Exceptional Waves in a Constrained Elastic Body

Chadwick, P.; Whitworth, A. M.

doi:10.1093/qjmam/39.2.309

Cited by 12 publications

(3 citation statements)

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“…where A 0 is the fourth-order tensor of instantaneous elastic moduli. In general it has a long expression for fibre-reinforced solids, with possibly 45 nonzero components, see for example [7,8]. For W in the form Eq.…”

Section: Incremental Deformationsmentioning

confidence: 99%

Surface Instability of Sheared Soft Tissues

Destrade

Gilchrist

Приказчиков

et al. 2008

Journal of Biomechanical Engineering

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When a block made of an elastomer is subjected to large shear, its surface remains flat. When a block of biological soft tissue is subjected to large shear, it is likely that its surface in the plane of shear will buckle (apparition of wrinkles). One factor that distinguishes soft tissues from rubber-like solids is the presence -sometimes visible to the naked eye -of oriented collagen fibre bundles, which are stiffer than the elastin matrix into which they are embedded but are nonetheless flexible and extensible. Here we show that the simplest model of isotropic nonlinear elasticity, namely the incompressible neoHookean model, suffers surface instability in shear only at tremendous amounts of shear, i.e., above 3.09, which corresponds to a 72 • angle of shear. Next we incorporate a family of parallel fibres in the model and show that the resulting solid can be either reinforced or strongly weakened with respect to surface instability, depending on the angle between the fibres and the direction of shear, and depending on the ratio E/µ between the stiffness of the fibres and that of the matrix. For this ratio we use values compatible with experimental data on soft tissues. Broadly speaking, we find that the surface becomes rapidly unstable when the shear takes place "against" the fibres, and that as E/µ increases, so does the sector of angles where early instability is expected to occur.

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Section: Incremental Deformationsmentioning

confidence: 99%

Surface Instability of Sheared Soft Tissues

Destrade

Gilchrist

Приказчиков

et al. 2008

Journal of Biomechanical Engineering

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“…An alternative formulation of a model of rubberlike thermo-elasticity in (18) was proposed in a later paper (30), wherein the concept of strictly entropic elasticity as applied to elastomeric materials was modified. This was developed to account for the observed experimental findings that the deviatoric stress is not entirely entropic in origin but includes a contribution from the internal energy, in contrast to the classical theory that regards rubber elasticity as entirely entropic.…”

Section: Nonlinear Thermo-elasticitymentioning

confidence: 99%

Peter Chadwick. 23 March 1931—12 August 2018

Ogden

2020

Biogr. Mems Fell. R. Soc.

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Peter Chadwick studied mathematics as an undergraduate at the University of Manchester, graduating with first-class honours in 1952, from where he moved to Cambridge and completed a PhD on the thermal history of the Earth in the Department of Geodesy and Geophysics under the supervision of Dr Robert Stoneley. His research then developed to focus primarily on the propagation of waves, and he made a major contribution to the mathematical theory of elastic wave propagation and became a world-leading authority in this area. He also made fundamental advances in the modelling of the thermo-elastic properties of rubberlike materials. At the University of East Anglia, where he was a professor for 26 years, he was the driving force behind the development of a research group in theoretical mechanics in the School of Mathematics and Physics, leading by example and supporting and encouraging fellow faculty members, especially the younger staff, academic visitors and students. He gave considerable service to the University of East Anglia in a number of capacities, including a period as Dean of the School, and to the scientific community, through substantial journal editorial activities and as a member of several national and international committees.

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“…This represents a non-dispersive shear wave travelling with a constant speed v"c which will leave any plane x "constant traction free. Such waves are usually termed exceptional and are important in the theory of surface waves and body wave re#ections at boundaries [14].…”

Section: Governing Equations For An Infinite Platementioning

confidence: 99%