A thermodynamically consistent approach to microplane theory. Part II. Dissipation and inelastic constitutive modeling

The main objective of the present work is to provide a general framework for constitutive laws based on the microplane theory applicable to any kind of rheological behavior. Therefore, a thermodynamically consistent concept of deriving microplane based constitutive equations is presented, Microscopic constitutive laws are formulated on characteristic material planes, the so-called microplanes, resulting in an overall anisotropic macroscopic material characterization. The microscopic strain components of one plane are derived by the projection of the macroscopic strain tensor, leading to a kinematically constrained model. As proposed in the first part of this paper, the introduction of individual potentials on each microplane yields thermodynamically consistent microplane laws. They can be related to the macroscopic material description through an integration over the hemisphere. The microplane laws are chosen such that the macroscopic version of the Clausius-Duhem inequality is satisfied. This generic concept will be applied to the classical models of elasticity, elasto-damage and elasto-plasticity. The results are documented by the analysis of pointwise texture evolution for the model problems of uniaxial tension and simple shear. (C) 2001 Elsevier Science Ltd. All rights reserved.