Nonlinear elasticity and viscoelasticity 
Nonlinear elasticity is the subject dealing with materials that are capable of large, reversible deformations. Of specific importance are deformations of polymeric composites and soft tissues. Of course in reality no deformations are perfectly reversible  this is an approximation and we are required to incorporate lossy effects such as viscoelasticity. Nonlinear elasticity and viscoelasticity are very active areas of research both in terms of the mathematical apparatus that underlies the topic and the application of the theory to problems in the applied sciences.
The picture to the right illustrates simple shear of porcine brain matter, illustrating the large deformations possible with soft tissue. Thanks to Michel Destrade (NUI Galway) for this nice image taken from his paper entitled "Extreme softness of brain matter in simple shear" to appear shortly in the International Journal of Nonlinear Mechanics.
Within the WICC group we are interested in the fundamental theory underlying nonlinear viscoelasticity. Recently we have reappraised the quasilinear theory of viscoelasticity originally proposed by Fung. Although this theory does have its limitations it does have merits and some of the recent criticisms in the literature are, in fact unfounded as we showed in our recent 2014 Proceedings paper, referenced below. One of its limitations is that the relaxation function is independent of strain. This is not sensible for many materials such as biological tissues. Our recent work in biological tissues has tried to ascertain the correct form of strain energy functions for hyperelastic behaviour of tendons and ligaments. We have also developed homogenization techniques in order to predict the associated effective nonlinear viscoelastic behaviour. This incorporates strain dependent relaxation via "fibril recruitment".
The picture to the right illustrates simple shear of porcine brain matter, illustrating the large deformations possible with soft tissue. Thanks to Michel Destrade (NUI Galway) for this nice image taken from his paper entitled "Extreme softness of brain matter in simple shear" to appear shortly in the International Journal of Nonlinear Mechanics.
Within the WICC group we are interested in the fundamental theory underlying nonlinear viscoelasticity. Recently we have reappraised the quasilinear theory of viscoelasticity originally proposed by Fung. Although this theory does have its limitations it does have merits and some of the recent criticisms in the literature are, in fact unfounded as we showed in our recent 2014 Proceedings paper, referenced below. One of its limitations is that the relaxation function is independent of strain. This is not sensible for many materials such as biological tissues. Our recent work in biological tissues has tried to ascertain the correct form of strain energy functions for hyperelastic behaviour of tendons and ligaments. We have also developed homogenization techniques in order to predict the associated effective nonlinear viscoelastic behaviour. This incorporates strain dependent relaxation via "fibril recruitment".
 Barnwell, E.G., Parnell, W.J. and Abrahams, I.D. (2016) (open access)
"Antiplane elastic wave propagation in prestressed periodic structures; tuning, bandgap switching and invariance"
Wave Motion 63, 98110.  Shearer, T., Parnell, W.J. and Abrahams, I.D. (2015) (open access)
"Antiplane wave scattering from a cylindrical cavity in prestressed nonlinear elastic media"
Proc. Roy. Soc. A. 471, 20150450  Shearer, T. (2015) (open access)
"A new strain energy function for modelling ligaments and tendons whose fascicles have a helical arrangement of fibrils"
J. Biomech. 48, 30173025  De Pascalis, R., Abrahams, I.D. and Parnell, W.J. (2015) (open access)
"Simple shear of a compressible viscoelastic material"
Int. J. Eng. Science 88, 6472.  Shearer, T. (2015) (open access)
"A new strain energy function for the hyperelastic modelling of ligaments and tendons based on fascicle microstructure"
J. Biomech. 48, 290297  Gilchrist, M., Murphy, J.G., Parnell, W.J. and Pierrat, B. (2014)
"Modelling the slight compressibility of anisotropic soft tissue"
Int. J. Solids Structures. 51, 38573865  De Pascalis, R., Abrahams, I.D. and Parnell, W.J. (2014) (open access)
"On nonlinear viscoelastic deformations  a reappraisal of Fung's quasilinear viscoelastic model"
Proc. Roy. Soc. A 470 (2166)  De Pascalis, R., Parnell, W.J. and Abrahams, I.D. (2013)
"Predicting the nonlinear pressurevolume curve of an elastic microsphere composite"
J. Mech. Physics Solids 61, 11061123
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