Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
63/2000

Variational approach to contact problems in nonlinear elasticity

Friedemann Schuricht

Abstract

We use variational methods to study problems in nonlinear 3-dimensional elasticity where the deformation of the elastic body is restricted by a rigid obstacle. For an assigned variational problem we first verify the existence of constrained minimizers whereby we extend previous results with different respects. Then we rigorously derive the Euler-Lagrange equation as necessary condition for minimizers, which was possible before merely with strong hypothetical smoothness assumptions for the solution. The Lagrange multiplier corresponding to the obstacle constraint provides structural information about the nature of frictionless contact and, in the case of contact with, e.g., a corner of the obstacle, we derive a qualitatively new contact condition taking into account the deformed shape of the elastic body. By our rigorous analysis it is shown the first time that energy minimizers really solve the mechanical contact problem.

Received:
Nov 4, 2000
Published:
Nov 4, 2000

Related publications

inJournal
2002 Repository Open Access
Friedemann Schuricht

Variational approach to contact problems in nonlinear elasticity

In: Calculus of variations and partial differential equations, 15 (2002) 4, pp. 433-449