Advertisement

Consistent Non Local Coupled Damage Model and Its Application in Impact Response of Composite Materials

  • George Z. VoyiadjisEmail author
  • Babur Deliktas
  • Peter I. Kattan
Part of the CISM Courses and Lectures book series (CISM, volume 525)

Abstract

In this work also the mechanics of small damage are also presented using a consistent mathematical and mechanical framework based on the equations of damage mechanics. In this regard, the new scalar damage variable is investigated in detail. The investigation in this work has been carried out for seeking a physical basis is sought for the damage tensor [M] that is used to link the damage state of the material with effective undamaged configuration. The approach presented here provides for a strong physical basis for this missing link. In particular, the authors have made an important link between the damage tensor and fabric tensors. Computational aspects of the presented theory are also discussed. Numerical integration algorithms, verification and validation process of the theory are discussed. The finite element simulations are also performed by implementing the presented model in the commercial finite element code ABAQUS [6.8.3] as a user defined subroutine (VUMAT).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abed, F. H., and Voyiadjis, G. Z., 2007. Adiabatic shear band Localizations in BCC metals at high strain rates and various initial temperatures. International Journal for Multiscale Computational Engineering 5, 325–349.CrossRefGoogle Scholar
  2. Abu Al-Rub, R. K., and Voyiadjis, G. Z., 2003. On the coupling of anisotropic damage and plasticity models for ductile materials. International Journal of Solids and Structures 40, 2611–2643.CrossRefGoogle Scholar
  3. Abu Al-Rub, R. K., and Voyiadjis, G. Z., 2004. Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro-and nano-indentation experiments. International Journal of Plasticity 20, 1139–1182.CrossRefGoogle Scholar
  4. Abu Al-Rub, R. K., and Voyiadjis, G. Z., 2005. A direct finite element implementation of the gradient-dependent theory. International Journal for Numerical Methods in Engineering 63, 603–629.CrossRefGoogle Scholar
  5. Abu Al-Rub, R. K., and Voyiadjis, G. Z., 2006. A finite strain plastic-damage model for high velocity impact using combined viscosity and gradient localization limiters: Part I — Theoretical formulation. International Journal of Damage Mechanics 15, 293–334.CrossRefGoogle Scholar
  6. Abu Al-Rub, R. K., Voyiadjis, G. Z., and Bammann, D. J., 2007. A thermodynamic based higher-order gradient theory for size dependent plasticity. International Journal of Solids and Structures 44, 2888–2923.CrossRefGoogle Scholar
  7. Aifantis, K. E., and Willis, J. R., 2005. The role of interface in enhancing the yield strength of composite and polycrystal. Journal of the Mechanics and Physics of Solids 53, 1047–1070.CrossRefGoogle Scholar
  8. Aifantis, K. E., and Willis, J. R., 2006. Scale effects induced by strain gradient plasticity and interfacial resistance in periodic and randomly heterogeneous media. Mechanics of Materials 38, 702–716.CrossRefGoogle Scholar
  9. Allix, O. P., Ladeveze, P., Gilleta, D., and Ohayon, R., 1989. A Damage Prediction Method for Composite Structures. International Journal of Numerical Methods in Engineering 27, 271–283.CrossRefGoogle Scholar
  10. Anand, L., Gurtin, M. E., Lele, S. P., and Gething, C., 2005. A one-dimensional theory of strain-gradient plasticity: Formulation, analysis, numerical results. Journal of the Mechanics and Physics of Solids 53, 1789–1826.CrossRefGoogle Scholar
  11. Armstrong, R. W., and Zerilli, F. J., 1994. Dislocation Mechanics Aspects of Plastic Instability and Shear Banding. Mechanics of Materials 17, 319–327.CrossRefGoogle Scholar
  12. Arnold, S. M., 1990. Quntification of numerical stifness for a unified viscoplastic constitutive model. Journal of Engineering Materials and Technology-Transactions of the Asme 112, 271–276.CrossRefGoogle Scholar
  13. Arnold, S. M., Saleeb, A. F., and Castelli, M. G., 1994. A fully associative’ nonlinear kinematic’ unified viscoplastic model for tinanium based matrices. In: NASA, (Ed., Washington D.C, pp. 203=209.Google Scholar
  14. Bammann, D. J., Chiesa, M. L., McDonald, A., Kawahara, W. A., Dike, J. J., and Revelli, V. D., 1990. Prediction of Ductile Failure in Metal Structures,. AMD 107, 7–12.Google Scholar
  15. Batra, R. C., and Wei, Z. G.,, 2006. Shear Bands Due to Heat Flux Prescribed at Boundaries. International Journal of Plasticity 22, 1–15.CrossRefGoogle Scholar
  16. Batra, R. C., and Chen, L., 1999. Shear Band Spacing in Gradient-Dependent Thermoviscoplastic Materials. Computational Mechanics 23, 8–19.CrossRefGoogle Scholar
  17. Batra, R. C., and Kim, C. H., 1988. Effect of material characterisctic length on the intiation, growth and band widh of adiabatic shear bands in dipolar materials. Journal De Physique 41–46.Google Scholar
  18. Batra, R. C., and Kim, C. H., 1990. The interaction among adiabatic shear bands in simple and dipolar materials International Journal of Engineering Science 28, 927–942.Google Scholar
  19. Bittencourt, E., Needleman, A., Gurtin, M. E., and Van der Giessen, E., 2003. A comparison of nonlocal continuum and discrete dislocation plasticity predictions. Journal of the Mechanics and Physics of Solids 51, 281–310.CrossRefGoogle Scholar
  20. Borvik, T., Clausen, A. H., Eriksson, M., Berstad, T., Hopperstad, O. S., and Langseth, M., 2005. Experimental and numerical study on the perforation of AA6005-T6 panels. International Journal of Impact Engineering 32, 35–64.CrossRefGoogle Scholar
  21. Borvik, T., Clausen, A. H., Hopperstad, O. S., and Langseth, M., 2004. Perforation of AA5083-H116 aluminium plates with conical-nose steel projectiles-experimental study. International Journal of Impact Engineering 30, 367–384.CrossRefGoogle Scholar
  22. Borvik, T., Dey, S., and Clausen, A. H., 2006. A preliminary study on the perforation resistance of high-strength steel plates. Journal De Physique Iv 134, 1053–1059.CrossRefGoogle Scholar
  23. Borvik, T., Hopperstad, O. S., Berstad, T., and Langseth, M., 2002. Perforation of 12 mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and, conical noses Part II: numerical simulations. International Journal of Impact Engineering 27, 37–64.CrossRefGoogle Scholar
  24. Bronkhorst, C. A., Cerreta, E. K., Xue, Q., Maudlin, P. J., Mason, T. A., and Gray, G. T., 2006. An experimental and numerical study of the localization behavior of tanatlum and stainless steel,”. International Journal of Plasticity 22, 1304–1335.CrossRefGoogle Scholar
  25. Budiansky, B., and O’Connell, R. J., 1976. Elastic Moduli of a Cracked Solid. International Journal of Solids and Structures, 12, 81–97.CrossRefGoogle Scholar
  26. Camacho, G. T., and Ortiz, M., 1997. Adaptive Lagrangian modelling of ballistic penetration of metallic targets. Computer Methods in Applied Mechanics and Engineering 142, 269–301.CrossRefGoogle Scholar
  27. Cauvin, A., and Testa, R., 1999. Damage Mechanics: Basic Variables in Continuum Theories. International Journal of Solids and Structures 36, 747–761.CrossRefGoogle Scholar
  28. Celentano, D. J., Tapia, P. E., and Chaboche, J.-L., 2004. Experimental and Numerical Characterization of Damage Evolution in Steels. In: G. Buscaglia, and E. Dari, O. Z., (Eds.), Mecanica Computacional, Vol. XXIII, Bariloche, Argentina.Google Scholar
  29. Cermelli, P., Fried, E., and Gurtin, M. E., 2004. Sharp-interface nematicisotropic phase transitions without flow. Archive for Rational Mechanics and Analysis 174, 151–178.CrossRefGoogle Scholar
  30. Chaboche, J. L., 1981. Continuous Damage Mechanics — A Tool to Describe Phenomena Before Crack Initiation. Nuclear Engineering and Design 64, 233–247.CrossRefGoogle Scholar
  31. Chelluru, S. K., 2007. Finite Element Simulation of Ballistic Impact of Metal and Composite Plates, Whichita State University.Google Scholar
  32. Chow, C., and Wang, J., 1987. An Anisotropic Theory of Elasticity for Continuum Damage Mechanics. International Journal of Fracture 33, 3–16.CrossRefGoogle Scholar
  33. Christiansen, E. L., and Friesen, L., 1997. Penetration equations for thermal protection materials. International Journal of Impact Engineering 20, 153–164.CrossRefGoogle Scholar
  34. Curran, D. R., Seaman, L., and Shockey, D. A., 1987. Dynamic Failure of Solids. Physics Reports Vol. 147.Google Scholar
  35. Deliktas, B., Voyiadjis, G. Z., and Palazotto, A. N., 2009. Simulation of perforation and penetration in metal matrix composite materials using coupled viscoplastic damage model. Composites Part B: Engineering 40, 434–442.CrossRefGoogle Scholar
  36. Doghri, I., 2000. Mechanics of Deformable Solids-Linear, Nonlinear, Analytical and Computational Aspects. Springer-Verlag, Berlin.Google Scholar
  37. Dorgan, R. J., and Voyiadjis, G. Z., 2003. Nonlocal dislocation based plasticity incorporating gradients of hardening. Mechanics of Materials 35, 721–732.CrossRefGoogle Scholar
  38. Dorgan, R. J., and Voyiadjis, G. Z., 2006. A mixed finite element implementation of a gradient-enhanced coupled damage-plasticity model. International Journal of Damage Mechanics 15, 201–235.CrossRefGoogle Scholar
  39. Dorgan, R. J., and Voyiadjis, G. Z., 2007. Functional forms of hardening internal state variables in modeling elasto-plastic behavior. Archives of Mechanics 59, 35–58.Google Scholar
  40. Dorgan, R. J., and Voyiadjis, G. Z., 2007. Nonlocal coupled damage-plasticity model incorporating functional forms of hardening state variables. Aiaa Journal 45, 337–346.CrossRefGoogle Scholar
  41. Eftis, J., Carrasco, C., and Osegueda, R. A., 2003. A constitutive-microdamage model to simulate hypervelocity projectile-target impact, material damage and fracture. International Journal of Plasticity 19, 1321–1354.CrossRefGoogle Scholar
  42. Fleck, N. A., and Willis, J. R., 2009. A mathematical basis for strain gradient plasticity theory-Part I: Scalar plastic multiplier. Journal of the Mechanics and Physics of Solids 57, 161–177.CrossRefGoogle Scholar
  43. Fleck, N. A., and Willis, J. R., 2009. A mathematical basis for strain gradient plasticity theory-Part II: Tensorial plastic multiplier. Journal of the Mechanics and Physics of Solids 57, 1045–1057.CrossRefGoogle Scholar
  44. Fredriksson, P., and Gudmundson, P., 2005. Size-dependent yield strength and surface energies of thin films. Materials Science and Engineering a-Structural Materials Properties Microstructure and Processing 400, 448–450.CrossRefGoogle Scholar
  45. Fredriksson, P., and Gudmundson, P., 2007. Competition between interface and bulk dominated plastic deformation in strain gradient plasticity. Modelling and Simulation in Materials Science and Engineering 15, S61–S69.CrossRefGoogle Scholar
  46. Fremond, M., and Nedjar, B., 1996. Damage, gradient of damage and principle of virtual power. Int. J. Solids Structures 33, 1103, 1996.CrossRefGoogle Scholar
  47. Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379–1406.CrossRefGoogle Scholar
  48. Gurtin, M. E., 2000. On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. Journal of the Mechanics and Physics of Solids 48, 989–1036.CrossRefGoogle Scholar
  49. Gurtin, M. E., 2004. A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin. Journal of the Mechanics and Physics of Solids 52, 2545–2568.CrossRefGoogle Scholar
  50. Gurtin, M. E., and Anand, L., 2009. Thermodynamics applied to gradient theories involving the accumulated plastic strain:The theories of Aifantis and Fleck and Hutchinson and their generalization. Journal of the Mechanics and Physics of Solids 57, 405–421.CrossRefGoogle Scholar
  51. Gurtin, M. E., and Needleman, A., 2005. Boundary conditions in smalldeformation, single-crystal plasticity that account for the Burgers vector. Journal of the Mechanics and Physics of Solids 53, 1–31.CrossRefGoogle Scholar
  52. Hansen, N. R., and Schreyer, H. L., 1994. A Thermodynamically Consistent Framework for Theories of Elastoplasticity Coupled with Damage. International Journal of Solids and Strucutres 31, 359–389.CrossRefGoogle Scholar
  53. Ireman, P., Klarbring, A., and Stromberg, B., 2003. A model of damage coupled to wear. International Journal of Solids and Structures 40, 2957–2974.CrossRefGoogle Scholar
  54. Johnson, G. R., and Cook, W. H., 1985. Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures. Engineering Fracture Mechanics 21, 31–48.CrossRefGoogle Scholar
  55. Ju, J. W., 1990. Isotropic and Anisotropic Damage Variables in Continuum Damage Mechanics. Journal of Engineering Mechanics, ASCE 116, 2764–2770.Google Scholar
  56. Kachanov, L., 1958. On the Creep Fracture Time. Izv Akad, Nauk USSR Otd Tech (in Russian) 8, 26–31.Google Scholar
  57. Kattan, P. I., and Voyiadjis, G. Z., 1993. Micromechanical Modeling of Damage in Uniaxially Loaded Unidirectional Fiber-Reinforced Composite Laminae. International Journal of Solids and Structures 30, 19–36.CrossRefGoogle Scholar
  58. Kattan, P. I., and Voyiadjis, G. Z., 1993. Overall Damage and Elastoplastic Deformation in Fibrous Metal-Matrix Composites. International Journal of Plasticity 9, 931–949.CrossRefGoogle Scholar
  59. Kattan, P. I., and Voyiadjis, G. Z., 1996. Damage-plasticity in a uniaxially loaded composite lamina: Overall analysis. International Journal of Solids and Structures 33, 555–576.CrossRefGoogle Scholar
  60. Kattan, P. I., and Voyiadjis, G. Z., 2001. Decomposition of damage tensor in continuum damage mechanics. Journal of Engineering Mechanics-Asce 127, 940–944.Google Scholar
  61. Krajcinovic, D., 1996. Damage Mechanics, Elsevier. The Netherlands.Google Scholar
  62. Ladeveze, P., and Lemaitre, J., Damage Effective Stress in Quasi-Unilateral Conditions. The 16th International Cogress of Theoretical and Applied Mechanics, Lyngby, Denmark., 1984.Google Scholar
  63. Ladeveze, P., Poss, M., and Proslier, L., 1982. Damage and Fracture of Tridirectional Composites, Progress in Science and Engineering of Composites. Proceedings of the Fourth International Conference on Composite Materials. Japan Society for Composite Materials, pp. 649–658.Google Scholar
  64. Lee, H., Peng, K., and Wang, J., 1985. An Anisotropic Damage Criterion for Deformation Instability and its Application to Forming Limit Analysis of Metal Plates. Engineering Fracture Mechanics 21, 1031–1054.CrossRefGoogle Scholar
  65. Lemaitre, J., 1984. How to Use Damage Mechanics. Nuclear Engineering and Design 80, 233–245.CrossRefGoogle Scholar
  66. Lemaitre, J., 1984. How to Use Damage Mechanics. Nuclear Engineering and Design 80, 233–245.CrossRefGoogle Scholar
  67. Lemaitre, J., and Chaboche, J. L., 1990. Mechanics of solid materials. Cambridge University New York.Google Scholar
  68. Lemaitre, J., Morchois. Y, Monthule. A, Noppe, J. M., and Riviere, C., 1970. Influence of Fatigue Damage on Strength Characteristics of Materials. Recherche Aerospatiale, 274–&.Google Scholar
  69. Loret, B., and Prevost, H., 1990. Dynamics Strain Localization in Elasto-(Visco-)Plastic Solids, Part 1: General Formulation and One-Dimensional Examples. Computer Methods in Applied Mechanics and Engineering 83, 247–273.CrossRefGoogle Scholar
  70. Lubarda, V., and Krajcinovic, D., 1993. Damage Tensors and the Crack Density Distribution. International Journal of Solids and Structures 30, 2859–2877.CrossRefGoogle Scholar
  71. Luccioni, B., and Oller, S., 2003. A Directional Damage Model. Computer Methods in Applied Mechanics and Engineering 192, 1119–1145.CrossRefGoogle Scholar
  72. Molinari, A., 1997. Collective Behavior and Spacing of Adiabatic Shear Bands. Journal of the Mechanics and Physics of Solids 45, 1551–1575.CrossRefGoogle Scholar
  73. Mori, T., and Tanaka, K., 1973. Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions. Acta Metallurgica 21, 571–574.CrossRefGoogle Scholar
  74. Murakami, S., 1983. Notion of Continuum Damage Mechanics and its Application to Anisotropic Creep Damage Theory. Journal of Engineering Materials and Technology 105, 99–105.CrossRefGoogle Scholar
  75. Needleman, A., 1988. Material Rate Dependent and Mesh Sensitivity in Localization Problems. Computer Methods in Applied Mechanics and Engineering 67, 69–85.CrossRefGoogle Scholar
  76. Nemat-Nasser, S., Isaacs, J. B., and Liu, M., 1998. Microstructure of high-strain, high-strain-rate deformed tantalum. Acta Metallurgica, 46:46, 1307–1325.Google Scholar
  77. Nichols, J. M., and Abell, A. B., 2003. Implementing the Degrading Effective Stiffness of Masonry in a Finite Element Model”, North American Masonry Conference, Clemson, South Carolina, USA.Google Scholar
  78. Nygards, M., and Gudmundson, P., 2004. Numerical investigation of the effect of non-local plasticity on surface roughening in metals. European Journal of Mechanics a-Solids 23, 753–762.CrossRefGoogle Scholar
  79. Park, T., and Voyiadjis, G. Z., 1997. Damage analysis and elasto-plastic behavior of metal matrix composites using the finite element method. Engineering Fracture Mechanics 56, 623–646.CrossRefGoogle Scholar
  80. Park, T., and Voyiadjis, G. Z., 1998. Kinematic description of damage. Journal of Applied Mechanics-Transactions of the Asme 65, 93–98.CrossRefGoogle Scholar
  81. Perez-Prado, M. T., Hines, J. A., and Vecchio, K. S., 2001. [Microstructural evolution in adiabatic shear bands in Ta and Ta-W alloys. Acta Materialia, 49: 2905–2917. 49, 2905–2917.CrossRefGoogle Scholar
  82. Philippon, S., Sutter, G., Dedourge, A., and Molinari, A., 2003. Etude experimentale du frottement. International Journal of Mechanical Production Systems Engineering, High Speed Machining, 57–60.Google Scholar
  83. Philippon, S., Sutter, G., and Molinari, A., 2004. An experimental study of friction at high sliding velocities Wear 257, 777–784.CrossRefGoogle Scholar
  84. Rabotnov, Y., Creep Rupture”, in, edited by 1968, Berlin, pp.. Twelfth International Congress of Applied Mechanics, Berlin, 1969, pp. 342–349.Google Scholar
  85. Sidoroff, F., Description of Anisotropic Damage Application to Elasticity. IUTAM Colloquium on Physical Nonlinearities in Structural Analysis, Berlin, 1981, pp. 237–244.Google Scholar
  86. Sluys, L. J., 1992. Wave Propagation, Localization and Dispersion in Softening Solids (Disertation), The Delft Univ. of Technology, Delft, Netherlands.Google Scholar
  87. Steinberg, D. J., and Lund, C. M., 1989. A Constitutive Model for Strain Rates from 10−4 to 106/s.,Journal of Applied Physics 65, 1528–1533.CrossRefGoogle Scholar
  88. Thiagarajan, G., and Voyiadjis, G. Z., 2000. Directionally constrained viscoplasticity for metal matrix composites. Journal of Aerospace Engineering 13, 92–99.CrossRefGoogle Scholar
  89. Tjernlund, J. A., Gamstedt, E. K., and Gudmundson, P., 2006. Length-scale effects on damage development in tensile loading of glass-sphere filled epoxy. International Journal of Solids and Structures 43, 7337–7357.CrossRefGoogle Scholar
  90. Voyiadjis, G. Z., 1988. Degradation of Elastic-Modulus in Elastoplastic Coupling with Finite Strains. International Journal of Plasticity 4, 335–353.CrossRefGoogle Scholar
  91. Voyiadjis, G. Z., and Abed, F. H., 2006. A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals. International Journal of Plasticity 22, 1398–1431.CrossRefGoogle Scholar
  92. Voyiadjis, G. Z., and Abed, F. H., 2006. Implicit algorithm for finite deformation hypoelastic-viscoplastici in fcc metals. International Journal for Numerical Methods in Engineering 67, 933–959.CrossRefGoogle Scholar
  93. Voyiadjis, G. Z., and Abu Al-Rub, R. K., 2005. Gradient plasticity theory with a variable length scale parameter. International Journal of Solids and Structures 42, 3998–4029.CrossRefGoogle Scholar
  94. Voyiadjis, G. Z., and Abu Al-Rub, R. K., 2006. A Finite Strain Plastic-Damage Model for High Velocity Impacts Using Combined Viscosity and Gradient Localization Limiters, Part II: Numerical Aspects and Simulations International Journal of Damage Mechanics 15, 335–373.CrossRefGoogle Scholar
  95. Voyiadjis, G. Z., and Abu Al-Rub, R. K., 2007. Nonlocal gradient-dependent thermodynamics for Modeling scale-dependent plasticity. International Journal for Multiscale Computational Engineering 5, 295–323.CrossRefGoogle Scholar
  96. Voyiadjis, G. Z., Abu Al-Rub, R. K., and Palazotto, A. N., 2003. Non-local coupling of viscoplasticity and anisotropic viscodamage for impact problems using the gradient theory. Archives of Mechanics 55, 39–89.Google Scholar
  97. Voyiadjis, G. Z., Abu Al-Rub, R. K., and Palazotto, A. N., 2004. Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory. International Journal of Plasticity 20, 981–1038.CrossRefGoogle Scholar
  98. Voyiadjis, G. Z., Abu Al-Rub, R. K., and Palazotto, A. N., 2006. “On the Small and Finite Deformation Thermo-elasto-viscoplasticity Theory: Algorithmic and Computational Aspects,” European Journal of Computational Mechanics (in press). European Journal of Computational Mechanics (Revue Européenne de Mécanique Numérique), 15, 945–987.Google Scholar
  99. Voyiadjis, G. Z., Al-Rub, R. K. A., and Palazotto, A. N., 2008. Constitutive modeling and simulation of perforation of targets by projectiles. AIAA Journal 46, 304–316.CrossRefGoogle Scholar
  100. Voyiadjis, G. Z., and Almasri, A. H., 2008. A physically based constitutive model for fee metals with applications to dynamic hardness. Mechanics of Materials 40, 549–563.CrossRefGoogle Scholar
  101. Voyiadjis, G. Z., and Deliktas, B., 1997. Damage in MMCs using the GMC: theoretical formulation. Composites Part B-Engineering 28, 597–611.CrossRefGoogle Scholar
  102. Voyiadjis, G. Z., and Deliktas, B., 2000. A coupled anisotropic damage model for the inelastic response of composite materials. Computer Methods in Applied Mechanics and Engineering 183, 159–199.CrossRefGoogle Scholar
  103. Voyiadjis, G. Z., and Deliktas, B., 2000. Multi-scale analysis of multiple damage mechanisms coupled with inelastic behavior of composite materials. Mechanics Research Communications 27, 295–300.CrossRefGoogle Scholar
  104. Voyiadjis, G. Z., and Deliktas, B., 2009. Modeling strengthening and softening in inelastic nanocrytalline materials with reference to the triple junction and grain boundaries using Strain Gradient Plasticity. Journal of the Mechanics and Physics of Solids(Submitted).Google Scholar
  105. Voyiadjis, G. Z., Deliktas, B., and Lodygowski, A., 2010. Non-local modeling of heterogeneous media to assess high velocity contact using coupled viscoplasticity damage model. (submitted to a journal).Google Scholar
  106. Voyiadjis, G. Z., and Kattan, P. I., 1992. A Plasticity-Damage Theory for Large Deformation of Solids.1. Theoretical Formulation. International Journal of Engineering Science 30, 1089–1108.CrossRefGoogle Scholar
  107. Voyiadjis, G. Z., and Kattan, P. I., 2006. Damage mechanics with fabric tensors. Mechanics of Advanced Materials and Structures 13, 285–301.CrossRefGoogle Scholar
  108. Voyiadjis, G. Z., and Kattan, P. I., 2007. Evolution of fabric tensors in damage mechanics of solids with micro-cracks: Part I-Theory and fundamental concepts. Mechanics Research Communications 34, 145–154.CrossRefGoogle Scholar
  109. Voyiadjis, G. Z., and Kattan, P. I., 2007. Evolution of fabric tensors in damage mechanics of solids with micro-cracks: Part II-Evolution of length and orientation of micro-cracks with an application to uniaxial tension. Mechanics Research Communications 34, 155–163.CrossRefGoogle Scholar
  110. Voyiadjis, G. Z., and Kattan, P. I., 2007. Evolution of fabric tensors in damage mechanics of solids with micro-cracks: Part II-Evolution of length and orientation of micro-cracks with an application to uniaxial tension. Mechanics Research Communications 34, 155–163.CrossRefGoogle Scholar
  111. Voyiadjis, G. Z., and Kattan, P. I., 2009. Mechanics of small damage in fiberreinforced composite materials. Composite Structures In Press, Corrected Proof, Available online.Google Scholar
  112. Voyiadjis, G. Z., Kattan, P. I., and Taqieddin, Z. N., 2007. Continuum approach to damage mechanics of composite materials with fabric tensors. International Journal of Damage Mechanics 16, 301–329.CrossRefGoogle Scholar
  113. Voyiadjis, G. Z., and Park, T., 1995. Anisotropic Damage of Fiber-Reinforced Mmc Using Overall Damage Analysis. Journal of Engineering Mechanics-Asce 121, 1209–1217.CrossRefGoogle Scholar
  114. Voyiadjis, G. Z., and Park, T., 1995. Local and Interfacial Damage Analysis of Metal-Matrix Composites. International Journal of Engineering Science 33, 1595–1621.CrossRefGoogle Scholar
  115. Voyiadjis, G. Z., and Park, T., 1997. Anisotropic damage effect tensors for the symmetrization of the effective stress tensor. Journal of Applied Mechanics-Transactions of the Asme 64, 106–110.CrossRefGoogle Scholar
  116. Voyiadjis, G. Z., and Park, T., 1997. Local and interfacial damage analysis of metal matrix composites using the finite element method. Engineering Fracture Mechanics 56, 483–511.CrossRefGoogle Scholar
  117. Voyiadjis, G. Z., Taqieddin, Z. N., and Kattan, P. I., 2007. Micromechanical approach to damage mechanics of composite materials with fabric tensors. Composites Part B-Engineering 38, 862–877.CrossRefGoogle Scholar
  118. Voyiadjis, G. Z., and Thiagarajan, G., 1996. A cyclic anisotropic-plasticity model for metal matrix composites. International Journal of Plasticity 12, 69–91.CrossRefGoogle Scholar
  119. Yun, S., and Palazotto, A., 2007. Damage mechanics incorporating two back stress kinematic hardening constitutive models. Engineering Fracture Mechanics 74 2844–2863.CrossRefGoogle Scholar
  120. Zhu, Y. Y., and Cescetto, S., 1995. Fully Coupled Elasto-Visco-Plastic Damage Theory for Anisotropic Materials. International Journal of Solids and Structures, 32, 1607–1641.CrossRefGoogle Scholar
  121. Zukas, J. A., 1990. High Velocity Impact Dynamics. Wiley, New York.Google Scholar

Copyright information

© CISM, Udine 2011

Authors and Affiliations

  • George Z. Voyiadjis
    • 1
    Email author
  • Babur Deliktas
    • 2
  • Peter I. Kattan
    • 1
  1. 1.Department of Civil and Environmental EngineeringLouisiana State UniversityBaton RougeUSA
  2. 2.Department of Civil EngineeringMustafa Kemal UniversityHatay, AntakyaTurkey

Personalised recommendations