On the Experimental Determination of Constitutive Equations

Abstract

The widespread and economical use of computers to solve partial differential equations by finite element or finite difference methods has made it possible to consider nonlinear problems in thermomechanics representing large deformations and complex material behavior. In fact, it is relatively simple to formulate some finite difference and finite element methods in such a way that the constitutive equations can be inserted in subroutines without disturbing the remainder of the computer code implementing the method. As a result, there has been an increase in interest in the development of constitutive equations purporting to represent “realistic” material behavior in the nonlinear range. In some cases empirical equations have been proposed which have been fitted in some, usually restricted, way to experimental data. These have been inserted without further ado into the codes, and numerical solutions for specific and often very complicated initial-boundary value problems have been obtained as a result of many hours of computer time. Little attention has been given to the character of the theory resulting from the constitutive formulation, or to validation of results against exact solutions or experiments representative of the problems being solved.