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Journal of Applied Mechanics and Technical Physics

2017 year, number 3

Symmetry Classes of Anisotropy Tensors of Quasielastic Materials and the Generalized Kelvin Approach

N. I. Ostrosablin
Lavrent'ev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: линейно-упругие материалы, квазиупругость, упругость по Коши, анизотропия, классы симметрии, собственные модули и состояния, linearly elastic materials, quasielasticity, Cauchy elasticity, anisotropy, symmetry classes, proper modes and states


The anisotropy matrices (tensors) of quasielastic (Cauchy-elastic) materials were obtained for all classes of crystallographic symmetries in explicit form. The fourth-rank anisotropy tensors of such materials do not have the main symmetry, in which case the anisotropy matrix is not symmetric. As a result of introducing of various bases in the space of symmetric stress and strain tensors, the linear relationship between stresses and strains is written in invariant form similar to the form in which generalized Hooke’s law is written for the case of anisotropic hyperelastic materials and contains six positive Kelvin proper modules. It is shown that the introduction of modified rotation deformations in the strain space can cause a transition to the symmetric anisotropy matrix observed in the case of hyperelasticity. For the case of transverse isotropy, there are examples of the determination of the Kelvin proper modules and proper bases and the rotation matrix in the strain space. It is shown that there is a possibility of existence of quasielastic media with a skew-symmetric anisotropy matrix with no symmetric part. Some techniques for the experimental testing of the quasielasticity model are proposed.