A Higher-Order Plate Element Formulation for Dynamic Analysis of Hyperelastic Silicone Plate

Most of previous work for modeling and analyzing various traditional linear elastic materials concentrated on numerical simulations based on lower-order absolute nodal coordinate formulation (ANCF) plate element, in which linear interpolation in transverse direction is utilized and stiffening effect caused by volumetric locking occurs. Relatively little attention is paid to modeling hyperelastic incompressible materials with nonlinear effect and large deformation. In view of this, a higher-order plate element formulation with quadratic interpolation in transverse direction for static and dynamic analysis of incompressible hyperelastic silicone material plate is developed in this investigation. The use of higher-order plate element can not only alleviate volumetric locking, but also improve accuracy in simulating large bending deformation as compared to improved lower-order plate element with selective reduced integration method and originally proposed lower-order plate element. Subsequently, experimental investigation that captures free-falling motion of silicone cantilever plate and corresponding simulations are implemented, the results obtained using higher-order plate element are in excellent accordance with experimental data, whereas the results gained applying other two types of plate elements are distinguished from experimental data. Finally, it is concluded that the developed higher-order plate element formulation achieves approving precision and has superiority in simulating large deformation motion of hyperelastic silicone plate.