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 fo r constitutive laws based on the microplane theory applicable to any kind o f rheological behavior. Therefore, a thermodynamically consistent concept o f deriving microplane based constitutive equations is presented, Microscopi c constitutive laws are formulated on characteristic material planes, the s o-called microplanes, resulting in an overall anisotropic macroscopic mater ial characterization. The microscopic strain components of one plane are de rived by the projection of the macroscopic strain tensor, leading to a kine matically constrained model. As proposed in the first part of this paper, t he introduction of individual potentials on each microplane yields thermody namically consistent microplane laws. They can be related to the macroscopi c material description through an integration over the hemisphere. The micr oplane laws are chosen such that the macroscopic version of the Clausius-Du hem inequality is satisfied. This generic concept will be applied to the cl assical models of elasticity, elasto-damage and elasto-plasticity. The resu lts are documented by the analysis of pointwise texture evolution for the m odel problems of uniaxial tension and simple shear. (C) 2001 Elsevier Scien ce Ltd. All rights reserved.