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MiS Preprint
29/1997

Regularity for shearable nonlinearly elastic rods in obstacle problems

Friedemann Schuricht

Abstract

Based on the Cosserat theory describing planar deformations of shearable nonlinearly elastic rods we study the regularity of equilibrium states for problems where the deformations are restricted by rigid obstacles. We start with the discussion of general conditions modeling frictionless contact. In particular we motivate a contact condition that, roughly speaking, the contact forces should be directed normally, in a generalized sense, both to the obstacle and to the deformed shape of the rod. We show that there is a jump in the strains in the case of a concentrated contact force, i.e., the deformed shape of the rod will have a corner. Then we assume some smoothness for the boundary of the obstacle and derive corresponding regularity for the contact forces. Finally we compare the results with the case of unshearable rods and obtain interesting qualitative differences.

Received:
Oct 27, 1997
Published:
Oct 27, 1997

Related publications

inJournal
1998 Repository Open Access
Friedemann Schuricht

Regularity for shearable nonlinearly elastic rods in obstacle problems

In: Archive for rational mechanics and analysis, 145 (1998) 1, pp. 23-49