A conventional thermomechanical elasto-plastic constitutive modelling framework is
proposed but which allows an effective physical interpretation of the micromechanical
internal variables and inherent parameters in a representative volume element (RVE).
The statistical distribution of the elastic-plastic parameters within the RVE is
described using a simple statistical method of probabilistic rearrangement (MPR).
This method facilitates deriving analytical approximating formulas to the
stress-strain response of the RVE under unidirectional monotonic loading conditions.
The applicability of the MPR is validated numerically by comparing the analytical
formulas against numerical experiments of a probabilistic boundary value problem
initially under monotonic conditions. The assumptions associated with the MPR are
embedded within the simple micro thermomechanical constitutive framework and
further evaluated numerically by applying the methodology for the case of
cyclic loads. For the limited experimental program the constitutive modelling
framework seems to give a rather effective estimation of the full boundary value
problem. The results for the cyclic case demonstrate how hysteresis behaviour of
materials could be modelled without incorporating kinematic hardening
parameters.
