Damage and plasticity in microplane theory

The paper deals with the microplane model, in which the stress-strain relations are defined independently on planes of all possible orientations in the microstructure, and the microplane stresses or strains are then constrained kinematically or statically to the macroscopic stress or strain tensor. The existing formulations of the microplane constitutive model for concrete are mainly based on the kinematic constraint. They have been shown capable of reproducing satisfactorily most experimental results available for concrete specimens, with the advantages of great conceptual simplicity, convenient numerical explicitness, intrinsic induced anisotropy and microcrack opening-closure conditions, etc. However, from the theoretical viewpoint little has been said about how these formulations relate to classical constitutive models of elasto-plasticity or continuum damage mechanics. In this paper, a new aperçu of microplane theory is achieved by systematically introducing damage and plasticity concepts into the microplane framework. New insight is provided on the role played by the split of the normal components, and on the role of the different possible types of micro-macro constraint. Specific formulations are developed and discussed within the new theoretical framework, which can be easily related to von Mises plasticity and to the existing models based on the second and fourth-order damage tensors.