Análise não linear de pórticos planos considerando modelos hiperelásticos pelo método dos elementos finitos posicional

Abstract

In this study, the development and implementation of the hyperelastic models Mooney-Rivlin, Neo-Hookean, Ogden, and Yeoh in a FORTRAN computational code were carried out. This code was built using the Positional Finite Element Method, along with Reissner kinematics and the Newton-Raphson method, to enable the nonlinear analysis of plane frames structures with elastomer samples added with different proportions of carbon black. After implementing the models, the Least Squares Method was employed to determine the constitutive coefficients of the hyperelastic models. Next, a comparative evaluation of the performance of each model was conducted by analyzing their force versus displacement curves. The results revealed that the Yeoh and Ogden models yielded consistent results, while the Neo-Hookean and Mooney-Rivlin models showed discrepancies. This observation was attributed to the number of constants present in the formulation of such models. Furthermore, it was concluded that the approach of the Positional Finite Element Method for nonlinear analysis of plane frames structures, using hyperelastic models, demonstrated good performance. Especially after the modifications proposed in this study, which included considering the first and second strain invariants of the simple shear formulation, aiming to improve the representation of distortion in the specific energy of deformation of the hyperelastic models.