А review of studies on the linear relationship between stress and strain tensors (strain rate) is given. Kelvin approach is used in the works reviewed, which reveals the structure of this connection, based on six eigenmodules and six eigenstates. The case of transverse anisotropy is investigated in detail. Features of a transversely isotropic elastic model of geomaterials, analytical and numerical methods for solving the corresponding dynamic equations are considered. A formulation of constitutive equations of plasticity for describing the processes of forming the panel of an airplane wing, with a transverse isotropic plastic properties is discussed.
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