Reliability-Oriented Continuum Damage Mechanic of Notched Plates Based on Isotropic Damage Under Uniaxial Loading

The aim of this paper is the reliability analysis of rectangular plates containing a central circular hole under tensile and compressive axial load using the continuum damage mechanics approach. First, based on continuum damage mechanics, a one-dimensional inelastic constitutive equation of material with isotropic damage with respect to the stress sign effect on damage development is developed. The Neuber Method with linear and nonlinear hardening is used for the notch effect and stress concentrations. Then, the theoretical model is combined with damage models and implemented in ABAQUS software by the subroutine. Failure functions for the reliability analysis of the notch plate under in-plane loading are obtained based on the rate of released density energy in each of the Neuber and damage models. By using random variables and Failure functions, the reliability analysis is performed using the first-order reliability method and second-order reliability method. Based on the theory of ductile damage mechanics, the damage contour maps force–displacement curves for different hole sizes are obtained. Finally, the probability of failure of each notched plate with different hole sizes is approximated, and a sensitivity analysis of the coefficient of variation is performed.