Nonlinear analysis of plane frames considering hyperelastic models through the finite element positional method

Abstract

Computational mechanics has become an essential tool in engineering, just as the use of hyperelastic materials has seen remarkable growth in everyday applications. Therefore, it is fundamental to study hyperelastic models that represent the behavior of these materials, such as elastomers and polymers. With that in mind, the Mooney-Rivlin, Neo-Hookean, Ogden, and Yeoh models were implemented in a computational code in FORTRAN using the Positional Finite Element Method with Reissner kinematics and the Newton-Raphson method for nonlinear analysis of plane frames with samples of elastomers added with different percentages of carbon black. Ultimately, it was concluded that the Yeoh and Ogden models presented coherent values and that the use of the formulation for nonlinear analysis of plane frame performs well after the modifications proposed by this work. These modifications consisted of adding the first and second strain invariants of the simple shear formulation to include the consideration of distortion in the specific strain energy of hyperelastic models.