Advanced computational modelling of the mechanical behaviour of rubber-like materials

To describe the material behaviour near a singular point, a relatively simple strain energy function for rubber-like materials has been proposed by Gao in 1997. This function represents the response to tension and compression and is successfully used to analyse singular problems. In this paper, it is demonstrated how Gao’s elastic law has been implemented in the DIANA finite element package. Basic analyses demonstrate that this model is reasonable to describe material behaviour and is stable in finite element calculations, in which very large deformations can be reached. Gao’s law is also compared with Ogden’s formula and Mooney-Rivlin’s formula by means of a theoretical and a numerical analysis. Following that, the material parameters are discussed in detail. As an application, the problem of a wedge loaded by a concentrated tensile force is analysed based on this elastic law.