Finite Strain Micromechanical Analysis of Rubber-like Matrix Composites incorporating the Mullins Damage Effect

Abstract

A model for hyperelastic rubber-like materials that includes the Mullins damage effect has been incorporated with a finite strain micromechanical analysis for composites with periodic microstructures. As a result, it is possible to predict the response of fiber-reinforced rubber-like matrix composites, including the Mullins effect, from the knowledge of the character and properties of the constituents and their volume ratios. This is expressed by the establishment of macroscopic constitutive equations that govern the behavior of the damaged composite undergoing finite deformations. The reliability and accuracy of the micromechanical prediction are demonstrated by comparisons with the response of four types of porous materials that are subjected to axisymmetric loading for which exact solutions can be established during loading, and with finite-difference solutions which are valid in both loading and unloading. Next, a master damage function that controls the Mullins effect of a monolithic (unreinforced) hyperelastic material is established from experimental data. This hyperelastic material and its associated damage function are employed to characterize a rubber-like matrix reinforced by continuous nylon fibers. The predicted responses of this composite to transverse normal, transverse shear, axial shear and off-axis loadings are shown.