Abstract
The paper deals with establishing a rheological equation connecting the mean stress and deformation tensors in a structurally inhomogeneous elastic medium. The problem is formulated in the dynamic terms, and the defining equations are sought in the form of linear operator relations. The expression for the elastic operator is obtained in the form of a perturbation series, the terms of which represent a superposition of the linear integral operators. Partial sums of the series are obtained using the method of changing the field variables (taking into account the multiple scattering). An expression for the elastic operator kernel is obtained consisting of three different type terms, namely the quasi-static, couple stress and nonlocal terms.
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