Nonlinearly Elastic Properties of Stochastically Non-Uniform Media.

Nonlinear elastic properties of a solid body whose moduli are statistically isotropic random functions of the coordinates are investigated. A nonlinear dependence between stresses and strains is accepted in Kauderer's form. Using the small parameter method in the first approximation, the value of the macroscopic coefficient of nonlinearity of a two-component material is found. The result obtained can be employed to determine the nonlinearly elastic properties of materials reinforced by grains, chaotically oriented fibers, etc.