A thermodynamic study of materials representable by integral expansions

Abstract

A thermodynamic formulation is developed for nonlinear compressible viscoelastic materials and is used to quantitatively study the thermodynamic states associated with fracture. The Helmholtz free energy is assumed to be approximated by a fourth order multiple integral expansion on the histories of the Lagrangian strain tensor and temperature, and the first and second laws are then utilized to develop a constitutive equation and dissipation function for the material. Simplified expressions are obtained for the special cases of slow motions and long term steady flows. An experimental study is then made on equi-temperature metamorphosed snow, a nonlinear viscoelastic material, to determine the states associated with fracture for a variety of deformation paths. In view of the experimental study, the author is able to conclude that this approach to fracture investigation can produce much insight on the strength properties and may be instrumental in the formulation of a useful fracture criterion of materials for which the fracture condition is history dependent. Additionally, due to the thermodynamic nature of this approach, the information gathered could be useful in investigations of crack growth in nonlinear viscoelastic materials such as snow or even in the formulation of structural constitutive equations.