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.

中文翻译：

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非线性弹性关系的变化

提出了各向同性弹性材料的非线性模型，该模型是对Murnagan模型的推广，其中使用Genki对数应变张量的幂级数扩展了应变的比势能。确定包括在获得的关系中的常数的物理含义。连同体积模量K和剪切模量G一起，使用了与三阶弹性模量关联的常数c ₁，c ₂，c ₃：常数c ₁反映了静水压力对体积变形的非线性依赖性，常数c ₂常数c ₃反映了扩张效应，而常数c ₃反映了应力状态角与变形状态角的偏差。本文致力于纪念杰出科学家AA Ilyushin和LA Tolokonnikov，他们的想法是在这项工作中提出的。