Elastobuoyant Heavy Spheres: A Unique Way to Study Nonlinear Elasticity

Large deformations in soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here, we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius a in an incompressibl...

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Bibliographic Details
Published inPhysical review. X Vol. 6; no. 4; p. 041066
Main Authors Chakrabarti, Aditi, Chaudhury, Manoj K., Mora, Serge, Pomeau, Yves
Format Journal Article
LanguageEnglish
Published College Park American Physical Society 28.12.2016
Subjects
Asymptotic properties
Computational fluid dynamics
Elastic deformation
Elastic media
Engineering Sciences
Materials
Mathematical models
Mechanics
Mechanics (physics)
Modulus of elasticity
Penetration depth
Polymer gels
Scaling laws
Soft tissues
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Summary:Large deformations in soft elastic materials are ubiquitous, yet systematic studies and methods to understand the mechanics of such huge strains are lacking. Here, we investigate this complex problem systematically with a simple experiment: by introducing a heavy bead of radius a in an incompressible soft elastic medium. We find a scaling law for the penetration depth (δ ) of the bead inside the softest gels as δ∼a3/2 , which is vindicated by an original asymptotic analytic model developed in this article. This model demonstrates that the observed relationship is precisely at the demarcating boundary of what would be required for the field variables to either diverge or converge. This correspondence between a unique mathematical prediction and the experimental observation ushers in new insights into the behavior of the deformations of strongly nonlinear materials.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.6.041066