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

Abstract

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.

Mechanical Deformation Analysis of a Flexible Finger in Terms of an Improved ANCF Plate Element

“…A dynamics simulation is carried out to calculate the movement process of the flat pendulum under the action of gravity (along the negative Z-axis), and the total calculation time is 0.4 s. The dynamics equation is established according to Equation (14), in which the damping matrix is distributed according to Rayleigh damping. The detailed explanation of each parameter is referred to in Xu's work [21]. It is noted that µ 10 , µ 20 , and µ 30 are material constants used to establish strain energy function, which requires µ 20 or µ 30 to be negative to meet the condition that the strain energy density is equal to or greater than zero and increases with deformation monotonically [24].…”

“…On the basis of eliminating the effect of volume lock, the accuracy of the constitutive model is verified further. A comparison is conducted between the results of the improved Yeoh model and the experimental results in the published reference [21]. It needs to be pointed out that the comparison here is the result of improving the low-order plate element (conventional plate element by using the SRI method) rather than the results of the high-order plate element.…”

“…This method was dedicated to the examination of several ANCF fully parameterized beam elements under an incompressible regime. Xu et al proposed a higher-order plate element formulation with quadratic interpolation in the transverse direction, which can not only alleviate volumetric locking but also improve accuracy in the simulation of large bending deformations compared to improved lower-order plate elements with the selectively reduced integration method [21].…”

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

“…Xu et al. [12] developed a four‐node plate element formulation with quadratic interpolation in the transverse direction for static and dynamic analysis of incompressible Yeoh hyperelastic silicone cantilever plates. Hansy‐Staudigl et al.…”

“…Wang et al [11] used a fifthorder expansion of the Piola-Kirchhoff stress in the transverse direction for prescribed deformation geometries (e.g., pure bending) of the incompressible neo-Hookean hyperelastic plates. Xu et al [12] developed a four-node plate element formulation with quadratic interpolation in the transverse direction for static and dynamic analysis of incompressible Yeoh hyperelastic silicone cantilever plates. Hansy-Staudigl et al [13] studied nonlinear bending of thin incompressible dielectric elastomeric neo-Hookean cantilever strips, using Kirchhoff's first-order plate theory.…”