Vol 73, No 2 (2018)

The unsteady collisions of plane counter-moving inviscid incompressible jets outflowing from channels are considered. The unsteady pattern of the flow is caused by a variation of pressure at the infinitely remote points of the channels. It is assumed that the velocity of the perturbed flow is small compared to the velocity of the steady flow. The Gurevich-Haskind method is used to solve the problem. A mixed boundary value problem for the complex potential of the perturbed flow is formulated and solved. For the case of straight channels and harmonic laws of pressure variation at the infinitely remote points, the equations for the deviation of free boundaries from their steady-state positions are numerically studied.

The analytic study of the nonlinear Maxwell-type constitutive relation for rheonomic materials with two material solutions is continued to reveal the capabilities of this relation to model rheological effects, its applicability scope, and the techniques of identification. The properties of the response to an arbitrary periodic loading program are considered. A criterion of its periodicity is obtained. A condition is found when the nonlinear Maxwell-type model adequately describes the stability effect as well as the hysteresis loop closure under symmetric cyclic loadings. It is shown that this condition is dependent on a single material function and is consistent with the simulation of resistance capabilities of materials.

A theory of constitutive relations describing the resistance of bodies to deformation is developed. This theory takes into account the presence of internal body forces and internal kinematic constraints. A number of axioms and a general reduced form of constitutive relations for classical media are proposed. For simple bodies it is proved that the Il'yushin and Noll constitutive relations are equivalent.