Nonlinear laminated plate theory for determination of third order elastic constants and acoustic nonlinearity parameter of fiber reinforced composites

The present article reports on the development of a nonlinear laminated plate theory for fiber reinforced composites. The model uses material nonlinearity, i.e. nonlinear stress-strain relationship to describe the effective second (Cij) and third order (Cijk) elastic constants for a laminated plate. Since each lamina can have different fiber orientation, the rotation of the second and third order stiffness matrices were also incorporated into the model. Theoretical results for variation of third order elastic constants and the acoustic nonlinearity parameter with rotation angle have been presented. To validate the laminated plate theory, Nonlinear Resonant Ultrasound Spectroscopy (NRUS) experiments were carried out on seven different laminate systems with different fiber orientations and laminate sequences. Literature values for the elastic constants were used to predict the acoustic nonlinearity parameter and third order elastic constant. These were further compared with experimentally determined values, and a good agreement in the trend was observed. Since there are several combinations of fiber orientation and laminate sequence, the present theory will be helpful to determine the effective nonlinear properties of any given laminate system.