Flat geometric-nonlinear shear strains

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Abstract


Aims. The problem of differential equation construction characteristics and balances is being analyzed; and also the definitions of the planar wave rotational deformation travel time in the continuum, the mechanical character of which is described by the mathematical models geometrically nonlinear analogues in continuous body, the stress-strain stain of which is described by the undefined, basically, by the cross-connections between the first tensor invariant and the second invariant deviator of the stresses and nonlinear deformations. Methods. As an example let’s plot the specific speed of the transverse waves depending on the intensive rotational transverse deformation and the meanings of the material mechanical constants for the three mathematical models of the continuum: model 1 corresponds to the geometrically nonlinear analogue of the elasticity linear theory; model 2 corresponds to the geometrically nonlinear analogue of the small quantity elastoplastic strain theory; model 3 corresponds to geometrically nonlinear analogue of deformation theory of the loose medium plasticity. Conclusions. It is stated that in half-subspace the mechanical behavior of which is described by the deformation theory equations of the loose medium plasticity, the shock waves can appear in continuous boundary conditions.


About the authors

Sergej V Bakushev

Penza State University of Architecture and Construction

Author for correspondence.
Email: bakuchsv@mail.ru
28 Titov St., Penza, 440028, Russian Federation

Dr Sci. (Eng.), Professor of the Department of Mechanics

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