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Research Papers

A Model for the Mullins Effect in Multinetwork Elastomers

[+] Author and Article Information
Mattia Bacca

Mechanical Engineering Department,
University of British Columbia,
Vancouver, BC V6T 1Z4, Canada

Costantino Creton

Laboratoire PPMD,
ESPCI Paris Tech,
10 Rue Vauquelin,
Paris 75231, France

Robert M. McMeeking

Materials and Mechanical
Engineering Departments,
University of California,
Santa Barbara, CA 93106;
School of Engineering,
University of Aberdeen,
King’s College,
Aberdeen AB24 3 UE, UK;
INM—Leibniz Institute for New Materials,
Campus D2 2,
Saarbrücken 66123, Germany

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 24, 2017; final manuscript received September 6, 2017; published online October 26, 2017. Editor: Yonggang Huang.

J. Appl. Mech 84(12), 121009 (Oct 26, 2017) (7 pages) Paper No: JAM-17-1400; doi: 10.1115/1.4037881 History: Received July 24, 2017; Revised September 06, 2017

Double and triple network (TN) elastomers can be made by infusing monomers into a single network (SN) polymer, causing it to swell, and then polymerizing and cross-linking the monomers. The result is a double network (DN) elastomer in which one network is stretched and the other is in hydrostatic compression. TN systems are made by repeating the process starting with the DN material. The multinetwork (MN) elastomers exhibit a Mullins effect in which softening occurs upon a first cycle of loading, with the elastomer stiffness recovered above the previous maximum strain. The Mullins effect is attributed to rupture of the stretched network, eliminating the constraint on the compressed network, thereby motivating straining at the lower stiffness of the remaining material. A model for this process is developed, based on the previous work of Horgan et al. (2004, “A Theory of Stress Softening of Elastomers Based on Finite Chain Extensibility,” Proc. R. Soc. A, 460(2046), pp. 1737–1754). In the proposed model, a composite stiffness for the MN system is developed and a damage process introduced to degrade the contribution of the stretched network. The damage model is designed to account for the progressive elimination of chains that are most highly loaded in the stretched network, so that the undamaged stiffness is restored when the strain rises above levels previously experienced. The proposed model reproduces the behavior of the Mullins effect in the MN system.

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Copyright © 2017 by ASME
Topics: Elastomers , Stress , Chain , Damage
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Figures

Grahic Jump Location
Fig. 1

Cauchy stress versus stretch curves for a triple network elastomer subject to cyclic loading. The material consists oftwo networks of polymethylacrylate compressed within stretched polyethylacrylate. The solid line represents the predicted results with the proposed model, while the circles represent the experimental results [2].

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