An augmented multicrack elastoplastic damage model for tensile cracking

In this paper we present the general formulation and numerical aspects of an augmented multicrack elastoplastic damage model aiming to reflect the crack induced anisotropy in concrete like quasi-brittle materials. Consistent evolution laws for the involved internal variables are derived based on the augmented Lagrangian method. The (time) discrete formulation and the corresponding variational structure are investigated, with the Euler-lagrangian equations defining the closest-point projection approximation of the proposed model. The numerical aspects, such as the stress updating algorithm and the algorithmic consistent tangent moduli, are also discussed in details. It is found that in the developed numerical algorithm the active loading surfaces are determined in such a posterior manner that potential numerical problems due to the iteratively updating procedure in classical algorithms can be avoided. The proposed model is applied to the modeling of tensile cracking in concrete. The behavior of a single crack is characterized by an elliptical cracking surface and a hyperbolic softening function, with the orientations of potential cracks determined by Mohr's postulate. The model is verified by calculating the single point stress vs. strain relations of concrete under several typical proportional and non-proportional loading cases. Finally, two benchmark tests of concrete structures, i.e. four-point bending beam under cyclic loading (Hordijk, 1992) and double edge notched specimens under mixed tension/shear forces (Nooru-Mohamed, 1992), are numerically simulated. Both predicted load vs. displacement curves and crack patterns agree well with the experimental data. (C) 2011 Elsevier Ltd. All rights reserved.