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ABAQUS 1997 Theory Manual, Hibbitt, Karlsson & Sorensen, Inc, Pawtucket, Rhode Island.

Abramowitz M and Stegun IA 1972 Handbook of Mathematical Functions, AMS 55, National Bureau

of Standards, US Department of Commerce.

Anderson JD 1989 Introduction to Flight, McGraw-Hill.

Anderson JD 1991 Fundamentals of Aerodynamics, McGraw-Hill.

Antman 1983 Regular and singular problems for large elastic deformations of tubes, wedges, and

cylinders. Arch. Rational Mech. Anal. 83, 1–52.

Arruda EM and Boyce MC 1993 A three-dimensional constitutive model for the large stretch behavior

of rubber elastic materials. J. Mech. Phys. Solids 41, 389–412.

Ashcraft C, Grimes RG, Pierce DJ and Wah DK 1999 The User Manual for SPOOLES, Release

2.2: An Object Oriented Software Library for Solving Sparse Linear Systems of Equations, Boeing

Shared Services Group, P.O Box 24346, Mail Stop 7L-22, Seattle, Washington 98124 USA, see

also http://netlib.bell-labs.com/netlib/linalg/spooles/spooles.2.2.html.

Ball JM 1977 Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational

Mech. Anal. 63, 337–403.

Barlow J 1976 Optimal stress locations in finite element models. Int. J. Numer. Methods Eng. 10,

243–251.

Bathe K-J 1995 Finite Element Procedures, Prentice Hall.

Beatty MF 1987 Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues

–with examples. Appl. Mech. Rev. 40, 1699–1734.

Belytschko T, Liu WK and Moran B 2000 Nonlinear Finite Elements for Continua and Structures,

Wiley.

Belytschko T and Bindeman LP 1993 Assumed strain stabilization of the eight node hexahedral

element. Comput. Methods Appl. Mech. Eng. 105, 225–260.

Belytschko T and Mish K 2001 Computability in non-linear solid mechanics. Int. J. Numer. Methods

Eng. 52, 3–21.

Bischoff M and Ramm E 1999 Solid-like shell or shell-like solid formulation? A personal view.

In ECCM ’99 Proc. European Conference on Computational Mechanics, Munich, Germany, 31

Aug–3 Sept 1999.

Bonet J and Wood RD 1997 Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge

University Press.

CalculiX 2003 CalculiX: A Three-Dimensional Structural Finite Element Program, Dhondt G and

Klaus W (programmers) “www.calculix.de”.

Chung J, Cho EH and Choi K 2003 A priori error estimator of the generalized–α method for structural

dynamics. Int. J. Numer. Methods Eng. 57, 537–554.

The Finite Element Method for Three-dimensional Thermomechanical Applications Guido Dhondt

2004 John Wiley & Sons, Ltd ISBN: 0-470-85752-8

330 REFERENCES

Ciarlet PG 1993 Mathematical Elasticity, Volume 1: Three Dimensional Elasticity, North Holland.

Crisfield MA 1983 An arc-length method including line searches and accelerations. Int. J. Numer.

Methods Eng. 19, 1269–1289.

Dacorogna B 1989 Direct Methods in Calculus of Variations, Applied Mathematical Sciences 78,

Springer-Verlag, Berlin.

Dhondt G 1993 General behaviour of collapsed 8-node 2-D and 20-node 3-D isoparametric elements.

Int. J. Numer. Methods Eng. 36, 1223–1243.

Dhondt G 2002 Mixed-mode K-calculations in anisotropic materials. Eng. Fract. Mech. 69, 909–922.

Doll S and Schweizerhof K 2000 On the development of volumetric strain energy functions. J. Appl.

Mech. 67, 17–21.

D¨uster A, Br¨oker H and Rank E 2001 The p-version of the finite element method for three-dimensional

curved thin walled structures. Int. J. Numer. Methods Eng. 52, 673–703.

D¨uster A, Hartmann S and Rank E 2003 p-FEM applied to finite isotropic hyperelastic bodies.

Comput. Methods Appl. Mech. Eng. 192, 5147–5166.

Eringen AC (ed.) 1975 Continuum Physics, Volume II: Continuum Mechanics of Single Substance

Bodies, Academic Press, New York.

Eringen AC (ed.) 1976 Continuum Physics, Volume IV: Polar and Nonlocal Field Theories, Academic

Press, New York.

Eringen AC 1980 Mechanics of Continua, Robert E. Krieger Publishing Company, Huntington, New

York.

Fedelich B 2002 A microstructural model for the monotonic and the cyclic mechanical behavior of

single crystals of superalloys at high temperatures. Int. J. Plast. 18, 1–49.

Flores GF and O˜nate E 2001 A basic thin shell triangle with only translational DOFs for large strain

plasticity. Int. J. Numer. Methods Eng. 51, 57–83.

Freitag LA and Knupp PM 2002 Tetrahedral mesh improvement via optimization of the element

condition number. Int. J. Numer. Methods Eng. 53, 1377–1391.

Gabald´on F and Goicolea JM 2002 Linear and non-linear finite element error estimation based on

assumed strain fields. Int. J. Numer. Methods Eng. 55, 413–429.

Geers MGD, Ubachs RLJM and Engelen RAB 2003 Strongly non-local gradient-enhanced finite

strain elastoplasticity. Int. J. Numer. Methods Eng. 56, 2039–2068.

George P-L and Borouchaki H 1998 Delauney Triangulation and Meshing: Application to Finite

Elements, Kogan Page.

Gradshteyn IS and Ryzhik IM 1980 Table of Integrals, Series and Products, Academic Press.

Graff KK 1975 Wave Motion in Elastic Solids, Ohio State University Press.

Greenberg MD 1978 Foundations of Applied Mathematics, Prentice Hall, Englewood Cliffs, New

Jersey.

Halphen B and Nguyen Quoc Son 1975 Sur les mat´eriaux standards g´en´eralis´es. Journal deMґecanique

14, 39–63.

Hartmann S 2001a Numerical studies on the identification of the material parameters of Rivlin’s

hyperelasticity using tension-torsion tests. Acta Mech. 148, 129–155.

Hartmann S 2001b Parameter estimation of hyperelasticity relations of generalized polynomial-type

with constraint conditions. Int. J. Solids Struct. 38, 7999–8018.

Hartmann S and Neff P 2003 Polyconvexity of generalized polynomial-type hyperelastic strain energy

functions for near-incompressibility. Int. J. Solids Struct. 40, 2767–2791.

Hartmann S 2003 Finite-Elemente Berechnung inelastischer Kontinua, Habilitationsschrift, Berichte

des Instituts f¨ur Mechanik (Bericht 1/2003), Universit¨at Kassel, Germany.

Havner KS 1992 Finite Plastic Deformation of Crystalline Solids, Cambridge University Press.

Hilber HM 1976 Analysis and Design of Numerical Integration Methods in Structural Dynamics, PhD

Thesis, University of California, Berkeley.

REFERENCES 331

Hilber HM and Hughes TJR 1978 Collocation, dissipation and ‘overshoot’ for time integration

schemes in structural dynamics Earthquake Eng. Struct. Dyn. 6, 99–117.

Hilber HM, Hughes TJR and Taylor RL 1977 Improved numerical dissipation for time integration

algorithms in structural dynamics. Earthquake Eng. Struct. Dyn. 5, 283–292.

Holzapfel GA 2000 Nonlinear Solid Mechanics, Wiley.

Holzapfel GA, Gasser TC and Ogden RW A 2000 new constitutive framework for arterial wall

mechanics and a comparative study of material models J. Elasticity 61, 1–48.

Hughes TJR 2000 The Finite Element method, Dover, New York.

Hulbert GM and Hughes TJR 1987 An error analysis of truncated starting conditions in step-by-step

time integration: consequences for structural dynamics Earthquake Eng. Struct. Dyn. 15, 901–910.

Incropera FP and DeWitt DP 2002 Fundamentals of Heat and Mass Transfer, Wiley.

Itskov M 2001 A generalized orthotropic hyperelastic material model with application to incompressible

shells. Int. J. Numer. Methods Eng. 50, 1777–1799.

Kachanov LM 1971 Foundations of the Theory of Plasticity, North Holland Publishing Company.

Kaliske M and Rothert H On the finite element implementation of rubber-like materials at finite

strains. Eng. Comp. 14, 216–232.

Kim JB, Yoon JW and Yang DY 2003 Investigation into the wrinkling behaviour of thin sheets in

the cylindrical cup deep drawing process using bifurcation theory. Int. J. Numer. Methods Eng.

56, 1673–1705.

Koiter WT 1960 General theorems for elastic-plastic solids. In Progress in Solid Mechanics 6, Sneddon

IN and Hill R (eds), North Holland, Amsterdam, 167–221.

Lee EH and Liu DT 1967 Finite-strain elastic-plastic theory of application to plane wave analysis. J.

Appl. Phys. 38, 19–27.

Lee EH 1969 Elastic plastic deformation at finite strains. J. Appl. Mech. 36, 1–6.

Lehoucq RB, Sorensen DC and Yang C 1998 ARPACK Users’ Guide, SIAM.

Lemaitre J and Chaboche JL 1990 Mechanics of Solid Materials, Cambridge University Press, Cambridge,

UK.

Liew KM and Rajendran S 2002 New superconvergent points of the 8-node serendipity plane element

for patch recovery. Int. J. Numer. Methods Eng. 54, 1103–1130.

Lubliner J 1985 A model of rubber viscoelasticity. Mech. Res. Commun. 12, 93–99.

Luenberger DG 1989 Linear and Nonlinear Programming, Addison-Wesley Publishing Company,

Reading, Massachusetts.

ML¨uhrs G, Hartmann S and Haupt P 1997 On the numerical treatment of finite deformations in

elastoviscoplasticity. Comput. Methods Appl. Mech. Eng. 144, 1–21.

Mackinnon RJ and Carey GF 1989 Superconvergent derivatives: a Taylor series analysis. Int. J.

Numer. Methods Eng. 28, 489–509.

Mang HA, Hellmich C, Lackner R and Pichler B 2001 Computational structural mechanics. Int. J.

Numer. Methods Eng. 52, 569–587.

Marsden JE and Hughes TJR 1983 Mathematical Foundations of Elasticity, Dover, New York.

Matthies H and Strang G 1979 The solution of nonlinear finite element equations. Int. J. Numer.

Methods Eng. 14, 1613–1626.

Meirovitch L 1967 Analytical Methods in Vibrations, The MacMillan Company, London.

Meissonnier FT, Busso EP and O’Dowd NP 2001 Finite element implementation of a generalised

non-local rate-dependent crystallographic formulation for finite strains. Int. J. Plast. 17, 601–640.

M´eric L and Cailletaud G 1991 Single crystal modeling for structural calculations: Part 2: Finite

element implementation. J. Eng. Mater. Tech. 113, 171–182.

M´eric L, Poubanne P and Cailletaud G 1991 Single crystal modeling for structural calculations: Part 1

Model presentation. J. Eng. Mater. Tech. 113, 162–170.

332 REFERENCES

Miehe C 1996a Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity

for single crystals. Int. J. Numer. Methods Eng. 39, 3367–3390.

Miehe C 1996b Multisurface thermoplasticity for single crystals at large strains in terms of Eulerian

vector updates. Int. J. Solids Struct. 33, 3103–3130.

Miranda I, Ferencz RM and Hughes TJR 1989 An improved implicit-explicit time integration method

for structural dynamics. Earthquake Eng. Struct. Dyn. 18, 643–653.

Mu˘gan A and Hulbert GM 2001a Frequency-domain analysis of time-integration methods for semidiscrete

finite element equations –Part I: Parabolic problems. Int. J. Numer. Methods Eng. 51,

333–350.

Mu˘gan A and Hulbert GM 2001b Frequency-domain analysis of time-integration methods for semidiscrete

finite element equations –Part II: Hyperbolic and parabolic-hyperbolic problems. Int. J.

Numer. Methods Eng. 51, 351–376.

Ogden RW 1984 Non-Linear Elastic Deformations, Dover, New York.

Popov EP 1968 Introduction to Mechanics of Solids, Prentice Hall, Englewood Cliffs, New

Jersey.

Press WH, Flannery BP, Teukolsky SA and Vetterling WT 1990 Numerical Recipes in Pascal, Cambridge

University Press.

Prudhomme S, Oden T, Westermann T, Bass J and Botkin ME 2003 Practical methods for a posteriori

error estimation in engineering applications. Int. J. Numer. Methods Eng. 56, 1193–1224.

Puso MA 2000 A highly efficient enhanced assumed strain physically stabilized hexahedral element.

Int. J. Numer. Methods Eng. 49, 1029–1064.

Ramamurti V and Seshu P 1990 On the principle of cyclic symmetry in machine dynamics. Commun.

Appl. Numer. Methods 6, 259–268.

Reddy JN and Gartling DK 2001 The Finite Element Method in heat Transfer and Fluid Dynamics,

CRC Press.

Reese S 1994 Theorie und Numerik des StabilitЁatsverhaltens hyperelastischer FestkЁorper, Dissertation,

Fachbereich Mechanik, Technische Hochschule Darmstadt, Germany.

Reese S, Raible T and Wriggers P 2001 Finite element modelling of orthotropic material behaviour

in pneumatic membranes. Int. J. Solids Struct. 38, 9525–9544.

Reese S 2001 Thermomechanische Modellierung gummiartiger Polymerstrukturen, Habilitationsschrift,

Institut f¨ur Baumechanik und Numerische Mechanik (Bericht F01/4), Universit¨at Hannover,

Germany.

Reese S 2002 On the equivalence of mixed element formulations and the concept of reduced integration

in large deformation problems. Int. J. Nonlin. Sc. Num. Sim. 3, 1–33.

Reese S 2003a On a consistent hourglass stabilization technique to treat large inelastic deformations

and thermo-mechanical coupling in plane strain problems. Int. J. Numer. Methods Eng. 57,

1095–1127.

Reese S 2003b Meso-macro modelling of fibre-reinforced rubber-like composites exhibiting large

elastoplastic deformation. Int. J. Solids Struct. 40, 951–980.

Reese S and Svendsen B 2003 On the use of evolving structure tensors to model initial and induced

elastic and inelastic anisotropy at finite deformation. J. Phys. IV France 105, 31–37.

Reese S and Wriggers P 2000 A stabilization technique to avoid hourglassing in finite elasticity. Int.

J. Numer. Methods Eng. 48, 79–109.

Riks E 1987 Progress in collapse analyses. J. Press. Vessel Tech. 109, 33–41.

Rumpel T and Schweizerhof K 2003 Volume-dependent pressure loading and its influence on the

stability of structures. Int. J. Numer. Methods Eng. 56, 211–238.

Save MA and Massonnet CE 1972 Plastic Analysis and Design of Plates, Shells and Disks, North

Holland Publishing Company.

REFERENCES 333

Schr¨oder J, Gruttmann F and L¨oblein J 2002 A Simple Orthotropic Finite Elasto-Plasticity Model

Based on generalized Stress-Strain measures, Report No 2, Institut f¨ur Mechanik, Fachbereich 10,

Universit¨at Essen, 45117 Essen, Germany.

Schr¨oder J and Neff P 2001 Invariant Formulation of Hyperelastic Transverse Isotropy Based on

Polyconvex Free Energy Functions, Report No 1, Institut f¨ur Mechanik, Fachbereich 10, Universit¨at

Essen, 45117 Essen, Germany.

Simo JC 1988a A framework for finite strain elastoplasticity based on maximum plastic dissipation

and the multiplicative decomposition: Part I: Continuum formulation. Comput. Methods Appl.

Mech. Eng. 68, 199–219.

Simo JC 1988b A framework for finite strain elastoplasticity based on maximum plastic dissipation

and the multiplicative decomposition: Part II: Computational aspects. Comput. Methods Appl. Mech.

Eng. 68, 199–219.

Simo JC and Hughes TJR 1997 Computational Inelasticity, Springer-Verlag, New York.

Simo JC and Miehe C 1992 Associative coupled thermoplasticity at finite strains: formulation, numerical

analysis and implementation. Comput. Methods Appl. Mech. Eng. 98, 41–104.

Simo JC and Taylor RL 1991 Quasi-incompressible finite elasticity in principal stretches. Continuum

basis and numerical algorithms. Comput. Methods Appl. Mech. Eng. 85, 273–310.

Sloan SW 1989 A FORTRAN program for profile and wavefront reduction. Int. J. Numer. Methods

Eng. 28, 2651–2679.

Spencer AJM 1971 Theory of invariants. In Continuum Physics, Volume I: Mathematics, Eringen

Cemal A (ed.), Academic Press, New York.

Stor˚akers B 1986 On material representation and constitutive branching in finite compressible elasticity.

J. Mech. Phys. Solids 34, 125–145.

Stroud AH 1971 Approximate Calculation of Multiple Integrals, Prentice Hall.

Sze KY, Chan WK and Pian THH 2002 An eight-node hybrid-stress solid-shell element for geometric

non-linear analysis of elastic shells. Int. J. Numer. Methods Eng. 55, 853–878.

Tautges TJ 2001 The generation of hexahedral meshed for assembly geometry: survey and progress.

Int. J. Numer. Methods Eng. 50, 2617–2642.

Timoshenko SP and Goodier JN Theory of Elasticity, International Student Edition, McGraw-Hill

Kogakusha Ltd.

Treloar LRG 1975 The Physics of Rubber Elasticity, Third Edition, Oxford University Press.

van den Bogert PAJ and de Borst R 1994 On the behaviour of rubber-like materials in compression

and shear. Arch. Appl. Mech. 64, 136–146.

Verron E, Marckmann G and Peseux B 2001 Dynamic inflation of non-linear elastic and viscoelastic

rubber-like membranes. Int. J. Numer. Methods Eng. 50, 1233–1251.

Wriggers P, Eberlein R and Reese S 1996 A comparison of three-dimensional continuum and shell

elements for finite plasticity. Int. J. Solids Struct. 33, 3309–3326.

Zienkiewicz OC and Taylor RL 1989 The Finite Element Method, Fourth Edition, McGraw-Hill,

London.

Zienkiewicz OC and Zhu JZ 1992a The superconvergent patch recovery and a posteriori error estimates.

Part 1: The recovery technique. Int. J. Numer. Methods Eng. 33, 1331–1364.

Zienkiewicz OC and Zhu JZ 1992b The superconvergent patch recovery and a posteriori error estimates.

Part 2: Error estimates and adaptivity. Int. J. Numer. Methods Eng. 33, 1365–1382.