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

By S. Göktepe, C. Miehé. 2005

203 citations recorded by the source corpus.

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 non-affine 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 observed permanent set in stress–strain diagrams is achieved by our model in a natural way as an anisotropy effect. The performance of the model is demonstrated by means of several numerical experiments including the solution of boundary-value problems.

Subfields: Biomedical Engineering, Fluid Flow and Transfer Processes, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/aa956599fdea8814dea24727711425a14aaecf1a

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In Biomedical Engineering

In Fluid Flow and Transfer Processes

In Mechanics of Materials

Citations in the corpus

A network evolution model for the anisotropic Mullins effect in carbon black filled rubbers (2009, background): “Quite recently, Göktepe and Miehe (2005) proposed an anisotropic extension of the theory by Govindjee and Simo (1992).”
Challenges in Multiscale Modeling of Polymer Dynamics (2013, background): “materials, with all the relevant physical mechanisms considered [19,29–33].”