Vol. 3, No. 5, 2008

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A thermomechanical framework of plasticity based on probabilistic micromechanics

Itai Einav and Ian F. Collins

Vol. 3 (2008), No. 5, 867–892

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.

micromechanics, thermomechanics, constitutive modelling, plasticity, probability, kinematic hardening
Received: 16 September 2007
Accepted: 10 December 2007
Published: 1 July 2008
Itai Einav
School of Civil Engineering
The University of Sydney
Sydney, NSW 2006
Ian F. Collins
Department of Engineering Science
The University of Auckland
Auckland 1142
New Zealand