ABSTRACT
CHAPTER 8
ELASTOPLASTIC CONSTITUTIVE
FRAMEWORK
This chapter provides a basic framework for the constitutive analysis of
elastoplastic materials. Such materials are capable of exhibiting, under cer-
tain loadings, purely elastic response at any stage of deformation. The de-
velopment is originally due to Hill and Rice (1973). Rate-independent and
rate-dependent plastic materials are both encompassed by this framework.
For rate-independent materials, purely elastic response results when stress
variations are directed within the current yield surface, which is introduced
for such materials. For rate-dependent materials, the response may be purely
elastic only in the limit, when stress variations are suÆciently rapid com-
pared to fastest rates at which inelastic processes can take place. We start
the analysis by dening elastic and plastic increments of stress and strain
tensors. Normality properties are then discussed for rate-independent plas-
tic materials which admit the yield surface. Formulations in both stress
and strain space are given. Plasticity postulates of Ilyushin and Drucker
are studied in detail. Conditions for the existence of ow potential for rate-
dependent materials are also examined.
