Error analysis of the compliance model for the Signorini problem

Abstract

The present paper is concerned with a class of penalized Signorini problems also called normal compliance models. These nonlinear models approximate the Signorini problem and are characterized both by a penalty parameter ε and by a "power parameter" α ≥ 1, where α = 1 corresponds to the standard penalization. We choose a continuous conforming linear finite element approximation in space dimensions d = 2, 3 to obtain an L 2 -error estimate of order h 2 when d = 2, α = 2, ε ≥ θh (θ large enough) and when the solution is W 2,3 -regular. A similar estimate is obtained when d = 3 under slightly more restrictive assumptions on ε.

Formulating and Heuristic Solving of Contact Problems in Hybrid Data Driven Computational Mechanics

“…8 shows the resulting beam deformation. Again, solving (NLP2) and (NLP3) for confirmation reproduces the solution of step (1).…”

“…Note also that every solution x k above must have zero objective value; otherwise it is a non-physical NLP solution because the constitutive equation is violated. We finally note that in the specific examples below we never obtain solutions of (MPCC) with (NLP2) or (NLP3): either the quick shot terminates successfully in step (0) or (1), or it remains unsuccessful.…”

“…Solving static or dynamic contact problems is of great interest in many engineering applications, and substantial efforts have been made to study these problems and to solve them numerically [18,24,22,1]. The focus of this article is on a general strategy for solving problems with inequalities, specifically contact problems, whose formulation is based on the latest paradigm in continuum mechanics known as Data-Driven Computational Mechanics, or DDCM in brief.…”