Mechanics

2005, No. 6

S.A. Lychev, Yu.N. Saifutdinov

MOTION EQUATIONS OF A 3-LAYERED SPHERICAL VISCOELASTIC SHELL

In the present study the differential motion equations of a 3-layered spherical viscoelastic shell with asymmetrical layer structure and corresponding boundary conditions are obtained. The thickness of inner layer is much grater then outer ones. Kinematic relations of inner layer are given in the form of Mindlin shell theory, of outer layers   in the form of membrane theory. The material of outer layers are supposed to be isotropic elastic, whereas that of inner one being isotropic viscoelastic. The boundary conditions are taken in the general form of elastic fixing.

Y.N.Radayev, N.A. Kurnysheva

ON HYPERBOLIC PROPERTY OF THE COUPLED (PLASTIC STRAIN–DAMAGE) EQUATIONS

In the present study the problem of mathematical modelling of a stress-strain state of rigid-plastic solid with scattered anisotropic microdamages is considered. Damage is represented by a symmetric second-rank damage tensor. The principle axes of the damage tensor are assumed to coincide with principle axes of the Cauchy stress tensor. Closed system of static and kinematic equations of coupled (plastic strain–damage) theory in isostatic coordinate net in their incremental forms is obtained which appears subsequently most convenient for the coupled analysis. In the paper those cases when the resolving equations belong to hyperbolic type are discussed. Particularly this holds in the case of plane strain thus allowing to generalize slip lines theory known from perfect plasticity to coupled states.