Finite-volume approach to thermoviscoelasticity

This article presents a development of the finite-volume method for solving linear thermoviscoelastic deformation problems. Hereditary continuum problems represented by spatially elliptic second-order partial differential equations with memory are considered. This is motivated by the need to develop numerical algorithms for the solution of thermoviscoelastic stress analysis problems, although it is expected that results presented will generalize to other Volterra problems. Assuming that the hydrostatic and deviatoric responses are uncoupled, and using the temperature-time equivalence hypothesis, the constitutive equations are expressed in an incremental form. Procedures for analyzing linear viscoelastic deformation are described, and numerical examples are given to demonstrate the effectiveness of the model and the numerical algorithms. The accuracy of the method is demonstrated through comparison with analytical and experimental results as well as with numerical solutions obtained elsewhere.