Investigation on Mullins effect of rubber materials by spherical indentation method

Abstract

Abstract Rubber-like soft materials usually experience load-induced softening behavior called the Mullins effect, in which the preloaded material exhibits a significantly more compliant response than the virgin material. However, rare quantitative and simple method of characterizing Mullins effect can be founded and corresponding accurate simulations in practice were severely restricted. In this paper, a simple measurement method was developed to characterize this mechanical response. A comprehensive theoretical, computational, and experimental study of the spherical indentation of rubber materials was undertaken to interpret parameters of the Mullins effect. Neo-Hookean model is used to describe nonlinear hyper-elastic deformation behavior and a pseudo-elastic model originally proposed by Ogden and Roxburgh is applied to interpret load-induced softening effects. Relationships between indentation loads, indentation depths, radius of the spherical indenter, and constitutive parameters of the material are obtained by dimensional analysis. Based on finite-element methods and parameter optimization procedure, a general method for determining the parameters of neo-Hookean and pseudo-elastic models was established. The approach was numerically and experimentally validated. This method provides a simple and accurate way of interpreting load-induced softening of rubber materials from spherical indentation tests, which will enrich the application of pseudo-elastic model using in vary cyclic loading conditions, capturing more new features in rubber-like soft materials and structures.