EXPLICIT MODELING THE HYSTERESIS LOOPS OF THE MULLINS EFFECT FOR RUBBER-LIKE MATERIALS

A multi-axial compressible strain energy function is propose to simulate the stress-strain hysteresis loops, which produced by the Mullins effect for rubber-like materials subjected to loading-unloading cycle by a direct, explicit method. The novelty of this paper is to introduce a new variable, which captures the property of dissipation into the potential, and give out a new multi-axial strain energy function. Two properties are incorporated into the new potential: Firstly, the new variable may not affect the potential in the process of loading. Therefore, we can exactly simulate the three benchmark tests, including uniaxial tension and compression, equal-axial tension and compression, and plane strain, by explicitly giving out the appropriate formulations of shape functions; Secondly, the new variable may become active in the process of unloading. The variable may affect the potential by changing with the unloading stress, and produce different stress-strain curves in the unloading process. As a result, the hysteresis loops may be produced in the loading-unloading cycles. We give out the change rules of the shape functions in the unloading process, and predict the stress-strain relation with different unloading stress by analysis the classical test data of the Mullins effects. Numerical results for model validation are in good accord with the three benchmark tests, and the experiments with hysteresis loops producing from the Mullins effect at the end of this paper.