Stochastic functional expansion in elasticity of heterogeneous solids
The Volterra-Wiener functional expansion is used to derive the elastic properties of random heterogeneous solids (elastic spheres as filler in an elastic matrix). An infinite set of equations is derived for the kernels in the integral expansion. The expansion is virial and truncating after the n-th equation gives statistical averages for the elastic properties correct to the n-th power of the sphere-filler volume concentration. Kernels for the first and second approximations are derived and related exactly and approximately (resp.) to the inclusion of one and two spheres in the matrix.
Kernels for the first and second approximations
scientific article; zbMATH DE number 3952084