A Novel Nonlinear Elasticity Approach for Analysis of Nonlinear and Hyperelastic Structures

Abstract

There are many materials that the linear elasticity theory cannot predict their mechanical behavior against applied loads. This research proposes a comprehensive theoretical method to obtain the mechanical response of hyperelastic models (with nonlinear elastic deformations) such as polymers and rubbers. They are vital in the design phase of complicated engineering structures like engine mounts and structural bearings in aerospace and automotive industries. The presented theory is implemented in detail and has no limitations in analyzing geometrically and physically nonlinear materials. As a test case, the governing equations of a sheet made of nonlinear elastic material are derived within the framework of this new approach. The derived governing equations are completely nonlinear in all major directions. Consequently, results can be one of the most accurate mathematical simulation results for nonlinear elastic material structures. Then, the obtained equations are solved using a meshless solution method named the semi-analytical polynomial method. The stress and deformation results of the structure under uniform and non-uniform transverse external loadings are obtained for different types of boundary conditions, loading, and material properties. Consequently, this research can be widely used as a suitable essential reference for researchers studying the mechanical behavior of nonlinear elastic structures.