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Research Papers

Plane Deformations of an Inhomogeneity–Matrix System Incorporating a Compressible Liquid Inhomogeneity and Complete Gurtin–Murdoch Interface Model

[+] Author and Article Information
Ming Dai

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China;
School of Mechanical Engineering,
Changzhou University,
Changzhou 213164, China
e-mail: m.dai@foxmail.com

Min Li

State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: mli5@foxmail.com

Peter Schiavone

Department of Mechanical Engineering,
University of Alberta,
Edmonton, AB T6G 1H9, Canada
e-mail: P.Schiavone@ualberta.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 8, 2018; final manuscript received September 7, 2018; published online October 1, 2018. Assoc. Editor: Yashashree Kulkarni.

J. Appl. Mech 85(12), 121010 (Oct 01, 2018) (5 pages) Paper No: JAM-18-1464; doi: 10.1115/1.4041469 History: Received August 08, 2018; Revised September 07, 2018

We consider the plane deformations of an infinite elastic solid containing an arbitrarily shaped compressible liquid inhomogeneity in the presence of uniform remote in-plane loading. The effects of residual interface tension and interface elasticity are incorporated into the model of deformation via the complete Gurtin–Murdoch (G–M) interface model. The corresponding boundary value problem is reformulated and analyzed in the complex plane. A concise analytical solution describing the entire stress field in the surrounding solid is found in the particular case involving a circular inhomogeneity. Numerical examples are presented to illustrate the analytic solution when the uniform remote loading takes the form of a uniaxial compression. It is shown that using the simplified G–M interface model instead of the complete version may lead to significant errors in predicting the external loading-induced stress concentration in gel-like soft solids containing submicro- (or smaller) liquid inhomogeneities.

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References

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Figures

Grahic Jump Location
Fig. 1

A liquid inhomogeneity in an infinite plane under a uniform remote in-plane loading

Grahic Jump Location
Fig. 2

Uniaxial compression-induced hoop stress around a circular liquid inhomogeneity for complete and simplified G–M models

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