Effective bending stiffness for plates with microcracks

In this paper, micromechanics methods are applied to characterize the damage of plate structures, both Love-Kirchhoff and Reissner-Mindlin plates, due to microcrack distribution. Analytical expressions for effective stiffness of a damaged plate with distributed microcracks are derived for the first time. The results are compared with the results based on continuum damage theory, and it is found that there are significant differences between the two. It is well known that constitutive relations at the structural level, e.g. curvature/moment relation, and shear/transverse strain relation, are fundamentally different from the constitutive relation at the material level, i.e. stress/strain relations. This is because a priori kinematic assumptions in engineering structural theories pose additional constitutive constraints on the relationships between stress resultant/couple and strain measures. The newly derived effective stiffness formulae for various plates reflect such constitutive constraints, and therefore are consistent with engineering plate theories. They provide an alternative means in structure designs and structure damage evaluations.