Hyperelasticity and the radial point interpolation method via the Ogden model

Abstract

Rubber-like and biological materials could show a hyperelastic behaviour, often studied using the Finite Element Method (FEM), limitations still exist due to the large deformations that this type of material experiment. Conversely, meshless methods are suitable for large deformations. The Ogden hyperelastic model can also represent the Neo-Hookean and Mooney–Rivlin models with ease, making it versatile but its implementation into meshless methods is yet to be done.In this work, the Ogden model was implemented into the Radial Point Interpolation Method (RPIM), a robust and accurate meshless method, within its iterative process allowing for future simulation of multi-material domains. Then, the implementation was tested with small deformations cases. The implementation was validated using three examples and a different hyperelastic model was used for each example, Mooney–Rivlin, Neo-Hookean, and Ogden, whilst their material properties were taken from the literature.The results were compared to FEM solutions and the literature, a good agreement was achieved with differences below 2%, indicating a successful implementation. This is the first implementation of the Ogden model into the RPIM. The ability to model hyperelastic structures together with the inherent advantages of meshless methods provides a good alternative for the analysis of industrial and biological structures.