Elastic Plastic and Damage Model for Concrete Materials: Part II: Elastic Plastic and Damage Model for Concrete Materials: Part II:
In this companion article, we present, within the finite element context, the numerical algorithms for the integration of the thermodynamically consistent formulation of the elastic plastic and damage model for concrete materials derived in part I of this work. The proposed unified integration scheme is based on the spectral return-mapping algorithm accounting for the use of the principal stresses along with the stress tensor invariants. An operator split structure is used, consisting of a trial stress state followed by corrector steps applied through imposing the generalized plastic and damage consistency conditions. Furthermore, a trivially incrementally objective integration scheme is established for the rate constitutive relations. The proposed elastic-predictor and uncoupled plastic and damage corrector algorithms allow for a straightforward integration scheme that can be easily implemented into the existing finite element codes. The nonlinear algebraic system of equations is solved by consistent linearization and the Newton–Raphson iteration scheme. The proposed model is implemented in the implicit finite element code ABAQUS via the user subroutine UMAT. Model capabilities are illustrated through its application to the analysis of Reinforced Concrete (RC) beams tested experimentally and available in literature. The simulated results illustrate the potential of the proposed model in dealing with the reduction of the effect of the well known mesh sensitivity problem through the application of the fracture energy concept-related parameters.