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| http://dx.doi.org/10.1098/rsta.2019.0090 | DOI Listing |
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Instabilities of soft dielectrics.
Philos Trans A Math Phys Eng Sci
May 2019
2 School of Mathematics and Statistics , University of Glasgow, Glasgow G12 8QQ , UK.
The basic modern theory of nonlinear electroelasticity and its use in the formulation of constitutive laws governing the behaviour of dielectric elastomer materials was summarized in a recent review article by Dorfmann & Ogden (Dorfmann & Ogden 2017 Proc. R. Soc.
View Article and Find Full Text PDFRevisiting the wrinkling of elastic bilayers I: linear analysis.
Philos Trans A Math Phys Eng Sci
May 2019
1 Mathematical Institute , University of Oxford, Oxford , UK.
Wrinkling is a universal instability occurring in a wide variety of engineering and biological materials. It has been studied extensively for many different systems but a full description is still lacking. Here, we provide a systematic analysis of the wrinkling of a thin hyperelastic film over a substrate in plane strain using stream functions.
View Article and Find Full Text PDFMechanical characterization of functionally graded soft materials with ultrasound elastography.
Philos Trans A Math Phys Eng Sci
May 2019
1 AML, Department of Engineering Mechanics, Institute of Biomechanics and Medical Engineering, Tsinghua University, Beijing 100084 , People's Republic of China.
Functionally graded soft materials (FGSMs) with microstructures and mechanical properties exhibiting gradients across a spatial volume to satisfy specific functions have received interests in recent years. How to characterize the mechanical properties of these FGSMs in vivo/in situ and/or in a non-destructive manner is a great challenge. This paper investigates the use of ultrasound elastography in the mechanical characterization of FGSMs.
View Article and Find Full Text PDFOn the existence of elastic minimizers for initially stressed materials.
Philos Trans A Math Phys Eng Sci
May 2019
MOX, Dipartimento di Matematica, Politecnico di Milano, 20133 Milano , Italy.
A soft solid is said to be initially stressed if it is subjected to a state of internal stress in its unloaded reference configuration. In physical terms, its stored elastic energy may not vanish in the absence of an elastic deformation, being also dependent on the spatial distribution of the underlying material inhomogeneities. Developing a sound mathematical framework to model initially stressed solids in nonlinear elasticity is key for many applications in engineering and biology.
View Article and Find Full Text PDFFlow of a new class of non-Newtonian fluids in tubes of non-circular cross-sections.
Philos Trans A Math Phys Eng Sci
May 2019
Department of Mechanical Engineering , Texas A& M University , College Station, TX 77483 , USA.
Fluids described by constitutive relations wherein the symmetric part of the velocity gradient is a function of the stress can be used to describe the flows of colloids and suspensions. In this paper, we consider the flow of a fluid obeying such a constitutive relation in a tube of elliptic and other non-circular cross-sections with the view towards determining the velocity field and the stresses that are generated at the boundary of the tube. As tubes are rarely perfectly circular, it is worthwhile to study the structure of the velocity field and the stresses in tubes of non-circular cross-section.
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