文档介绍：CHAPTER 5
CONSTITUTIVE MODELS
By Brian Moran
Northwestern University
Department of Civil Engineering
Evanston, IL 60208
©Copyright 1998
In the mathematical description of material behavior, the response of the material is
characterized by a constitutive equation which gives the stress as a function of the
deformation history of the body. Different constitutive relations allow us to distinguish
between a viscous fluid and rubber or concrete, for example. In one-dimensional
applications in solid mechanics, the constitutive relation is often referred to as the stress-
strain law for the material. In this chapter, some of the mon constitutive models
used in solid mechanics applications are described. Constitutive equations for different
classes of materials are first presented for the one-dimensional case and are then generalized
to multiaxial stress states. Special emphasis is placed on the elastic-plastic constitutive
equations for both small and large strains. Some fundamental properties such as
reversibility, stability and smoothness are also dsicussed. An extensive body of theory
exists on the thermodynamic foundations of constituive equations at finite strains and the
interested reader is referred to Noll (1973), Truesdell and Noll (1965) and Truesdell
(1969). In the present discussion, emphasis is on the mechanical response, although
coupling to energy equations and thermal effects are considered.
The implementation of the constitutive relation in a finite element code requires a
procedure for the evaluation of the stress given the deformation (or an increment of
deformation from a previous state). This may be a straightforward function evaluation as
in hyperelasticity or it may require the integration of the rate or incremental form of the
constitutive equations. The algorithm for the integration of the rate form of the constitutive
relation is called a stress update algorithm. Several stress update algorithms are presented
and disc