Multi-scale modeling of fiber-reinforced concrete structures

A computationally-efficient multi-scale model is developed for the analysis of fiber- reinforced concrete (FRC) structures. At the macro-scale, the structural behaviour under mechanical loading is analysed using the Finite Element Method, where in each integration point the effective constitutive response of the FRC is computed considering a representative collection of cohesive particles, fibers and air voids and applying a homogenization technique known as the Granular Mi- cromechanics Approach. The micro-scale kinematic measures are calculated from the strain tensor in the material point by adopting the kinematic hypothesis. The micro-scale constitutive responses of the particle contacts and fibers are specified through path-dependent elasto-damage formulations. Theconstitutive laws of the particle contacts account for a strain-softening behavior for inter-granular tension and shear, and a strain-hardening behavior for inter-granular compression. The constitutive law for the fibers mimics the effect of elastic bonding between fiber and matrix, followed by fiber debonding and sliding under an increasing tensile load, eventually leading to complete pull-out. Un- der compression, the constitutive behaviour of fibers is determined by an initial, elastic branch, which continues into a failure branch that captures their combined buckling and crushing behaviour. The distribution of the fiber orientations is defined via a probability density function, and the homoge- nized Cauchy stress in a macro-scale material point is calculated by applying the Hill-Mandel micro- heterogeneity condition. The numerical solution procedure is strain-driven, where the macroscopic stress and tangential stiffness tensors are incrementally updated from the homogenized elasto-damage behavior of the particle contacts and fibers. The accuracy and efficiency of the multi-scale model are demonstrated by performing FEM simulations on the failure behavior of FRC samples subjected to uniaxial tensile load, and comparing the results to experimental data reported in the literature.