Takayuki ODA

On the numerical integration of three-invariant elastoplastic constitutive models

Yasuhiro MIYAKI

The objective of this paper is to implement a class of stress-point integration algorithms appropriate
for three-invariant isotropically hardening plasticity models that explicitly accounts for the rotation
of principal stress axes and to investigate the performance of a numerical algorithm for the integration
of isotropically hardening three-invariant elastoplastic constitutive models with convex yield surfaces.
The algorithm is based on a spectral representation of stresses and strains for infinitesimal and finite
deformation plasticity, and a return mapping in principal stress directions.In the present paper,
we propose to use the same return mapping in principal stress axes to handle the presence of all three stress
invariants in the plasticity theory.Many three-invariant plasticity models are conveniently expressed in terms
of the principal stresses themselves, so a return mapping in principal axes is a natural way of numerically
integrating the elastoplastic rate-constitutive relations in the presence of all three stress invariants.
Among the three-invariant plasticity models investigated in this paper are the Matsuoka-Nakai models,
widely used for representing the behavior of cohesive-frictional materials such as concrete, soil and rock.