In this work a two-dimensional formulation, that describe the fracture process in rein-forced concrete, is developed, implemented and validated. The cracks in the material are captured by means of the continuum strong discontinuity approach (CSDA) (Oliver 1996) and the constitutive model of composite material is defined through the mixing theory (Trusdell & Toupin 1960).
The material is constituted by one or two groups of long fibers (steel bars) embed-ded within a matrix of concrete. Likewise, each component is characterized by a con-stitutive model. The concrete is described by a damage model with degradation in ten-sion and compression (Oliver, Cervera et al. 1990). A uniaxial plasticity model (Simó & Hughes 1998) is used for the steel. Also, phenomenon like bond-slip fiber-matrix and dowel action are included and represented by additional models.
The initiation and propagation of cracks are understood as a strain localization proc-ess and then are described by means of CSDA. A bifurcation analysis of composite material is proposed to establish the bifurcation time and direction of the crack.
The model has been implemented in a two-dimensional analysis program using the finite element method (FEM), where it is assumed material non-linearity and infinitesi-mal strains. An implicit-explicit integration scheme for the constitutive equation (Oliver, Huespe et al. 2004; Oliver, Huespe et al. 2006) ensures a positive defined stiff-ness matrix of the problem and increases the robustness and stability of the solution. On the another hand, a strategy to tracking discontinuity paths (Samaniego 2002; Oliver & Huespe 2004), allows that discontinuity paths match among elements.
According to the proposed formulation, on each point of solid, the deformation and tension fields of composite material like reinforced concrete are described.
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