154
3 Continuum Mechanics and Nonlinear Elasticity
Fung YC (1990) Biomechanics: motion, flow, stress, and growth. Springer, New York
Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New York
Fung YC, Fronek K, Patitucci P (1979) Pseudoelasticity of arteries and the choice of its
mathematical expression. Am J Physiol 237:H620–631
Green AE, Adkins JE (1970) Large elastic deformations. Oxford University Press, London
Green AE, Zerna W (1968) Theoretical elasticity. Oxford University Press, London
Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley,
New York
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
Humphrey JD (2002) Cardiovascular solid mechanics: cells, tissues, and organs. Springer, New
York
Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall,
Englewood Cliffs
Mow VC, Kwan MK, Lai WM, Holmes MH, Schmid-Schonbein GW, Woo SLY, and Zweifach BW
(1986) A finite deformation theory for nonlinearly permeable soft hydrated biological tissues.
Frontiers in biomechanics. Springer, New York, pp 153–179
Mow VC, Lai WM, Hou JS (1990) Triphasic theory for swelling properties of hydrated charged
soft biological tissues. Appl Mech Rev 43:S134–S141
Mooney M (1940) A theory of large elastic deformation. J. Appl. Phys. 11:582–592
Narasimhan MN (1993) Principles of continuum mechanics. Wiley-Interscience, Hoboken
Ogden RW (1972) Large deformation isotropic elasticity on the correlation of theory and
experiment for incompressible rubberlike solids. Proc R Soc Lond A Math Phys Eng Sci
326:565–584
Ogden RW (1984) Non-linear elastic deformations. Halsted Press, New York
Rivlin RS (1947) Torsion of a rubber cylinder. J. Appl. Phys. 18:444–449
Rivlin RS (1956) Large elastic deformations. In: F. R. Eirich (Ed.), Rheology: Theory and
applications. Academic Press, New York pp. 351–385
Rivlin RS, Barenblatt GI, Joseph DD (1997). Collected papers of R.S. Rivlin. Springer, New York
Sandersius SA, Chuai M, Weijer CJ, Newman TJ (2011) A ‘chemotactic dipole’ mechanism for
large-scale vortex motion during primitive streak formation in the chick embryo. Phys Biol
8:045008
Simon BR (1992). Multiphase poroelastic finite element models for soft tissue structures. Appl
Mech Rev 45:191–218
Spencer AJM (1980) Continuum mechanics. Wiley, New York
Spencer AJM (1984) Constitutive theory for strongly anisotropic solids. Continuum theory of the
mechanics of fibre-reinforced composites. Springer, New York, pp 1–32
Taber LA (1995) Biomechanics of growth, remodeling, and morphogenesis. Appl Mech Rev
48:487–545
Taber LA (2004) Nonlinear theory of elasticity: applications in biomechanics. World Scientific,
New Jersey
Timoshenko S, Goodier JN (1969) Theory of elasticity. McGraw-Hill, New York
Truesdell C (1991) A first course in rational continuum mechanics. Academic, New York
Truesdell C, Noll W (1992) The non-linear field theories of mechanics. Springer, Berlin
Wang V, Nielsen P, Nash M (2015). Image-based predictive modeling of heart mechanics. Ann Rev
Biomed Eng 17:351–383
Zheng QS (1994) Theory of representations for tensor functions — a unified invariant approach to
constitutive equations. Appl Mech Rev 47:545–587
3 Continuum Mechanics and Nonlinear Elasticity
Fung YC (1990) Biomechanics: motion, flow, stress, and growth. Springer, New York
Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New York
Fung YC, Fronek K, Patitucci P (1979) Pseudoelasticity of arteries and the choice of its
mathematical expression. Am J Physiol 237:H620–631
Green AE, Adkins JE (1970) Large elastic deformations. Oxford University Press, London
Green AE, Zerna W (1968) Theoretical elasticity. Oxford University Press, London
Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley,
New York
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
Humphrey JD (2002) Cardiovascular solid mechanics: cells, tissues, and organs. Springer, New
York
Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall,
Englewood Cliffs
Mow VC, Kwan MK, Lai WM, Holmes MH, Schmid-Schonbein GW, Woo SLY, and Zweifach BW
(1986) A finite deformation theory for nonlinearly permeable soft hydrated biological tissues.
Frontiers in biomechanics. Springer, New York, pp 153–179
Mow VC, Lai WM, Hou JS (1990) Triphasic theory for swelling properties of hydrated charged
soft biological tissues. Appl Mech Rev 43:S134–S141
Mooney M (1940) A theory of large elastic deformation. J. Appl. Phys. 11:582–592
Narasimhan MN (1993) Principles of continuum mechanics. Wiley-Interscience, Hoboken
Ogden RW (1972) Large deformation isotropic elasticity on the correlation of theory and
experiment for incompressible rubberlike solids. Proc R Soc Lond A Math Phys Eng Sci
326:565–584
Ogden RW (1984) Non-linear elastic deformations. Halsted Press, New York
Rivlin RS (1947) Torsion of a rubber cylinder. J. Appl. Phys. 18:444–449
Rivlin RS (1956) Large elastic deformations. In: F. R. Eirich (Ed.), Rheology: Theory and
applications. Academic Press, New York pp. 351–385
Rivlin RS, Barenblatt GI, Joseph DD (1997). Collected papers of R.S. Rivlin. Springer, New York
Sandersius SA, Chuai M, Weijer CJ, Newman TJ (2011) A ‘chemotactic dipole’ mechanism for
large-scale vortex motion during primitive streak formation in the chick embryo. Phys Biol
8:045008
Simon BR (1992). Multiphase poroelastic finite element models for soft tissue structures. Appl
Mech Rev 45:191–218
Spencer AJM (1980) Continuum mechanics. Wiley, New York
Spencer AJM (1984) Constitutive theory for strongly anisotropic solids. Continuum theory of the
mechanics of fibre-reinforced composites. Springer, New York, pp 1–32
Taber LA (1995) Biomechanics of growth, remodeling, and morphogenesis. Appl Mech Rev
48:487–545
Taber LA (2004) Nonlinear theory of elasticity: applications in biomechanics. World Scientific,
New Jersey
Timoshenko S, Goodier JN (1969) Theory of elasticity. McGraw-Hill, New York
Truesdell C (1991) A first course in rational continuum mechanics. Academic, New York
Truesdell C, Noll W (1992) The non-linear field theories of mechanics. Springer, Berlin
Wang V, Nielsen P, Nash M (2015). Image-based predictive modeling of heart mechanics. Ann Rev
Biomed Eng 17:351–383
Zheng QS (1994) Theory of representations for tensor functions — a unified invariant approach to
constitutive equations. Appl Mech Rev 47:545–587