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Mathematics and Mechanics of Solids
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Complete Elasticity Solution to the Stress Problem in a Planar Grained Structure

Shmuel Vigdergauz

R&D Division, The Israel Electric Corporation, Haifa 31000, Israel

This paper considers a planar elastic composite fonned by identical inclusions of a smooth shape embedded periodically in a background. Both materials are taken to be homogeneous and linearly isotropic. The paper addresses two major topics related to such media: the problem of solving their stress states and the attendant problem of computing the composite effective parameters. At given averages, the local stresses/strains are calculated to high accuracy using the well-known Kolosov-Muskhelishvili potentials, which perform well in many situations. This paper's contribution to this approach is twofold. First, the author introduces a new representation of the potentials that incorporates the stress periodicity and given average fields in a simple manner. Second, the author formulates the initial boundary value problem in a nonintegral form that saves computational effort when solving the resultant system of algebraic equations.

Mathematics and Mechanics of Solids, Vol. 4, No. 4, 407-439 (1999)
DOI: 10.1177/108128659900400402
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