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

Abstract

In recent years, there has been an increase in the use of hyperelastic materials in structures, such as vulcanized or natural polymers. As a result, it becomes relevant to expand the knowledge regarding the mechanical performance of these materials through the development of numerical models that simulate their behavior and that are capable of presenting more realistic predictions. For materials represented by hyperelastic models, the consideration of physical and geometric nonlinearities is more adequate to represent their mechanical behavior when subjected to large deformations. Thus, the present work aims at the implementation of a computational code, with the purpose of analyzing and comparing the mechanical behavior of trusses considering the physical non-linearity, described by hyperelastic models, and the geometric non-linearity using the positional formulation in finite elements. The Riks-Wempner arc length method associated with the Newton-Rapshson iterative method was used to trace equilibrium paths with snapthrough and snap-back phenomena. The Neo-Hookean, Mooney-Rivlin, Polynomial, Yeoh, Ogden and Arruda-Boyce hyperelastic models were considered. The validation of the implemented program took place through the comparison with analytical solutions and numerical and experimental results of scientific papers.