Adiabatic heating effect in elastic-plastic contraction / expansion of spherical cavity in isotropic incompressible material

Abstract

The paper presents an analytical solution to the coupled problem of spherically symmetric elastic-plastic deformation accompanied by heating of the material due to the plastic dissipation, which in turn changes the mechanical properties of the material. The dependence of both elastic and plastic mechanical properties of the material on temperature can be arbitrary. Both elastic and plastic deformations are assumed to be finite. The thermal expansion of material is neglected. Heating is assumed to be adiabatic. Instead of a spatial coordinate, temperature is considered as an independent monotonic variable. This made it possible to reduce the problem to solving the first order ODE. The obtained solution is valid for any incompressible hyperelastic solid with arbitrary pressure-independent non-singular yield condition, perfectly-plastic or isotropic strain-hardening/softening. Example of solution for the linear thermal-softening and strain hardening material with tension-compression asymmetry in yielding is given.