VARIOUS MODELS OF INTERNAL FRICTION USING IN CALCULATIONS OF HYPERELASTIC SHELLS DYNAMIC DEFORMING

Physically and geometrically nonlinear initial boundary value problem statement concerning hyperelastic shell of revolution deforming taking into account internal friction is represented in the work. Three models of viscosity are considered – Voigt, Maxwell and large viscoelastic strains. For problem solution method of lines combined with parameter continuation method is used. At this time derivatives of resolving variables are replaced by their four-point approximations. Thus nonlinear initial boundary value problem is reduced to a nonlinear boundary value problem, solved consequently for each time layer. Differentiation parameter for this problem is used in the form suggested by V.I. Shalashilin. As an example the problem of spherical shell made of neohookean material inflation is considered. Cases of suddenly applied constant pressure and harmonic pressure are investigated. Parameters of classical models of internal friction are chosen in such a way that for Maxwell and large viscoelastic strains models values of relaxation time coincide, and for Maxwell and Voigt models values of damping coefficient coincide. For the case of shell inflation by constant pressure large viscoelastic strains model using leads to occurrence of oscillation process with constant amplitude which is much smaller than shell oscillations amplitude without taking internal friction into account. In the case of harmonic pressure acting the same character of differences of calculation results obtained using large viscoelastic strains model and Voigt or Maxwell models remains. Investigation of time dependence of elastic and viscous strains calculated by Maxwell and large viscoelastic strains showed existence of elastic strain oscillations characterized by the smallest frequency for Maxwell model.