Prediction of Laminate Stiffness Reduction by Regression Equations for Damage Variables Obtained From the Stress-Based Variational Model

Abstract

Continuous fiber-reinforced materials have low strength under loads perpendicular to the fibers, and transverse cracks easily occur parallel to the fibers. Since transverse cracks cause a reduction in stiffness and strength of continuous fiber-reinforced laminates, understanding the mechanical behavior of cracked laminates is of great importance, and many studies have been conducted. Among these studies, there is the continuum damage mechanics (CDM) model, which directly reflects the effect of damage modes in the constitutive law with the idea of damage variables, and the stress-based variational model, which uses the principle of minimum complementary energy to obtain a three-dimensional stress field in a cracked laminate to predict stiffness. Although the variational model can accurately predict the stiffness degradation of a cracked laminate, it is much more complicated than the continuum damage mechanics model in terms of the expression of the theoretical solution and the computational process. In this study, we derived explicit closed-form expressions for damage variables within the CDM framework, based on the variational model's calculations, estimating both the in-plane and out-of-plane laminate thermoelastic properties. This combines the simplicity of CDM with the accuracy of the variational approach. The damage variables are expressed explicitly using normalized values, incorporating cracked ply material and geometrical properties, crack geometry, and adjacent ply properties, making them applicable to a wide range of laminate materials and crack configurations. The validity of the regression equations was verified by comparing them with the previous CDM model's results, finite element analysis results, and experimental data.