Analysis of localized fracture in 3D reinforced concrete structures using volume averaging technique

In this paper, the propagation of localized damage in reinforced concrete structures is investigated in three dimensional domain. A mesoscale approach is employed whereby the material is perceived as a composite medium comprising two constituents, i.e. concrete matrix and steel reinforcement. The response at the macroscale is obtained via a homogenization procedure that incorporates the volume averaging. After the onset of cracking in concrete, a traction-separation law is introduced for the fractured zone, in which the Timoshenko beam theory is used to assess the stiffness characteristics in the presence of reinforcement. A general 3D scheme for tracing the crack geometry is incorporated, which employs a smoothening algorithm. The mathematical formulation is implemented in Abaqus user subroutine UMAT to verify the performance of the proposed methodology against the available experimental data. A number of numerical examples are given that examine the crack pattern formation and the associated fracture mechanism in concrete beams at different intensity of reinforcement.