Efficient higher-order zig-zag theory for viscoelastic laminated composite plates

An efficient higher-order plate theory for viscoelastic materials is developed to predict the time-dependent mechanical behaviors of composite laminates. In-plane displacement fields are constructed by superimposing a cubic varying displacement field on a linear zig-zag varying field. Time-dependent relaxation moduli have the form of Prony series, which can be determined by the master curve based on experimental data. The constitutive equation of linear viscoelastic materials in the form of the Boltzmann superposition integral is simplified by the convolution theorem of the Laplace transform to avoid direct integration as well as to improve both computational accuracy and efficiency. By using the equivalent linear elastic stress-strain relationship in the corresponding Laplace domain, the transverse shear stress-free conditions at the top and bottom surfaces and the transverse shear stress continuity conditions at the interfaces between layers are satisfied conveniently. Finally, the viscoelastic responses in the time domain are obtained through various numerical inverse Laplace transforms. To validate the present theory, the numerical results for graphite/epoxy GY70/339 material are obtained and compared with the solutions of elastic composite laminated plates.