Regularity for shearable nonlinearly elastic rods in obstacle problems

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...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 1998-11, Vol.145 (1), p.23-49
Main Author: SCHURICHT, F
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Mechanical contact (friction...)
Physics
Solid mechanics
Structural and continuum mechanics
Studies
Tribology and mechanical contacts
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Summary: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, requires the contact forces to 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 has 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.[PUBLICATION ABSTRACT]
ISSN:0003-9527
1432-0673
DOI:10.1007/s002050050123