A micro-macro approach to rubber-like materials. Part III: The micro-sphere model of anisotropic Mullins-type damage


GÖKTEPE S. , Miehe C.

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, vol.53, no.10, pp.2259-2283, 2005 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 10
  • Publication Date: 2005
  • Doi Number: 10.1016/j.jmps.2005.04.010
  • Title of Journal : JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
  • Page Numbers: pp.2259-2283
  • Keywords: micromechanics, rubber-like materials, Mullins effect, network models, permanent set, experiments, simulations, PSEUDO-ELASTIC MODEL, CARBON-BLACK, CONSTITUTIVE MODEL, PERMANENT SET, BEHAVIOR, FORMULATION, POLYMERS

Abstract

A micromechanically based non-affine network model for finite rubber elasticity and viscoelasticity was discussed in Parts I and II [Miehe, C., Goktepe, S., Lulei, F., 2004. A micro-macro approach to rubber-like materials. Part I: The non-affine micro-sphere model of rubber elasticity. J. Mech. Phys. Solids 52, 2617-2660; Miehe, C., Goktepe, S., 2005. A micro-macro approach to rubber-like materials. Part II: Viscoelasticity model for polymer networks. J. Mech. Phys. Solids, published on-line, doi:10.1016/j.jmps.2005.04.006.] of this work. In this follow-up contribution, we further extend the micro-sphere network model such that it incorporates a deformation-induced softening commonly referred to as the Mullins effect. To this end, a continuum formulation is constructed by a superimposed modeling of a crosslink-to-crosslink (CC) and a. particle-to-particle (PP) network. The former is described by the nonaffine elastic network model proposed in Part I. The Mullins-type damage phenomenon is embedded into the PP network and micromechanically motivated by a breakdown of bonds between chains and filler particles. Key idea of the constitutive approach is a two-step procedure that includes (i) the set up of micromechanically based constitutive models for a single chain orientation and (ii) the definition of the macroscopic stress response by a directly evaluated homogenization of state variables defined on a micro-sphere of space orientations. In contrast to previous works on the Mullins effect, our formulation inherently describes a deformation-induced anisotropy of the damage as observed in experiments. We show that the experimentally