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

Date

2005-10-01

Author

Göktepe, Serdar

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

243
views

0
downloads

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

Subject Keywords

Mechanical Engineering, Mechanics of Materials, Condensed Matter Physics

URI

https://hdl.handle.net/11511/34331

Journal

JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS

DOI

https://doi.org/10.1016/j.jmps.2005.04.010

Collections

Department of Civil Engineering, Article

Suggestions

OpenMETU
Core

A micro macro approach to rubber like materials Part II The micro sphere model of finite rubber viscoelasticity Christian, Miehe; Göktepe, Serdar (Elsevier BV, 2005-10-01) A micromechanically based non-affine network model for finite rubber elasticity incorporating topological constraints was discussed in Part 1 (2004. J. Mech. Phys. Solids 52, 2617-2660) of this work. In this follow-up contribution we extend the non-affine microsphere model towards the description of time-dependent viscoelastic effects. The viscoelastic network model is constructed by an additive split of the overall response into elastic equilibrium-stress and viscoelastic overstress contributions. The equi...
A variational multiscale constitutive model for nanocrystalline materials Gürses, Ercan (Elsevier BV, 2011-03-01) This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rate-independent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation m...
A variational approach for the two-dimensional magnetopolaron Erçelebi, Atila; Saqqa, Bassam H. (IOP Publishing, 1989-12-18) The problem of a two-dimensional magnetopolaron is investigated on the basis of a variational theory consisting of an adiabatic polaronic wavefunction combined with a perturbative correction by which it is possible to interrelate the strong and weak coupling counterparts of the coupled electron-phonon system. It is seen that the theory conveniently reproduces the desirable asymptotic limits in the different regimes of the problem. Furthermore, it is suggested that a satisfying improvement should be achieved...
A NEW METHOD FOR HARMONIC RESPONSE OF NONPROPORTIONALLY DAMPED STRUCTURES USING UNDAMPED MODAL DATA Özgüven, Hasan Nevzat (Elsevier BV, 1987-09-08) A method of calculating the receptances of a non-proportionally damped structure from the undamped modal data and the damping matrix of the system is presented. The method developed is an exact method. It gives exact results when exact undamped receptances are employed in the computation. Inaccuracies are due to the truncations made in the calculation of undamped receptances. Numerical examples, demonstrating the accuracy and speed of the method when truncated receptance series are used are also presented. ...
A NEW FAMILY OF MODE-SUPERPOSITION METHODS FOR RESPONSE CALCULATIONS AKGUN, MA (Elsevier BV, 1993-10-22) A new family of mode-superposition methods for the computation of the forced response of proportionally damped systems with and without rigid body modes is investigated. The method may be considered to be an extension of the mode-acceleration method. It allows response calculations to be done with a very small subset of the modes of the system. Numerical examples are given for systems of order 20 and 40. Execution times and number of modes required for convergence are recorded. The particular order of the m...

Citation Formats

S. Göktepe, “A micro-macro approach to rubber-like materials. Part III: The micro-sphere model of anisotropic Mullins-type damage,” JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, pp. 2259–2283, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34331.