Dominant negative Poynting effect in simple shearing of soft tissues

Journal of Engineering Mathematics

Volumn 95, Issue 1, 2015, Pages 87-98

  Destrade, M ^a   Horgan, C O ^b   Murphy, J G ^a,c  

^a NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^b University of Virginia   (United States)

^c DUBLIN CITY UNIVERSITY   (Ireland)

Author keywords

Elasticity; Modelling; Poynting effect; Simple shear; Soft tissue; Transverse isotropy

Indexed keywords

ELASTICITY; MODELS; SHEARING; SHEARING MACHINES; STRAIN ENERGY; TISSUE;

ANISOTROPIC INVARIANTS; DOMINANT NEGATIVE; POYNTING EFFECT; SIMPLE SHEAR; SOFT TISSUE; STRAIN ENERGY FUNCTIONS; TRANSVERSE ISOTROPY; TRANSVERSELY ISOTROPIC;

SHEAR FLOW;

EID: 85028229093     PISSN: 00220833     EISSN: 15732703     Source Type: Journal    
DOI: 10.1007/s10665-014-9706-5     Document Type: Article

References (28)

1. British Standard BS ISO 8013:2006 Rubber, vulcanized—determination of creep in compression or shear
2. Poynting JH (1909) On pressure perpendicular to the shear planes in finite pure shears, and on the lengthening of loaded wires when twisted. Proc R Soc Lond Ser A 82:546–559
3. Rivlin RS (1948) Large elastic deformation of isotropic materials iv: further developments of the general theory. Philos Trans R Soc Lond Ser A 241:379–397
4. Mihai LA, Goriely A (2011) Positive or negative poynting effect? the role of adscititious inequalities in hyperelastic materials. Proc R Soc Lond A 467:3633–3646
5. Destrade M, Murphy JG, Saccomandi G (2012) Simple shear is not so simple. Int J Non-Linear Mech 47:210–214
6. Horgan CO, Smayda M (2012) The importance of the second strain invariant in the constitutive modeling of elastomers and soft biomaterials. Mech Mater 51:43–52
7. Janmey PA, McCormick ME, Rammensee S, Leight JL, Georges PC, MacKintosh FC (2007) Negative normal stress in semiflexible biopolymer gels. Nat Mater 6:48–51
8. Destrade M, Gilchrist MD, Motherway J, Murphy JG (2012) Slight compressibility and sensitivity to changes in Poisson’s ratio. Int J Numer Methods Eng 90:403–411
9. Horgan CO, Murphy JG (2011) On the normal stresses in simple shearing of fiber-reinforced nonlinearly elastic materials. J Elast 104:343–355
10. Wu MS, Kirchner HOK (2010) Nonlinear elasticity modeling of biogels. J Mech Phys Solids 58:300–310
11. Spencer AJM (1984) Constitutive theory for strongly anisotropic solids. In Spencer AJM (ed) Continuum theory of the mechanics of fibre-reinforced composites. CISM Courses and Lectures Series No. 282. Springer-Verlag, Vienna
12. Murphy JG (2013) Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants. Eur J Mech A/Solids 42:90–96
13. Dokos S, Smaill BH, Young AA, LeGrice IJ (2002) Shear properties of passive ventricular myocardium. Am J Physiol Heart Circ Physiol 283:H2650–H2659
14. Saccomandi G, Beatty MF (2002) Universal relations for fiber-reinforced elastic materials. Math Mech Solids 7:95–110
15. Ogden RW (2003) Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue. In Biomechanics of soft tissue in cardiovascular systems. CISM Courses and Lectures Series No. 441. Springer, Vienna, pp 65–108
16. Merodio J, Ogden RW (2005) Mechanical response of fiber-reinforced incompressible non-linearly elastic solids. Int J Non-Linear Mech 40:213–227
17. Vergori L, Destrade M, McGarry P, Ogden RW (2013) On anisotropic elasticity and questions concerning its finite element implementation. Comput Mech 52:1185–1197
18. Gennisson J-L, Catheline S, Chaffaõ S, Fink M (2003) Transient elastography in anisotropic medium: application to the measurement of slow and fast shear wave speeds in muscles. J Acoust Soc Am 114:536–541
19. Papazoglou S, Rump J, Braun J, Sack I (2006) Shear wave group velocity inversion in MR elastography of human skeletal muscle. Magn Reson Med 56:489–497
20. Sinkus R, Tanter M, Catheline S, Lorenzen J, Kuhl C, Sondermann E, Fink M (2005) Imaging anisotropic and viscous properties of breast tissue by magnetic resonance-elastography. Magn Reson Med 53:372–387
21. Morrow DA, Haut Donahue TL, Odegard GM, Kaufman KR (2010) Transversely isotropic tensile material properties of skeletal muscle tissue. J Mech Behav Biomed Mater 3:124–129
22. Truesdell C, Noll W (1965) The non-linear field theories of mechanics. In: Flugge S (ed) Encyclopedia of Physics, vol III/3, 3rd edn. Springer-Verlag, Berlin
23. Beatty MF (1989) Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissue. Appl Mech Rev 40:1699–1734
24. Feng Y, Okamoto RJ, Namani R, Genin GM, Bayly PV (2013) Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter. J Mech Behav Biomed Mater 23:117–132
25. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61:1–48
26. Le Tallec P (1994) Numerical methods for nonlinear three-dimensional elasticity. In: Ciarlet PG, Lions JL (eds) Handbook of Numerical Analysis, vol III. Elsevier, Amsterdam
27. ADINA R&D Inc (2005) ADINA theory and modeling guide. ADINA R&D Inc, Watertown
28. ARES Rheometer manual (2006) Rheometrics series user manual. Revision J, TA Instrument-Waters LLC, New Castle