A plasticity model and algorithm for mode‐I cracking in concrete

A class of plasticity models which utilize Rankine's (principal stress) yield locus is formulated to simulate cracking in concrete and rock under monotonic loading conditions. The formulation encompasses isotropic and kinematic hardening/softening rules, and incremental (flow theory) as well as total (deformation theory) formats are considered. An Euler backward algorithm is used to integrate the stresses and internal variables over a finite loading step and an explicit expression is derived for a consistently linearized tangent stiffness matrix associated with the Euler backward scheme. Particular attention is paid to the corner regime, that is when the two major principal stresses become equal. A detailed comparison has been made of the proposed plasticity‐based crack formulations and the traditional fixed and rotating smeared‐crack models for a homogeneously stressed sample under a non‐proportional loading path. A comparison between the flow‐theory‐based plasticity crack models and experimental data has been made for a Single Edge Notched plain concrete specimen under mixed‐mode loading conditions.