Three-dimensional analytical model for effective elastic constants of transversely isotropic plates with multiple cracks: Application to stiffness reduction and steady-state cracking of composite laminates

An analytical three-dimensional effective elastic constant of transversely isotropic plates that include ply cracks is proposed using a continuum damage mechanics approach. Two damage parameters associated with tensile and shear damage are formulated as functions of ply crack density using local stress fields that satisfy the equilibrium equations. Three-dimensional laminate theory is then employed to formulate the effective compliance of the laminate using the effective compliance of a damaged ply, and an analytical steady-state cracking model is established. The proposed model reproduces the thermomechanical properties and the crack initiation stress of laminates.