three-dimensions in small and large deformations with $N2/S0$ and $N3/S1$ elements.