Integration of Constitutive Equations in Soil Plasticity

Abstract

Explicit and implicit integration of elastoplastic constitutive relations subjected to the constraint of undrained behavior is investigated. The effect on numerical efficiency of various modes in terms of total stress and strain components is considered. The suggested explicit integration algorithm employs the appropriate tangent relation that incorporates the incompressibility condition and requires no iterations. The fully implicit algorithm used in this paper, on the other hand, is based on complete strain control and satisfies, in an iterative manner, the incompressibility constraint as well as equilibrium pertinent to any prescribed total stress component. The constitutive equation that is considered is a three-invariant generalized cam-clay model with volumetric hardening/softening as well as deviatoric hardening. Both the explicit and implicit methods seem reliable and efficient for reasonable load steps, even for nonconventional control paths.