Variant of Nonlinear Elasticity Relations

Abstract

A nonlinear model of an isotropic elastic material is proposed, which is a generalization of the Murnagan model, in which the expansion of the specific potential energy of the strains in a series in powers of the Genki logarithmic strain tensor is used. The physical meaning of the constants included in the obtained relations is determined. Along with bulk modulus K and shear modulus G, constants c₁, c₂, c₃ associated with third-order moduli of elasticity were used: the constant c₁ reflects the nonlinear dependence of the hydrostatic stress on volumetric deformation, the constant c₂ reflects the dilatation effect, and the constant c₃ reflects the deviation of the stress state angle from the deformed state angle. The article is dedicated to the blessed memory of outstanding scientists A. A. Ilyushin and L. A. Tolokonnikov, whose ideas were developed in this work.