Stressed-deformed state in composite in conditions of inelastic pure shear

Formulation of the problem. In the mechanics of deformable solids and in the support of materials, as well as in the mechanics of composite materials, the main simple types of stress-strain state are used such as: pure tensile, pure compression and pure shear. In the case of pure tension (compression), in addition to longitudinal deformations (deformations along the direction of uniaxial stress), transverse deformations arise (deformations are normal to the load axis). With a pure shear, normal deformations to the shear planes are not taken into account. However, as shown in Part 1 and Part 2 of inelastic clean shear studies [10], in homogeneous materials with different resistance of tension and compression there are deformations normal to the displacement planes. In composite materials, such studies have not been conducted. The solution of tasks of this type in the mechanics of a deformable solid and in the support of materials, as well as in the mechanics of composite materials is not provided. Goal. On the basis of the methods and conditions of the mechanics of deformable solids and the resistance of materials, as well as earlier studies on inelastic clean shear [10], to determine the effect of linear continuous reinforcement of a composite on its deformation properties under pure shear. Conclusions. The stiffness of a composite at displacement (with a matrix having different plastic properties under tension and compression) beyond the elasticity of the matrix increases with increasing stiffness of the reinforcing elements even if the reinforcing elements are not capable of accepting the shearing forces. In studies of a stress-strain state in equations and systems of equations of equilibrium of effort it is necessary to take into account the deformation properties of materials both in tension and compression.