Geometric and material nonlinear effects in elastic-plastic and failure analyses of anisotropic laminated structures
In this study, an analytical procedure to predict the strength and failure of laminated composite structures under monotonically increasing static loads is presented. A degenerated 3-D shell finite element that includes linear elastic and plastic material behavior with full geometric nonlinearity is used to determine stresses at selected points (Gauss quadrature points in each element) of the structure. Material stiffness (constitutive) matrices are evaluated at each Gauss point, in each lamina and in each element, and when the computed stress state violates a user selected failure criterion, the material stiffness matrix at the failed Gauss point is reduced. The reduction procedure involves setting the material stiffnesses to unity. Examples of isotropic, orthotropic, anisotropic and composite laminates are presented to illustrate the validity of the procedure developed and to evaluate various failure theories. Maximum stress, modified Hills (Mathers), Tsai-Wu (F₁₂ = 0), and Hashin's failure criteria are included.
The results indicate that for large length-to-thickness ratios, the geometric nonlinear effect should be incorporated for both isotropic and anisotropic structures. The nonlinear material model influences the behavior of isotropic structures with small length-to-thickness ratios, while having nearly no effect at all on laminated anisotropic structures. Of the four failure theories compared, each predicts failure at nearly the same load levels and locations. Hashin's criterion is particularly noteworthy in that the mode is also predicted.