Hyperbolic/elliptic‐ CAP formulation for FRCC based on microplane constitutive theory

Abstract

The present work describes an elasto-plastic constitutive formulation aimed at simulating the failure behavior of Fiber Reinforced Cementitious Composites (FRCCs). This proposal, based on the Microplane Theory and Smeared Crack Approach (SCA), assumes a hyperbolic maximum strength criterion for the cementitious matrix in terms of normal and shear (micro-)stresses, evaluated on generally oriented planes (microplanes). A combination of an associated/ non-associated plastic flow rule in conjunction with a fracture energy-based softening law is defined to complete the modeling approach. The Mixture Theory is applied with the aim of characterizing the fiber-to-concrete interactions, described by considering two fundamental interaction phenomena: bridging debonding effects and dowel actions. Numerical analysis of FRCC failure behavior at the constitutive level is performed. Particularly, the soundness and capabilities of this approach are assessed against experimental data from tensile, shear, and compressive tests on FRCC samples. Simple shear tests are also evaluated to analyze the influence of the microplanes approximation over the unit microplane hemisphere. Comparisons against a discontinuous zero-thickness interface model are proposed. Numerical results also illustrate the capabilities of the proposed constitutive theory to reproduce brittle or localized failure modes in limit stress states through discontinuous bifurcation analysis.