Holpzaphel_-_Nonlinear-Solid-Mechanics-a-Contin

420 References

:Flory, P.J. .[1976], Statistical thermodynamics of random networks, Proceedings of the Royal Society of London A351, 35 l-J80. {7)

Flory, PJ., and Erman, B. fl 982], Theory of elasticity of polymer networks, Macromolecul.es

15, 800-806. (6)

Fung, Y.C. [1965], Foundation of Solid Mechanics, Prentice-Hall, Englewood Cliffs, New Jer- sey. (8)

Fung, Y.C. [1.990], Biomechanics. Motion, Flow, Stress, and Grmvth, Springer-Verlag, New York. (6)

Fung, Y.C. [ 1993], Biomeclumics. Mechanical Properties o..f Living Tissues., 2nd edn., SpringerVer1ag, New York. (6)

Fung, Y.C. fl 997], Biomechanics. Circulation, 2-nd edn., Springer-Verlag, New York. (6)

Fung, Y.C., Fronek, K., and :Patitucci, P. [1979], Pseudoelasticily of arteries and the choice of its mathematical expression, American Phyj·iological Society 237, H620-H63 L (6)

Gent, A.N. [1962], Relaxation processes in vulcanized rubber. I. Relation amo.ng ·stress relaxation, creep, recovery and hysteresis, Jouma.l ofApplied Polymer Science 6, 433-44l. (6)

Glowinski, R.., and Le Tallcc, P. [1984], Finite element analysis in nonlinear .incompressible elasticity, in: J.T. Oden, and G.F. Carey, eds., Finite elements, Special Problems in Solid Mechanics, Volume V, Prentice-Hall, Englewood ·Cliffs, New Jersey. (8)

Glowinski, R., and Le Tallec, P. [I. 989], i\ugmellf.ed Lagrangian mu/ Operator Splitting lvleth- ods in Nonlinear Meehan.less, SIAM, Philadelphia. (8)

Gough, J. [1805], A description o.f a property of Caoutchouc or :indian rubber; with some rellections on the case of the e.lasticity .of this substance,

sophical Society of Manchester 1, 288-295. (7)

Govindjee, S.? and Simo, J.C. [1991], A micro-mechanically based continuum ·damuge model for carbon black-filled rubbers .incorporating the ·Mullins' effect, Journal ofthe Mechanics and Physics of Solids 39, 87-.112. (6)

Govindjee, S., and Simo, J.C. ["I 992a], Transition from micro-mechanics to computalionally efficient phenomenology: carbon black filled rubbers incorporating Mullins' effect.. Joumal

of tire Mechanics and Physics ofSolids 40, 213-233. (6)

Gov.indjee, S., and Simo, J.C. [1992b], Mullins' .effect and the strain amplitude .dependence of the storage modulus, International Journal of Solids and Structures 29, 1.737-1751.. (6)

Govindjee, S., and Simo, J.C. [I 993], Coupled stress-diffusion: case II, Journal ofthe Mechanics and Physics of Solids 41, 863-867,. (6)

Green, A.E., and Adkins, J.E. .(1970], Large Elastic De.formations, 2nd edn.~ Oxford University Press, Oxford. (6)

Green, M.S., and Tobolsky, A. V. [1946], A new approach to the theory of relaxing polymeric

Guth, E.. I1966].., Statistical mechanics of polymers, Joumal of Polymer Science C.12.. 89-

1.09. (7)

Guth, E., and Mark, H. {1935], Zur innermolekularen Stutistik, insbesonde.re bei Kenen-

molekiilen I, Monatshe.fte fiir Chemie wul verwandte Teile anderer Wisse11scha.fren 65,

93-]21. (7)

Haddow, J.B,., and Ogden, R.W. [1990], Thermoelasticity of rubber-like solids at small strains, in: G. Eason, and R.W. Ogden't eds., Elastidty, Mathematical Methods and Applications, the Ian N. Sne<ldon 70th Birthday Volume, Ems Horwood, Chichester, 165-1.79. (7)

Halmos, P.R. :[1958], Fi11ite-Dime11sio11al Vector Spaces, 2nd edn., Van Nostrand-Reinhold,

New York. (I)

, Harwood, J.A.C., and .Payne, A.R. [1966a]., Stress softening in natural rubber vulcanizates. Part UL Carbon black-filled vulcanizalcs, Journal ~(Applied Polymer Science 10, 315-324. (6)

Harwood, J.A.C., and .Payne, A.R. f.l 966bJ, Stress softening in natural rubber vulcanizates. Parl IV. Unfilled vulcanizatcs, Journal c~fApplied Polymer Science 10., .1203-1211. (6)

Harwood, J.A.C., ·Mullins, L,., and Payne, A.R. [1965], Stress softe.ning in natural rubber vulcanizates. Part II. Stress softening effects in pure gum and filler loaded rubbers, Joumal

<?fApplied .Polymer Science 9, 30.11-3021. (6)

Haughton, D.M. [l 980), Post-bifurcation of perfect and imperfect spherical elastic membranes, lmemarional Journal ofSolids mu/ Structures 16, 1123-1133. (6)

Haughton, D.M. p987], Inf.lation and bifurcation of thick-walled compressible e1astic spherical shells, /MA Joumal ofApplied .Mathematics 39., 259-272. {6)

Haughton, D.M.., and Ogden, R.W. ll 978], On the incremental equations in non-linear elastic- ity - U. Bifurcation of pressurized spherical shells, Journal ofthe Mechanics and Physics of Solids 26, .l 1. l-138. (6)

Haupt, P. [l 993a], On the mathematical modelling of material behavior in continuum mechanics., Acta Mechanica 100, .129-.154. (6)

Joule, J.P. [1859], On some thermo-dynamic properties of solids, Philosophical .Transaction..'i of the Royal Society of London A149, 91-131. (7)

Kachanov, L.M. [I. 958], Time of the rupture process under creep conditions, /zvestija Akademii Nauk Sojuza Sovetskiclz Socialisticeskiclz Respubliki (SSSR) Otdelenie Teclmiceskich

Nauk (Moskra) "8, 26-31. (6)

Kachanov, L.M. [1986], Introduction to Cmztimmm Damage Mechanics, Marlinus Nijhoff Publishers_, Dordrechl, The Netherlands. (6)

Kaliske, M., and Rothert, H. fl 997], Formulation and implementation of three-dimensional viscoelasticity at small and finite strains, Computational Meclumics 19, 228-239. (6)

.Kawabata, S.t and Kawai, H. [ 1977], Strain energy density functions of rubber vulcanizations from .biaxial extension, in: H.-J. Cantow et al., -eds., Advances in Polymer Science, Volume 24, Springer-Verlag, Berlin, 90-124. (6)

Kestin, J. [ 1979], A Course in Thermodym1m.ics, Volume l,II, McGraw-Hill, New York. (4)

Knauss, W., and Emri, I. [.I 981], Non-linear viscoelasticity based on Free volume considerations, Computers and Structures 1.3, 123-128. (6)

Koh, S.L., and Eringen, A.C. [1963], On lhe foundations of non-linear thenno-v.iscoelasticily., lmema.tional Journal of Engineering Science 1, 19.9-229. (6)

Krajcinovic, D. [.1996], Damage Mechanics, North-Holland, Amsterdam. (6)

Krawitz, A. "[1986], Materialrheorie. Mathematisclze Beschreilmng des Pliiinomenologischen Thermomechatzischen Verhaltens, Springer..Verlag, Ber.Jin. (7)

Kuhn, W. [1938], Die Bedeutung der Ncbenvalenzkraflc fur die elastischen Eigenschaften hochmolekularer Stofte, Ange1va11dte Clzemle 51, 640-647. (7)

Kuhn, W. fl 946], Dependence of the average lransversal on the longitudinal dimensions of statistical coils formed by chain mo.lccules, Journal of Polymer Science 1., 380-388. (7)

Kuhn, W., and Griin, F. [1942]., Beziehungen zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe, Kolloid-Zeitsclzr{ft 101, 248-27]. (7)

Lee, E.H. [1969], Elastic-plastic defonnation at finite strains, Journal ofApplied Mechanics 36,

1-6. (6)

Lee., S.M., ed.. U990), llllernatio11al E11cyclopedia of Cmnposites., Volume l ,2.,3, VCH Publishers, New York. (6)

Lee, S.M.. , ed. [199.I], lntenwtional Encyclopedia ofComposites, vo·-lume 4,5., VCH Publishers,

New York. (6)

Lee, T.C.P., .Sperling, L.H., and Tobolsky, A.V. [1.966]. Thermal stabi.lity of elastomeric networks ut high temperatures, Journal ofApplied Polyn1er Science 10, 1831-1836. (7)

Lemaitre, l [1996], A Course on Damage Mechanics, 2nd revised and enlarged edn., Springer-

Verlag, .Berlin. (6)

Lemaitre, J., and Chaboche, J.-L. [1990], Mechanics ofSolid Materials., Cambridge University Press, Cambridge. (6)

Le Tallec, P. [1994}, Numerical methods for nonlinear three-dimensional -elasticity, in: P.G.

Ciaflet, and J.L. Lions, eds.., Handbook of Numerical Analysis., Volume Ill, North-

.Holland, Elsevier, 465-622. (6,8)

Lion, A. [1996], A constitutive model for carbon black filled rubber: experimental investiga- tions and mathematical representation, Continuum l\4echanics and Thermodynamics 6,

.153-169. (6)

Lion, A. I1997.a], On the large deformation behavior of reinforced rubber at different temperatures, Journal of the Mechanic~._ and Physics of Solids 45, 1805-t 834. (6)

.Lion, A. [ l 997b], A physically based method to represent the thermo-mechanical behaviour of

elastomers, Acta Mechanica 123, 1-25. (7)

Lubliner, J. [1985], A model of rubber viscoelasticity, Medumics Research Communications

12, 93-99. (6)

Luenberger, D.G. [1984], Linear .and Nonlinear Programming, Addison..Wesley Publishing

Company, Reading, Massachusetts. (8)

Malkus, D.S., and Hughes, T.J.R. [1978], Mixed finite clement methods - reduced and selective integration techniques:A uni.ft.cation of concept, Computer Methods in Applied Mechanics and Engineering 15, 63-8.l. (8)

Malvern, L.E. [ 1969], Introduction to the MeclumicJ of a Cominuous Medium, Prentice-Hall,

Englewood Cliffs, New Jersey. (2.,3,4,6,7)

l\llan, C.-S .., and Guo, Z.-H. [199.3], A basis-free formula for time rate of Hill's strain tensors, lntematiomzl Journal ofSolids and Structures 30, 2819-2842. (2)

Marchuk, G.l [ 1982], Methods of Nwnerical A1atlrematics, 2nd edn.., Springer-Verlag, New York. (7)

Mark, J.E., and Erman, B. [1988], Rubberlike Elasticity a Molecular Primer, John WHey ~

Sons, New York. (6,7)

:Marsden, J.E., and Hughes, T.J.R. [1994], Mathematical Foundatiol"ls (~fElasticity, Dovert New

York. {l ,2,6,8)

McCrum, N.G., .Buckley, C.P.., and Bucknall, C.B. [1997], Principles of Polymer Engineering,

2nd edn., Oxford University Press, Oxford. (6,7)

Miehe, C. [ 1988.], Zur numerischen Behandlung thennomechanischer Prozesse, Technischer

.Bericht F 88/6, Forschungsund Seminarberichlc nus dem Bereich der Mechanik .der

Universitlit Hannover. (7)

Miehe, C. [1994], Aspects of the formulation and finite .elemenl implementation of large strain isotropic .elasticity, llllemationa/ Joumal for Numerical .Methods in Engineering

37' 1981-2004. (2,6)

Miehe, C. .(J 995a], Discontinuous and continuous damage evolution in Ogden..type large-strain elastic materials, European Journal of Meclumics, 1VSolids 14, 697-720. (6)

Miehe, C. ['1995b], Entropic thermoelasticity al finite strains. Aspects of the formulation and

numerical implemenlalion, Computer Metlwds in ;\pplied Mechanics and Engineering

120, 243-269. (7)

M.iche, C. f 1996], Numerical computation of algorithmic .(consistent) tangent moduli in lurgcstrain computaLional ine.lastic.ity, Computer Methods in Applied Mechatzk't and Engineer-

ing 134, 223-240. (6)

·Miehe, C., and Keck~ J. [2000J, Superimposed finite elastic-viscoclastic-pla.stoelastic stress response w.ith damage in filled rubbery polymers. Expcrjmcnts, modelling .and algorithmic implementation, Journal <~lthe Mechanic..\' and Plzysics of Solids,. Lo appear. (6)

Miehe, C., and Stein, E. [ 1992], A canonical model of multiplicative elasto-plasticity. For- mulation and aspects ·Of the .numerical implementation., European Journal of Mechanics, A/Solids 11., 25-43. (6)

Mooney, ·M. fl 940], A theory of large elastic deformation, Journal ofApplied Physics .11, 582-

592. (6)

·Morman, Jr., K.N. [1986], The generalized strain measure with application to nonhomogeneous deformation~ in rubber-like solids, Journal .ofApplied Mechanics 53, 726-728. (2)

Muller, I. [1985], Thermodynamics, Pitman Advanced Publishing Program, Boston. (7)

Mullins, L. I1947], Effect of stretching on Lhe properties of rubber, Joumal ofRubber Rese.arch

16, 275-289. (6)

Mullins, L. -[1969], Softening of rubber·~y deformation, Rubber Chemistry and Technology 42,

339-362. (6)

·Mull.ins, L., and Thomas~ A.:G. "[1960], Determ.inatio.n of degree of crosslinking in natural rub.. bcr vulcanizates. Part V. Effocl of network flaws due to free chain ends, Journal t~fPolymer

Science 43, "1"3-21. (7)

strain ampIificalion factor to describe the elastic behavior of fi lier-reinforced vulcanized rubber., Journal ofApplied Polymer Science 9, 299J-3009. (6)

Naghdi, P.M., and Trapp, J.A. [1975], The significance of formufating plaslicity theory with

reference to .loading surfaces in strain space, Jmemational Journal ofEngineering Science

13, 785-797.. (6)

Nagtegaal, J.C., Parks_, D.M... and Rice, J.R. [ 1974], On numerically accurate finite element.

solutions in the fully plastic range, Computer Methods in Applied Mechanics and Engi-

neering 4, I53-177.. (8)

Needleman.. A. [1977], Inflation of spherical -rubber balloons, International Journal of Solids and Structures 13, 409--421. (6)

Needleman, A., Rabinowitz, S.A., Bogen, D.K., and McMahon, T.A. [ 1983), A finite clcmenl model of .the infarclcd left ventricle., Jouma/ of Biomecha11ics 16, 45-58. (6)

NickeU, R.E., and Sackman, J.L. [1968], Approximate solutions in linear, coup.led .thermoelas- ticity, Joumal ofApplied Mechanics 35, 255-266. (7)

Oden, J.T. [1969], Finite element analysis of nonlinear problems in the dynamical theory of coupled thermoelasticily, Nuclear Engineering and Design 10, 465--475. (7)

Oden, J.T. [ 1972], Finite Elements of Nonlinear Cominua, McGraw-Hill, New York. (7,.8)

Oden, J.T., and Reddy, J.N. [ 1976], Variational Melhods in Theoretical Meclumics, Springcr-

Ver-lag, Heidelberg. (8)

Ogden, R.W. [1972a], Large deformation isotropic efasticity - on the correlation of -theory and experiment for incompressible rubberlike solidst Proceedings ofthe Royal Society of London A326, 565-584. (6,7)

Ogden, R.W. [I 972b], Large deformation -isotropic .elasticity: on the correlation of theory and experiment for compressible rubberlikc solids, Proceedings of the Royal Society of London A328, 567-583. (6,7)

Ogden, R.W. U982], Elastic defonnations of rubberlike solids, in: H.G. Hopkins, and M.J. Sewcll,-cds., Mechanics of Solids, the Rodney Hill 60tli Anniversary Volume, Pergamon Press, Oxford., 499-537. (6)

Ogden, R.W. [I 9.86]t Recent advances in the phcnomenolog-ical theory of rubber elasticity,

Rubber Chemistry and Tec;lmology 59, 26.1-383. (6)

Ogden, R. W. [ 1987], Aspects of t-he phenomenological theory of rubber thennoelasticity, Po/y.. mer 28, 379-385. (6)··

References

Ogden, R.W. .[I 992a], Nonlinear elasticity: Incremental equations and bifurcation phenomena,

No11li11ear Equations in the Applied Sciellces 2, 437-468. (6)

Ogden, R.W. [ l 992b]t On the thermoelastic modeling of rubberlike solids, Journal of Thermal

Stresses 15, 533-557. (7)

Ogden, R.W. [1997], Non-linear Elastic Defomzations, Dover, New York. (1,.2,5,6,8)

Ogden, R.W., and Rox·burgh, D.G. [1999a], A pseudo-elastic model for the Mullins ·effect in filled rubber, Proceedings of the Royal Society of London A455, 2861-2877. (6)

Ogden, R.W., and Roxburgh, D.G. fl999b], An energy-based model of the Mullins effect, in:

A. Dorfmann, and A. Muhr, eds., Constitutive Models for Rubber, Balkema, Rotterdam,

23-28. (6)

Ortiz, M. [ 1999], Nanomechanics of defects in solids, in: Advances in Applied Mechanics,

Volume 36, Academic Press, New York, .t-79. -(2)

Price, C. [ 1976], Thennodynamics of rubber elasticity, Proceedings of the Roylll Society of

London A351~ 331-350. (7)

Raoult, A. .[:1986], Non..polyconvex.ity of the stored -energy function of a Saint Vcnant-Kirchhoff material~ Aplikace Matltematiky 6, 417-419. (6)

Reddy, J.N. [1.993], An /11troduction to the Finite Element Method, 2nd edn._, McGraw-Hill, Boston. (8)

Reese, S~. and Govindjee, S. [1998a], A theory of fini.te viscoelastici~y and numerical aspects, lntemational Journal ofSolids and Structures 35, 3455-3482. (6)

Reese, S., and Govindjee, S. [1998b], Theoretical and numerical aspects in the thcrmoviscoelastic material behavior of rubber-like polymers, Atfechanics of time-dependent materials ·1,

357-396. (7)

Reissner, E. [1950], On a variational theorem in elasticity, Journal .ofMathematics and Physics

2·9, 90-95. (8)

Rhodin, J.A.G. [19.80], Archilecture of the vessel wall, in-: D.F. Bohr, A.D. S.omlyo, and H. V.

Sparks, Jr., eds., Handbook of Physiology, The Cardiovascular System., Section 2, Vo.f- ume 2, American Physiologial Society, Bethesda, Maryland, 1-3.l. (6)

Rivlin, R.S.. [1948], Large elastic deformations of isotropic materials. IV. Further developments of the general theory, Philosophical Transactions of the Royt1l Society of London A241, 379-397. (6)

Rivlin, R.S. [ l949a], Large elastic deformations of .isotropic materials. V. The problem of flexure, Proceedi118s oftlze Royal Society of London A195, 463--473. (6)