Equilibrium condition nonlinear modeling of a cracked concrete beam using a 2D Galerkin finite volume solver

A constitutive model based on two–dimensional unstructured Galerkin finite volume method (GFVM) is introduced and applied for analyzing nonlinear behavior of cracked concrete structures in equilibrium condition. The developed iterative solver treats concrete as an orthotropic nonlinear material and considers the softening and hardening behavior of concrete under compression and tension by using two equivalent uniaxial stress–strain relations. The concepts of current strength in a principal stress space and secant stiffness matrix are utilized to describe the biaxial behavior of concrete and the post–peak progress of stress–strain relation is modeled using the fracture energy method. Moreover, a smeared rotating crack method (SRCM) formulation is implemented in the solver to spot the nonlinear behavior of damaged structure. In order to demonstrate the performance of the model at a structural level, available experimental results of a notched beam under three point bending are presented. With the intention of demonstrating the post–peak performance of the model, the procedure of loading is simulated by imposing an incremental monotonic displacement. The envelope curve of equivalent load versus crack mouth opening displacement (CMOD) is utilized to evaluate the accuracy of the introduced method.