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Within the theory of small deformations superposed on a finite one, a consistent
linearization for the nonlinear equations of the mechanics of an originally isotropic elastic
body in a neighborhood of some initial stress state is carried out in the Lagrange coordinate
system. As the elastic potential for the originally isotropic body, we use the representation of
the specific strain energy through the algebraic invariants of the Green-Lagrange strain tensor.
The linearized constitutive relations and the equations of motion of the prestressed medium
are derived that allow taking into account the nonlinear effects of the initial deformation on
the elastic properties of the originally isotropic body.
Keywords: initial stress, prestressed, initial deformation, elastic moduli of III orders, elastic moduli of IV orders, linearized theory, large initial deformations, elastic potential of IV orders |
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