Multi-scale analysis of viscoelastic–viscoplastic laminated composite plates using generalized differential quadrature method

Multi-scale analysis of laminated composite plates with viscoelastic–viscoplastic behavior of matrix is studied. Simplified unit cell method is developed to derive a new formulation for analysis of composite materials, including viscoelastic–viscoplastic matrix. The viscoelastic behavior of the matrix is modeled using Boltzmann superposition principle and the creep compliance is modeled using Prony series. Zapas–Crissman functional model is applied to obtain viscoplastic behavior of the matrix. In structural level, equations of equilibrium of laminated composite plate in terms of displacements have been derived using first order shear deformation theory with von Karman kinematic nonlinearity type. The nonlinear equations of equilibrium of plate are solved using generalized differential quadrature method. The details of the multi-scale analysis process have been discussed. Results include the effect of different parameters on creep behavior of composite materials in microscale and also micro-macro analysis.