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Mathematics and Mechanics of Solids
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Stress Distribution Around a Crack in Anti-Plane Micropolar Elasticity

E. Shmoylova

Department of Civil and Environmental Engineering, Tufts University, Medford, MA 02155, USA

S. Potapenko

Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

In this paper we formulate the boundary value problem of anti-plane micropolar elasticity for a domain containing a crack in Sobolev spaces and prove the existence and continuous dependence on the data of the corresponding weak solutions. We consider the cases of both finite and infinite domain and find the solutions in terms of modified single layer and modified double layer integral potentials with distributional densities.

Key Words: Anti-plane micropolar elasticity • weak solutions • boundary integral equation method • cracks in micropolar medium

This version was published on April 1, 2008

Mathematics and Mechanics of Solids, Vol. 13, No. 2, 148-171 (2008)
DOI: 10.1177/1081286506074881
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