Gradient-enhanced Coupled Plasticity- anisotropic Damage Model for Concrete Fracture: Computational Aspects and Applications RASHID K. ABU AL-RUB* Zachry Department of Civil Engineering, Texas A&M University College Station, TX 77843, USA GEORGE Z. VOYIADJIS Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70803, USA ABSTRACT: It is widely studied that classical continuum damage theory for con- crete fracture exhibits an extreme sensitivity to the spatial discretization in the finite element simulations. This sensitivity is caused by the fact that the mathematical description becomes ill-posed at a certain level of accumulated damage. A well-posed problem can be recovered by using a gradient-enhanced damage model in which a material length scale is introduced as a localization limiter. In this work, a nonlocal gradient-enhanced fully coupled plastic-damage constitutive model for plain concrete is developed. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. In order to account for different effects under tensile and compressive loadings, nonlocal damage variables that account for the progressive degradation of mechanical properties under stress states of prevailing tension and compression and two internal length scales, one for tension and the other for compression, are introduced as localization limiters. Therefore, two nonlocal damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. In order to solve the time step problem, a decoupled elastic predictor and plastic corrector steps are performed first in the effective configuration where damage is absent, and then a nonlocal damage corrector step is applied in order to update the final stress state. The algorithmic treatment of both tension and compression is presented in a unified way. A simple procedure to calculate the gradient of the tensile/compressive damage International Journal of DAMAGE MECHANICS, Vol. 18—March 2009 115 1056-7895/09/02 115–40 $10.00/0 DOI: 10.1177/1056789508097541 ß SAGE Publications 2009 Los Angeles, London, New Delhi and Singapore *Author to whom correspondence should be addressed. E-mail: rabualrub@civil.tamu.edu Figures 2–4, 7 and 11 appear in color online: http://ijd.sagepub.com