Two-Dimensional Elastic Compliances of Materials with Holes and Microcracks

Details Two-Dimensional Elastic Compliances of Materials with Holes and Microcracks Two-Dimensional Elastic Compliances of Materials with Holes and Microcracks

Feb 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997rspsa.453..353z&link_type=abstract

Proceedings: Mathematical, Physical and Engineering Sciences, Volume 453, Issue 1957, pp. 353-364

Physics

7

Scientific paper

Recent work has reported the independence of the effective Young's modulus, E, of a two-dimensional (2D) isotropic matrix containing holes from the matrix material Poisson's ratio, ν m, if the effective medium remains isotropic. The present work gives the explicit relations between the effective and matrix elastic properties for an isotropic 2D matrix containing given holes and microcracks of any density, size, shape, distribution, and orientation in either isotropic or anisotropic arrangement. To this general case, it is rigorously proved that EmH, i.e. the damage compliance H (which is the difference S - Sm between the effective compliance S and the matrix compliance Sm) multiplied by the matrix Young's modulus Em is independent from both Em and the matrix material Poisson's ratio ν m. Consequently, the effective Young's modulus is independent of ν m, and the dependent relations of the effective shear and area bulk moduli on the matrix material Young's shear, area bulk moduli and Poisson's ratio are given. We also show that the 2D elastic properties of an isotropic or anisotropic solid can be written in terms of the area bulk modulus and the orientation distribution function of the extension modulus.

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