Finite element analysis of 2-D thermoviscoelastic responses based on the free volume theory and a recursive formulation

A two-dimensional thermoviscoelastic problem is analyzed by the finite element method based on free volume theory and thermoviscoelasticity. The stresses are computed according to a shift factor; the shift factor is in turn calculated from the free volume ratio, defined as the free volume divided by the total volume. The free volume ratio depends on normal stress as well as hydrostatic pressure, in addition to temperature. The effect of hydrostatic pressure on the free volume ratio can be approached by an equivalent temperature effect. A finite element analysis is developed, in which the constitutive equations are formulated In recursive form. As a nonlinear analysis, the procedure finds the solution iteratively, using a shift factor as the convergence parameter. For poly(vinyl acetate) stress-strain curves under several loading conditions are discussed with respect to temperature and pressure.