DYNAMICS OF A VISCOELASTIC SPHERICAL-SHELL WITH A NONCONVEX STRAIN-ENERGY FUNCTION

We study the radial motion of an incompressible viscoelastic spherical shell. with a nonconvex strain energy function that models a material that can undergo a phase transition. In addition to the classical New tonian viscosity for viscoelastic materials, we consider a material wi th two microstructural coefficients that are supposed to sense local c onfigurational changes that take place during a deformation. Condition s necessary to show the effect of the nonconvexity of the strain energ y function during a phase transition of the material, are determined, and the resulting dynamics is analyzed. It is shown that, though small periodic vibrations are possible, the system can easily revert into a mode of large amplitude motion as a result of small external excitati on. Such motion may be transient to periodic motion or to chaotic moti on. Boundaries in parameter space for the occurrence of this type of m otion are determined and examples are given.