Linear elasticity with isotropic lognormal Young's modulus: localization of stresses and strains and effective stiffness tensor

摘要

We analyze the stresses σ and strains e in linear elastic solids when Young's modulus E varies spatially as an isotropic lognormal random field and Poisson's ratio v is constant. Under ergodicity conditions (when the spatial fluctuations of In E are of high frequency relative to the size of the solid), we study the localization properties of σ and ε and obtain an expression for the effective stiffness tensor K_(eff).