On Constitutive Relations at Finite Strain: Hypo-elasticity and Elasto-plasticity with Isotropic or Kinematic Hardening*

The question of ‘generalization’ to finite strains of the constitutive relations of infinitesimal strain theory of elasticity, and classical elasto-plasticity with isotropic and kinematic hardening, is critically examined. Simple generalizations, which lead to physically plausible material behaviour, are presented. The current controversies surrounding (i) the choice of stress-rate in the above generalization and (ii) the ‘anomaly’ of oscillatory stresses in kinematic hardening plasticity, as discussed by E.H. Lee and others, are analyzed. It is found that these ‘controversies’ are easily resolvable.