SOLUTION OF LONGITUDINAL SHEAR PROBLEMS OF PHYSICALLY NONLINEAR BODIES WITH PROPERTIES DEPENDING ON THE TYPE OF STRESS STATE

Deformation properties of structural materials, rocks, composite materials, etc. depend on the type of external action, and the degree of this dependence is determined by the structural features of the materials. These materials are characterized by a relationship between volume and shear deformation. Deformation curves are nonlinear even at small deformations. This paper presents constitutive relations describing the nonlinear behavior of these materials under small deformations. It is shown that classical hypotheses of anti-plane shear cannot be applied. The problem of anti-plane shear of a long prismatic body with a square cross-section containing a round through hole in the plane of the cross-section is solved numerically. It is shown that under shear loading conditions, the body is characterized by a triaxial stress state and a change in volume.