Alternative methods for the solution of hyperelastic problems with incompressibility

Abstract

A new approach for analysing incompressible hyperelastic and rubber-like material behaviour is discussed. The approach is based on extending the linear analysis bubble function concept into nonlinear analysis. To eliminate external or residual forces on the bubble function or nodeless degrees of freedom, two iterative methods are discussed. The new approach is compared to other approaches available in the literature including multified principle, reduced integration penalty and average constraint procedures. A unified numerical treatment for handling various constitutive relations of hyperelastic and rubber-like materials is presented. Numerical examples and comparisons include thick-walled cylinder subjected to internal pressure, inflation of a circular rubber plate and inflation of a hollow sphere.