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Computational micro-macro material testing

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References

  1. Aboudi, J. (1992),Mechanics of composite materials—a unified micromechanical approach, Elsevier, 29.

  2. Ainsworth, M. and Oden, J.T. (2000),A posterori error estimation in finite element analysis, John-Wiley.

  3. Allix, O., Ladevéze, P. and Corigliano, A. (1994), Damage analysis of interlaminar fracture specimens.Composites Structures. 31, 61–74.

    Article  Google Scholar 

  4. Ames, W.F. (1977),Numerical methods for partial differential equations, 2nd edition, Academic Press.

  5. Amieur, M., Hazanov, S. and Huet, C. (1993), “Numerical and experimental study of size and boundary conditions effects on the apparent properties of specimens not having the representative volume”, InMicromechanics of Concrete and Cementitious Composite, C. Huet (Ed.).

  6. Amieur, M. (1994), “Etude numérique et expérimentale des effets d'échelle et de conditions aux limites sur des éprouvettes de béton n'ayant pas le volume représentatif,” Doctoral dissertation No 1256, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland.

    Google Scholar 

  7. Amieur, M., Hazanov, S. and Huet, C. (1995), “Numerical and experimental assessment of the size and boundary conditions effects for the overall properties of granular composite bodies smaller than the representative volume,” InIUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics, D. F. Parker and A. H. England (Eds.), Kluwer Academic Publishers, 149–154, The Netherlands.

    Google Scholar 

  8. Axelsson, O. (1994),Iterative solution methods, Cambridge University Press.

  9. Ball, J.M. (1977), “Convexity conditions and existence theorems in nonlinear elasticity,”Arch. Rational Mech. Anal.,63, 337–403.

    Article  MATH  Google Scholar 

  10. Bolzon, G. and Corigliano, A. (1997), “A discrete formulation for elastic solids with damaging interfaces,”Computer Methods in Applied Mechanics and Engineering,140, 329–359.

    Article  MATH  Google Scholar 

  11. Bonet, J. and Wood, R.D. (1997),Nonlinear continuum mechanics for finite element analysis, Cambridge University Press.

  12. Briggs, W. (1987),A multigrid tutorial, Siam Issue.

  13. Budiansky, B. (1965), “On the elastic moduli of some heterogeneous materials”,Journal of the Mechanics and Physics of Solids,13, 223–227.

    Article  Google Scholar 

  14. Carol, I., Rizzi, E. and Willam, K. (1994), “A unified theory of elastic degradation and damage based on a loading surface”,The International Journal of Solids and Structures,31, No. 20, 2835–2865.

    Article  MATH  Google Scholar 

  15. Chandrasekharaiah, D.S. and Debnath, L. (1994),Continuum mechanics, Academic press.

  16. Cherkaev, A.V. and Gibiansky, L. V. (1992), “The exact coupled bounds for effective tensors of electrical and magnetic properties of two-component two-dimensional composites,”Proc. of Royal Soc. of Edinburgh,122A, 93–125.

    MathSciNet  Google Scholar 

  17. Christensen, R. (1990), “A critical evaluation for a class of micromechanics models”,Journal of the Mechanics and Physics of Solids,38, No. 3, 379–404.

    Article  Google Scholar 

  18. Ciarlet, P.G. (1993),Mathematical Elasticity, Elsevier.

  19. Corigliano, A. (1993), “Formulation, identification and use of interface models in the numerical analysis of composite delamination”,The International Journal of Solids and Structures,30, 2779–2811.

    Article  MATH  Google Scholar 

  20. Courant, R. (1943), “Variational methods for the solution of problems of equilibrium and vibration”,Bull. Am. Math. Soc.,49, 1–23.

    Article  MathSciNet  MATH  Google Scholar 

  21. Crank, J. (1975),The Mathematics of Diffusion, 2nd edition, Oxford Science Publications.

  22. da Silva, M.G. and Ramesh, K.T. (1997), “The rate-dependent deformation and localization of fully dense and porousTi−6Al−4VMater. Sci. Eng.,A232, 11–22.

    Article  Google Scholar 

  23. Davidon, W.C. (1959), “Variable metric method for minimization”, Research and development report. ANL-5990 (Ref.), U.S. Atomic Energy Commision, Argonne National Laboratories.

  24. Drucker, D.C. (1959), “A definition of a stable inelastic material”,J. Appl. Mech.,26, 101–106.

    MathSciNet  MATH  Google Scholar 

  25. Eshelby, J.D. (1957), “The elastic field of an ellipsoidal inclusion, and related problems”,Proc. Roy. Soc.,A241, 376–396.

    Article  MathSciNet  MATH  Google Scholar 

  26. Eustathopoulos, N. and Mortensen, A. (1993), “Capillary phenomena, interfacial bonding and reactivity”, InFundamentals of metal matrix composites, Suresh, S., Mortensen, A. and Needleman, A. (Eds.), Butterworth-Heineman publishers.

  27. Frankel, S.P. (1950), “Convergence rates of iterative treatments of partial differential equations”,Math. Tables Aids Comp.,4, 65–75.

    Article  MathSciNet  Google Scholar 

  28. Gibson, L. and Ashby, M. (1997),Cellular solids. Structure and properties, 2nd edition, Cambridge.

  29. Hashin, Z. and Shtrikman, S. (1962), “On some variational principles in anisotropic and nonhomogeneous elasticity”,Journal of the Mechanics and Physics of Solids,10, 335–342.

    Article  MathSciNet  Google Scholar 

  30. Hashin, Z. and Shtrikman, S. (1963), “A variational approach to the theory of the elastic behaviour of multiphase materials”,Journal of the Mechanics and Physics of Solids,11, 127–140.

    Article  MathSciNet  MATH  Google Scholar 

  31. Hashin, Z. (1983), “Analysis of composite materials: a survey”,ASME Journal of Applied Mechanics,50, 481–505.

    Article  MATH  Google Scholar 

  32. Hazanov, S. and Huet, C. (1994), “Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume”,Journal of the Mechanics and Physics of Solids,42, 1995–2011.

    Article  MathSciNet  MATH  Google Scholar 

  33. Hazanov, S. and Amieur, M. (1995), “On overall properties of elastic heterogeneous bodies smaller than the representative volume”,Int. J. Eng. Science,33,9, 1289–1301.

    Article  MATH  Google Scholar 

  34. Hill, R. (1952), “The Elastic Behaviour of a Crystalline Aggregate”,Proc. Phys. Soc. (Lond.),A65, 349–354.

    Article  Google Scholar 

  35. Hill, R. (1965), “A self consistent mechanics of composite materials”,Journal of the Mechanics and Physics of Solids,13, 213–222.

    Article  Google Scholar 

  36. Hill, R. (1963), “Elastic Properties of reinforced solids: some theoretical principles”,Journal of the Mechanics and Physics of Solids,11, 357–372.

    Article  MATH  Google Scholar 

  37. Huet, C. (1981), “Remarques sur l'assimilation d'un matériau hétérogéne á un milieu continu équivalent”, In C. Huet and A. Zaoui (Eds.),Rheological behaviour and Structure of Materials, 231–245, Presses ENPC, Paris.

    Google Scholar 

  38. Huet, C. (1982), “Universal conditions for assimilation of a heterogeneous material to an effective medium”,Mechanics Research Communications,9 (3), 165–170.

    Article  MATH  Google Scholar 

  39. Huet, C. (1984), “On the definition and experimental determination of effective constitutive equations for heterogeneous materials”.Mechanics Research Communications,11 (3) 195–200.

    Article  Google Scholar 

  40. Huet, C. (1990), “Application of variational concepts to size effects in elastic heterogeneous bodies”,Journal of the Mechanics and Physics of Solids,38, 813–841.

    Article  MathSciNet  Google Scholar 

  41. Huet, C. (1991), “Hierarchies and bounds for size effects in heterogeneous bodies”, InContinuum Models and discrete systems, G.A. Maugin (Ed.), Vol.2, 127–134.

  42. Huet, C., Navi, P. and Roelfstra, P.E. (1991), “A homogenization technique based on Hill's modification theorem”, InContinuum models and discrete systems.

  43. Huet, C. (1997),Activities 1989–1996. Laboratory for Building Materials. P. Navi and A. Tolou (Eds.), Department of Materials Report.

  44. Huet, C. (1997), “An integrated micromechanics and statistical continuum thermodynamics approach for studying the fracture behaviour of microcracked heterogeneous materials with delayed response”,Engineering Fracture Mechanics, Special Issue,58, 5–6, 459–556.

    Article  Google Scholar 

  45. Huet, C. (1999), “Coupled size and boundary condition effects in viscoelastic heterogeneous bodies”,Mechanics of Materials,31,12, 787–829.

    Article  Google Scholar 

  46. Hughes, T.J.R. (1989),The finite element method, Prentice Hall.

  47. Jikov, V.V. Kozlov, S.M. and Olenik, O.A. (1994),Homogenization of differential operators and integral functionals, Springer-Verlag.

  48. Ju, J.W. (1989), “On energy-based coupled elastoplastic damage theories: constitutive modeling and computational aspects”,The International Journal of Solids and Structures,25, 803–833

    Article  MATH  Google Scholar 

  49. Kachanov, L.M. (1986),Introduction to continuum damage mechanics, Martinus Nijoff, Dordricht.

    MATH  Google Scholar 

  50. Kitchen, J. (1966), “Concerning the convergence of iterates to fixed points”,Studia Math.,27, 247–249.

    MathSciNet  MATH  Google Scholar 

  51. Krajcinovic, D. (1996),Damage Mechanics, North Holland.

  52. Kröner, E. (1972),Statistical Continuum Mechanics, CISM Lecture Notes,92, Springer-Verlag.

  53. Ladeveze, P. and Leguillon, D. (1983), “Error Estimate Procedure in the Finite Element Method and Applications”,SIAM J. Numerical Anal.,20, 485–509.

    Article  MathSciNet  MATH  Google Scholar 

  54. Ladaveze, P., Gasser, A. and Allix, O. (1994), “Damage modeling for ceramic composites”,J. of Engineering Mat. and Tech.,116, 331–336.

    Article  Google Scholar 

  55. Lemaitre, J. (1985), “Coupled elasto-plasticity and damage constitutive equations”,Computer Methods in Applied Mechanics and Engineering,51, 31–49.

    Article  MATH  Google Scholar 

  56. Lemaitre, J. and Chaboche, J.-L. (1990),Mechanics of solid materials, Cambridge Univ. Press, Cambridge.

    MATH  Google Scholar 

  57. Le Tallec, P. (1994), “Domain Decomposition Methods in Computational Mechanics”,Computational Mechanics Advances,1, 121–220.

    MathSciNet  MATH  Google Scholar 

  58. Maxwell, J.C. (1867), “On the dynamical theory of gases”,Philos. Trans. Soc. London,157, 49.

    Article  Google Scholar 

  59. Maxwell, J.C. (1873),A treatise on electricity and magnetism, 3rd. Ed., Clarendon Press, Oxford.

    Google Scholar 

  60. Metals Handbook (1975),Failure Analysis and Prevention,8, The American Society for Metals.

  61. Michaud, V. (1992), “Liquid state processing”, InFundamentals of metal matrix composites Suresh, S., Mortensen, A. and Needleman, A. (Eds.)

  62. Mori, T. and Tanaka, K. (1973), “Average stress in matrix and average energy of materials with misfitting inclusions”Acta. Metall.,21, 571–574.

    Article  Google Scholar 

  63. Mura, T. (1993),Micromechanics of defects in solids, 2nd Edition, Kluwer Academic Publishers.

  64. Needleman, A. (1987), “A continuum model for void nucleation by inclusion debonding”,J. Appl. Mech.,54, 525–531.

    MATH  Google Scholar 

  65. Needleman, A. (1990), “An analysis of decohesion along an imperfect interface”,Int. J. Fracture,42, 21–40.

    Article  Google Scholar 

  66. Needleman, A. (1990), “An analysis of tensile decohesion along an interface”,Journal of the Mechanics and Physics of Solids,38, 289–324.

    Article  Google Scholar 

  67. Needleman, A. (1992), “Micromechanical modeling of interfacial decohesion”,Ultramicroscopy,40, 203–214.

    Article  MathSciNet  Google Scholar 

  68. Needleman, A., Nutt, S., Suresh, S. and Tvergaard, V. (1993), “Matrix reinforcement, and interfacial failure”, InFundamentals of metal matrix composites, Suresh, S., Mortensen, A. and Needleman, A. (Eds.), Butterworth-Heineman publishers.

  69. Nemat-Nasser, S. and Hori, M. (1999),Micromechanics: overall properties of heterogeneous solids, 2nd Edition, Elsevier, Amsterdam.

    Google Scholar 

  70. Oden, J.T. and Zohdi, T.I. (1997), “Analysis and adaptive modeling of highly heterogeneous elastic structures”,Computer Methods in Applied Mechanics and Engineering,148, 367–391.

    Article  MathSciNet  MATH  Google Scholar 

  71. Ogden, R.W. (1999),Nonlinear Elasticity, Dover reissue.

  72. Orowan, E. (1944),Proc. Instn. Mech. Engrs.,151, 133, discussion of paper by H. O'Neill).

    Google Scholar 

  73. Ortega, J. and Rockoff, M. (1966), “Nonlinear difference equations and Gauss-Seidel type iterative methods”SIAM J. Numer. Anal.,3, 497–513.

    Article  MathSciNet  MATH  Google Scholar 

  74. Ortiz, M. and Pandolfi, A. (1999), “Finite deformation irreversible cohesive elements for three-dimensional crack-propagation analysis”,The International Journal of Numerical Methods in Engineering,44, 1267–1282.

    Article  MATH  Google Scholar 

  75. Ostrowski, A. (1957), “Les points d'attraction et de répulsion pour l'itération dans l'espace a'n dimensions”,C. R. Acad. Sci. Paris,244, 288–289.

    MathSciNet  Google Scholar 

  76. Ostrowski, A. (1966),Solution of equations and systems of equations, Academic Press, New York.

    MATH  Google Scholar 

  77. Perron, O. (1929), “Über Stabilität und asyptotisches, Verhalten der Lösungen eines Systems endlicher Differenzengleichungen”,J. Reine Angew. Math.,161, 41–64.

    MATH  Google Scholar 

  78. Rayleigh, J.W. (1892), “On the influence of obstacles arranged in rectangular order upon properties of a medium”,Phil. Mag.,32, 481–491.

    Google Scholar 

  79. Reuss, A. (1929), “Berechnung der Fliessgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle”,Z. angew. Math. Mech.,9, 49–58.

    Article  MATH  Google Scholar 

  80. Ruiz, G., Ortiz, M. and Pandolfi, A. (2000), “Three-dimensional finite-element simulation of the dynamic Brazilian tests on concrete cylinders”,The International Journal of Numerical Methods in Engineering,48, 963–994.

    Article  MATH  Google Scholar 

  81. Suresh, S., Mortensen, A. and Needleman, A. (1993),Fundamentals of metal matrix composites, Butterworth-Heineman publishers.

  82. Szabo, B. and Babúska, I. (1991),Finite element analysis, Wiley Interscience.

  83. Torquato, S. (1991), “Random heterogeneous media: microstructure and improved bounds on effective properties”,Appl. Mech. Rev.,44, 37–76.

    MathSciNet  Google Scholar 

  84. Torquato, S. and Lado, F. (1992), “Improved bounds on the effective elastic moduli of random arrays of cylinders”,J. Appl. Mech.,59, 1–6.

    Article  MathSciNet  Google Scholar 

  85. Torquato, S. (1997), “Effective stiffness tensor of composite media I. Exact series expansions”,Journal of the Mechanics and Physics of Solids,45, 1421–1448.

    Article  MathSciNet  MATH  Google Scholar 

  86. Torquato, S. (1998), “Effective stiffness tensor of composite media I. Applications to isotropic dispersions”,Journal of the Mechanics and Physics of Solids,46, 1411–1440.

    Article  MathSciNet  MATH  Google Scholar 

  87. Voigt, W. (1889), “Über die Beziehung zwischen den beiden Elastizitätskonstanten isotroper Körper”,Wied. Ann.,38, 573–587.

    Google Scholar 

  88. Wriggers, P. (2001),Nichtlineare Finite-Element-Methoden, Springer-Verlag.

  89. Wriggers, P., Zavarise, G. and Zohdi, T.I. (1998), “A computational study of interfacial debonding damage in fibrous composite materials”,Computational Materials Science,12, 39–56.

    Article  Google Scholar 

  90. Yazdani, S. and Schreyer, H.L. (1990), “Combined plasticity and damage mechanics model for plain concrete”,ASCE J. of Eng. Mech.,116, No. 7, 1435–1450.

    Article  Google Scholar 

  91. Zohdi, T.I., Oden, J.T. and Rodin, G.J. (1996), “Hierarchical modeling of heterogeneous bodies”,Computer Methods in Applied Mechanics and Engineering,138, 273–298.

    Article  MathSciNet  MATH  Google Scholar 

  92. Zohdi, T.I., Feucht, M., Gross, D. and Wriggers, P. (1998), “A description of macroscopic damage via microstructural relaxation”,The International Journal of Numerical Methods in Engineering,43, 493–507.

    Article  MATH  Google Scholar 

  93. Zohdi, T.I. and Wriggers, P. (1999), “A domain decomposition method for bodies with microstructure based upon material regularization”,The International Journal of Solids and Structures,36, No. 17, 2507–2526.

    Article  MathSciNet  MATH  Google Scholar 

  94. Zohdi, T.L. and Wriggers, P. (1999), “On the effects of microstress on macroscopic diffusion processes”,Acta Mechanica,136, No. 1-2, 91–107.

    Article  MATH  Google Scholar 

  95. Zohdi, T.I. and Wriggers, P. (2000), “A computational model for interfacial damage through microstructural cohesive zone relaxation”,The International Journal of Fracture,101 No.3, L9-L14.

    Google Scholar 

  96. Zohdi, T.I. and Wriggers, P. (2000), “On the sensitivity of homogenized material responses at infinitesimal and finite strains”,Communications in Numerical Methods in Engineering,16, 657–670.

    Article  MATH  Google Scholar 

  97. Zohdi, T.I. and Wriggers, P. (2001), “Aspects of the computational testing of the mechanical properties of microheterogeneous material samples”,The International Journal of Numerical Methods in Engineering,50, 2573–2599.

    Article  MATH  Google Scholar 

  98. Zohdi, T.I. and Wriggers, P. (2001), “A model for simulating the deterioration of structural-scale material responses of microheterogeneous solids”,Computer Methods in Applied Mechanics and Engineering,190, 22–23, 2803–2823.

    Article  MATH  Google Scholar 

  99. Zohdi, T.I. and Wriggers, P. (2001), “Modeling and simulation of the decohesion of particulate aggregates in a binding matrix”,Engineering Computations,18, 1/2, 79–95.

    Article  MATH  Google Scholar 

  100. Zohdi, T.I. (2000), “Overall solution-difference bounds on the effects of material inhomogeneities”,The Journal of Elasticity,58, (3), 249–255.

    Article  MathSciNet  MATH  Google Scholar 

  101. Zohdi, T.I., Wriggers, P. and Huet, C. (accepted), “A method of substructuring large-scale computational micromechanical problems”,Computer Methods in Applied Mechanics and Engineering.

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Dedicated to Christian Huet and J. Tinsley Oden on the occasion of their 65th birthdays.

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Zohdi, T.I., Wriggers, P. Computational micro-macro material testing. Arch Computat Methods Eng 8, 131–228 (2001). https://doi.org/10.1007/BF02897871

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