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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December 2018
Research-Article
Plane Deformations of an Inhomogeneity–Matrix System Incorporating a Compressible Liquid Inhomogeneity and Complete Gurtin–Murdoch Interface Model
Ming Dai,
Ming Dai
State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China;
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
Changzhou University,
Changzhou 213164, China
e-mail: m.dai@foxmail.com
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Min Li,
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
Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China
e-mail: mli5@foxmail.com
Search for other works by this author on:
Peter Schiavone
Peter Schiavone
Department of Mechanical Engineering,
University of Alberta,
Edmonton, AB T6G 1H9, Canada
e-mail: P.Schiavone@ualberta.ca
University of Alberta,
Edmonton, AB T6G 1H9, Canada
e-mail: P.Schiavone@ualberta.ca
Search for other works by this author on:
Ming Dai
State Key Laboratory of Mechanics and
Control of Mechanical Structures,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China;
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
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
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
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. Dec 2018, 85(12): 121010 (5 pages)
Published Online: October 1, 2018
Article history
Received:
August 8, 2018
Revised:
September 7, 2018
Citation
Dai, M., Li, M., and Schiavone, P. (October 1, 2018). "Plane Deformations of an Inhomogeneity–Matrix System Incorporating a Compressible Liquid Inhomogeneity and Complete Gurtin–Murdoch Interface Model." ASME. J. Appl. Mech. December 2018; 85(12): 121010. https://doi.org/10.1115/1.4041469
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