Modeling geometrically nonlinear large deformation behaviors of matrix cracked hybrid composite deep shells containing CNTRC layers

Stiffness degradation due to matrix cracks is the main initial form of damage in composite laminates. This paper presents a framework to model geometrically nonlinear large deformation behaviors of matrix cracked hybrid composite double-curved deep shell containing carbon nanotube reinforced composite (CNTRC) layers. Two types of structures, namely Structure-I and Structure-II, are investigated. The CNTRC layers in Structure-I are considered with CNTs arranged in uniformly distributions, while Structure-II is arranged in functionally graded distributions. The degraded stiffness of cracked layers is modeled via the self-consistent model (SCM) micromechanical framework. To describe the geometrically nonlinear large deflection behaviors and account for deep and moderate thick shells, the von Kármán geometric nonlinearity assumptions and the term 1/(1+ς/R) are considered in the relationship between displacement and strain. The IMLS-Ritz method is employed to discretize the non-linear partial differential equations. The modified Newton–Raphson method in combination with the arc-length iteration technique is adopted to solve the discretized equations. Comparison studies indicate that the proposed predictive model can furnish very accurate results for linear and nonlinear behaviors of thin to moderately thick as well as shallow and deep laminated doubly-curved shells. Parametric studies on the effect of CNT distribution, matrix crack density, load type, length-to-thickness ratio, radius-to-length ratio, aspect ratio, boundary condition, and fiber ply-angle on the geometrically nonlinear large deformation behaviors of spherical hybrid composite shells are investigated.