Waves in pre-stressed media
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Cloaking of antiplane shear waves.
Polymer-based composite materials are commonly used in underwater engineering applications. The ocean exerts great pressures on these materials leading to inhomogeneous stress fields local to the inhomogeneities present in the composites. Since these materials are often used for sound-reduction purposes, it is of interest to understand how this pre-stress affects the propagation and scattering of elastic waves.
Pre-stress can have a considerable effect on a material's properties, both inducing anisotropy, and potentially affecting the material's density. This causes a wave's speed to vary both with location and direction, thus making the resulting governing equations considerably challenging to solve. In order to investigate the effect of pre-stress on elastic wave propagation, we have studied several canonical problems.
Pre-stress has also been utilised to create cloaks, in order to prevent the detection of a cylindrical cavity. It has also been used to tune the band gaps of phononic media, or alternately one can show that with specially chosen materials these band gaps are invariant or closely invariant to pre-stress. This is an important result for applications.
The effects of loss are also important in the context of wave propagation in soft matter and our group works on developing the fundamental theory of wave propagation in pre-stressed nonlinearly viscoelastic materials.
Pre-stress can have a considerable effect on a material's properties, both inducing anisotropy, and potentially affecting the material's density. This causes a wave's speed to vary both with location and direction, thus making the resulting governing equations considerably challenging to solve. In order to investigate the effect of pre-stress on elastic wave propagation, we have studied several canonical problems.
Pre-stress has also been utilised to create cloaks, in order to prevent the detection of a cylindrical cavity. It has also been used to tune the band gaps of phononic media, or alternately one can show that with specially chosen materials these band gaps are invariant or closely invariant to pre-stress. This is an important result for applications.
The effects of loss are also important in the context of wave propagation in soft matter and our group works on developing the fundamental theory of wave propagation in pre-stressed nonlinearly viscoelastic materials.
- Parnell, W.J. and R. De Pascalis, R. (2019) (open access)
"Soft metamaterials with dynamic viscoelastic functionality tuned by pre-deformation"
Phil. Trans. A, 377, 2144. - Zhang, P. and Parnell. W.J. (2018) (open access)
"Hyperelastic antiplane ground cloaking."
J Acoust. Soc. America 143 (5) - Gower, A.L., Shearer, T. and Ciarletta, P. (2017) (open access)
"A new restriction for initially stressed elastic solids"
Quarterly Journal of Mechanics and Applied Mathematics 70(4), 455-478. - Barnwell, E.G., Parnell, W.J. and Abrahams, I.D. (2017) (open access)
"Tunable elastodynamic band gaps"
Extreme Mechanics Letters 12, 23-29. - Zhang, P. and Parnell, W.J. (2017)
"Soft phononic crystals with deformation-independent band gaps"
Proc. R. Soc. A: 473, 20160865 - Zhang, P. and Parnell, W.J. (2017)
"Band gap formation and tunability in stretchable serpentine interconnects."
ASME J. Applied Mechanics. 84(9) 091007 - Barnwell, E.G., Parnell, W.J. and Abrahams, I.D. (2016) (open access)
"Antiplane elastic wave propagation in pre-stressed periodic structures; tuning, band-gap switching and invariance"
Wave Motion 63, 98-110. - Shearer, T., Parnell, W.J. and Abrahams, I.D. 2015 "Antiplane wave scattering from a cylindrical cavity in pre-stressed nonlinear elastic media", Proceedings of the Royal Society A 471, 20150450.
- Shearer, T., Abrahams, I.D., Parnell, W.J. and Daros, C.H. 2013 "Torsional wave propagation in a pre-stressed hyperelastic annular circular cylinder", Quarterly Journal of Mechanics and Applied Mathematics 66, 466-487.
- Shearer, T. 2012. "Waves in non-linear elastic media with inhomogeneous pre-stress", PhD Thesis, University of Manchester
- Parnell, W.J. and Abrahams, I.D. 2012 "Scattering from a cylindrical void in a pre-stressed incompressible neo-Hookean material", Communications in Computational Physics 11, 367-382.
- Parnell, W.J. and Shearer, T. 2013 "Antiplane elastic wave cloaking using metamaterials, homogenization and hyperelasticity", Wave Motion 50, 1140-1152.
- Parnell, W.J., Norris, A.N. and Shearer, T. 2013 "Elastodynamic cloaking: transformation elasticity with pre-stressed hyperelastic solids", Proceedings of Meetings on Acoustics 17, 070093.
- Parnell, W.J., Norris, A.N. and Shearer, T. 2012 "Employing pre-stress to generate finite cloaks for antiplane elastic waves", Applied Physics Letters 100, 171907.
Our collaborators
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From the UK
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From around the world
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