Multi-scale constitutive model for fiber-reinforced concrete with FEM analyses of structural failure

A multi-scale constitutive model is developed for the efficient computational analysis of fiber-reinforced concrete structures. In a macro-scale material point the effective constitutive response of the fiber-reinforced concrete material is calculated by homogenizing the micro-scale behavior of its three constituents – fibers, cemented aggregate particles and air voids – across a representative volume element. The constitutive contact law for the cemented particles accounts for the fracture behavior under intergranular tension and shear, and the compaction/crushing behavior under intergranular compression. For the fibers, the tensile constitutive law is characterized by an initial elastic bonding between fiber and matrix, followed by fiber debonding and sliding and eventually complete pull-out. Under compression, the constitutive behavior of fibers is determined by an initial, elastic branch, which continues into a failure branch that captures their combined buckling and crushing behavior. The orientation distributions of the particle contacts and fibers are defined by separate probability density functions, and the effective Cauchy stress in a macro-scale material point is calculated by applying the Hill–Mandel micro-heterogeneity condition. Using an incremental-iterative update algorithm, the hierarchical multi-scale constitutive model is implemented within an Finite Element Method (FEM) framework. In order to accurately and robustly perform FEM simulations on complex boundary-value problems, the constitutive model is generalized towards a rate-dependent formulation. The applicability of the multi-scale model is exemplified by performing FEM simulations of the failure behavior of fiber-reinforced concrete samples under uniaxial tension, biaxial compression, triaxial compression, and four-point bending. The numerical results clearly indicate how the structural failure response of the samples is influenced by changes in loading direction, confining pressure, and fiber orientation distribution. The significance of the FEM results is further demonstrated through a comparison with experimental data reported in the literature, which shows that the model is well capable to accurately describe experimental responses for concrete samples with various fiber material properties and fiber volume fractions.