Experimental and numerical analysis of hyperelastic plates using Mooney-Rivlin strain energy function and meshless collocation method

In this research, the flexural behavior of a hyperelastic plate made of silicone under uniformly distributed loading was investigated. The displacements and strains were formulated using the first-order shear deformation plate theory (FSDPT). The right Cauchy-Green tensor and Mooney-Rivlin strain energy function were employed to formulate hyperelastic silicone plate governing equations. The strong-form of the governing equations of the silicone plate using Mooney-Rivlin strain energy function and Euler-Lagrange relations were derived for the first time. In the governing equations, the effects of geometrical and material nonlinearity effects were considered simultaneously. The meshless collocation method (MCM) and thin-plate spline radial basis function were utilized to discretize the governing equations. The arc-length continuation algorithm was also used for analyzing the system of non-linear equations. MCM results were compared to those of the experimental test to validate the results of the meshless method. For this purpose, a square silicone plate with simply supported boundary conditions under uniformly distributed loading was investigated via the digital image correlation (DIC) technique. According to the obtained results, the MCM based on radial basis function is an adequate method for non-linear analysis of hyperelastic plates with Mooney-Rivlin strain energy function under uniformly distributed loading.