Accurate eccentric impact analysis of the preloaded SMA composite plates, based on a novel mixed-order hyperbolic global-local theory

Various high-order polynomial, trigonometric, exponential, and hyperbolic plate theories have recently been proposed. Majority of these theories have described the displacement field through odd functions to satisfy the zero shear traction condition on the top and bottom surfaces of the plate and thus are mainly suitable for symmetric lamination schemes or material properties distributions. In the present paper, a higher-order global-local hyperbolic plate theory that includes both odd and even functions and consequently, is especially adequate for description of the general asymmetric displacement fields, is proposed. This theory is employed to investigate the complicated responses of a pre-stressed composite plate with SMA wires subjected to a low velocity eccentric impact. Non-uniform and time-dependent distributions of the phases of the SMA wires are considered instead of using the simple recovery stress or uniform martensite volume fraction distribution approaches. A refined contact law based on a proper homogenization technique is proposed instead of using the traditional Hertz law. The resulting highly nonlinear finite element governing equations are solved by an iterative algorithm within each time step. Different contact laws are considered for the loading and unloading phases. A comprehensive parametric study is accomplished to study effects of the pre-stresses, eccentricity, and lamination schemes.