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Mechanics of Solids with a Progressively Deteriorating Structure

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Application of Fracture Mechanics to Cementitious Composites

Part of the book series: NATO ASI Series ((NSSE,volume 94))

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Abstract

This report summarizes the applications of the continuum damage theory to problems of mechanics of rocks and concrete. The report discusses the basic aspects of the theory such as the selection of the internal variable describing the distribution of microdefects, establishment of the ‘damage laws’, the essential structure of the governing equations etc. Finally, the discussion focuses on a number of as yet unresolved problems of some theoretical and practical significance.

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References

  1. Bazant Z.P., Kim S. S. (1979), Plastic-Fracturing Theory for Concrete, Journal of Engineering Mechanics Division, ASCE, 105, p. 429–446.

    Google Scholar 

  2. Budianshy B., O’Connell R.J. (1976), Elastic Moduli of a Cracked Solid, International Journal of Solids and Structures, 12, p. 81–97.

    Article  Google Scholar 

  3. Chaboche J. L. (1978), Description Thermodynamique et Phenamenologique de la Viscoplasticite Cyclique avec Endommagement, ONERA, Publ. No. 1978–3.

    Google Scholar 

  4. Chaboche J. L. (1979), Concept of Effective Stress Applied to Problems of Elasticity and Viscoplasticity Combined with Anisotropic Damage (Le Concept de Contrainte Effective Applique a l’Elasticite et la Viscoplasticite on Presence d’un Endommagement Anisotrope), ONERA, T.P. No. 1979–77.

    Google Scholar 

  5. Costin L. S. (1983), A Microcrack Model for the Deformation and Failure of Brittle Rock, Journal of Geophysical Research, 88, p. 9485–9492.

    Article  ADS  Google Scholar 

  6. Curran D. R., Seaman L., Shockey D. A., (1977) Dynamic Failure in Solids, Physics Today, 30, p. 46–55.

    Article  ADS  Google Scholar 

  7. Davison L., Stevens A. L., Kipp M. E., (1977), Theory of Spall Damage Accumulation in Ductile Metals, Journal of Mechanics and Physics of Solids, 25, p. 11–28.

    Article  ADS  Google Scholar 

  8. Dougill J. W., (1976), On Stable Progressively Fracturing Solids, ZAMP, 27, p. 423–437.

    Article  ADS  MATH  Google Scholar 

  9. Dougill J. W., Lau J. C., Burt N. J., (1977), Toward a Theoretical Model for Progressive Failure and Softening in Rock, Concrete and Similar Material, ASCE-EMD 1976, University of Waterloo Press, p. 335–355.

    Google Scholar 

  10. Dragon A., Mroz Z., (1979), A Continuum Model for Plastic-Brittle Behavior of Rock and Concrete, International Journal of Engineering Science, 17, p. 121–137.

    Article  MATH  Google Scholar 

  11. Evans B., Wong T. F., (1983), Shear Localization in Rocks Induced by Tectonic Deformation, in W. Prager Symposium on Mechanics of Geomaterials: Rocks, Concretes, Soils, Ed. Z.P. Bazant.

    Google Scholar 

  12. Goodman M. A., Cowin S. C., (1972), A Continuum Theory for Granular Material, Archive for Rational Mechanics and Analysis, 44, p. 249–266.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Grady D. E., Kipp M. E., (1980), Continuum Modelling of Explosive Fracture in Oil Shale, International Journal for Rock Mechanics, Mineral Sciences and Geomechanics, 17, p. 147–157.

    Google Scholar 

  14. Halbauer D. K., Wagner H., Cook N. G. W., (1973), Some Observations Concerning The Microscopic and Mechanical Behavior of Quartzite Specimens in Stiff, Triaxial Compression Tests, International Journal for Rock Mechanics, Mineral Sciences and Geomechanics, 10, p. 713–726.

    Google Scholar 

  15. Halphen B., Son N. Q., (1975), On the Generalized Standard Materials, (Sur les Materiaux Standards Generalises), Journal de Mecanique, 14, p. 39–63.

    MATH  Google Scholar 

  16. Hill R., (1967), The Essential Structure of Constitutive Laws for Metal Composites and Polycrystals, Journal of Mechanics and Physics of Solids, 15, p. 79–95.

    Article  ADS  Google Scholar 

  17. Hill R., Rice J. R., (1972), Constitutive Analysis of Elastic — Plastic Crystals at Arbitrary Strain, Journal of Mechanics and Physics of Solids, 20, p. 401–413.

    Article  ADS  MATH  Google Scholar 

  18. Hoagland R. G., Hahn G. T., Rosenfeld A.R., (1973), Influence of Microstructure on Fracture Propagation in Rock, Rock Mechanics, 5, p. 77–106.

    Article  Google Scholar 

  19. Holmen J. O., (1982), Fatigue of Concrete by Constant and Variable Amplitude Loading, in Fatigue of Concrete Structures, ed. S. P. Shah, ACI Publication SP-75.

    Google Scholar 

  20. Horii H., Nemat-Nasser S., (1983), Overall Moduli of Solids with Microcracks: Load Induced Anisotropy, Journal of Mechanics and Physics of Solids, 31, p. 155–171.

    Article  ADS  MATH  Google Scholar 

  21. Hutchinson J. W., (1976), Elastic-Plastic Behavior of Polycrystalline Metals and Composites, Proceedings of the Royal Society, Series A, 319, p. 247–272.

    Article  ADS  Google Scholar 

  22. Jaeger J. C., Cook N.G.W., (1979), Fundamentals of Rock Mechanics, third edition, Chapman and Hall, London.

    Google Scholar 

  23. Kachanov L. M., (1958), On the Creep Rupture Time, Izvestia AN SSSR, OTN, No. 8, p. 26–31 (in Russian).

    Google Scholar 

  24. Kachanov M. (1980), Continuum Model of Medium with Cracks, Journal of the Engineering Mechanics Division, ASCE 106, EM5, p. 1039–1051.

    Google Scholar 

  25. Kachanov M. L., (1982), A Microcrack Model of Rock Inelasticity, Parts I–III, Mechanics of Materials, 1, 19–41, 123–129.

    Article  Google Scholar 

  26. Kestin I., Bataille J., (1978), Irreversible Thermodynamics of Continua and Internal Variables, in Continuum Models of Discrete systems, ed. Provan J.W., University of Waterloo Press, Study No. 12.

    Google Scholar 

  27. Kovari K., Tisa A., (1974), Upper and Lower Strength of Rocks in Triaxial Testing, (Hoechstfestigkeit und Restfestigkeit von Gesteinen im Triazialversuch), ETH, Mitteilung Nr. 26.

    Google Scholar 

  28. Krajcinovic D., (1979), A Distributed Damage Theory of Beams in Pure Bending, Journal of Applied Mechanics, 46, p. 592–596.

    Article  ADS  MATH  Google Scholar 

  29. Krajcinovic D., (1983), Constitutive Equations for Damaging Materials, Journal of Applied Mechanics, 50, p. 355–360.

    Article  ADS  MATH  Google Scholar 

  30. Krajcinovic D., (t.b.p.), Continuous Damage Mechanics Revisited, submitted for publication.

    Google Scholar 

  31. Krajcinovic D., Fonseka G. U., (1981), The Continuous Damage Theory of Brittle Materials, Parts I, II, Journal of Applied Mechanics, 48, p. 809–824.

    Article  ADS  MATH  Google Scholar 

  32. Krajcinovic D., Selvaraj S., (1983), Constitutive Equations for Concrete, in Proceedings of International Conference on Constitutive Laws for Engineering Materials, ed. Desai C. S., Gallagher R. H., Tucson Az.

    Google Scholar 

  33. Krajcinovic D., Sestan J. Z., (1983), Design Methods for Analysis of Damage Accumulating Structures, Proceedings of 7th International SKIRT Conference, Vol.L, 8/4, Chicago, IL.

    Google Scholar 

  34. Krajcinovic D., Silva M. A. G., (t.b. p.), Damage to Colliding Concrete Cubes, to appear in Journal of Structural Mechanics Division, ASCE.

    Google Scholar 

  35. Krajcinovic D., Srinivasan M. G., (1983), Dynamic Fracture of Concrete, in Time-Dependent Failure Mechanisms and Assessment Methodologies, ed. Early J.G., Cambridge University Press.

    Google Scholar 

  36. Kroener E., (1962), Dislocation: A New Concept in the Continuum Theory of Plasticity, Journal of Mathematics and Physics, 42, p. 27–37.

    Google Scholar 

  37. Lade P. W., (1982), Three–Parameter Failure Criterion for Concrete, Journal of the Engineering Mechanics Division, ASCE, 108, p. 850–863.

    Google Scholar 

  38. Leckie F. A., (1978), The Constitutive Equations of Continuum Creep Damage Mechanics, Philosophical Transaction of the Royal Society, Series A, 288, p. 27–47.

    Article  ADS  Google Scholar 

  39. Lemaitre J., Chaboche J. L., (1978), Phenomenological Aspects of Rupture through Damage, (Aspect Phenomenologique de la Rupture par Endommagement), Journal de Mecanique Appliquee, 2, p. 317–365.

    Google Scholar 

  40. Lemaitre J., Mazars J., (1982), Application of the Damage Theory in Nonlinear Response and Rupture of Concrete Structures, (Application de 1a theorie de l’andommagement au comportement non lineare et a la rupture du beton de structure), Annales de l‘ITBTP, No. 401.

    Google Scholar 

  41. Litewka A., Sawczuk A., (1981), A Yield Criterion for Perforated Sheets, Ingenieur-Archiv, 50, p. 393–400.

    Article  MATH  Google Scholar 

  42. Loland K. E., (1981), Mathematical Modelling of Deformational and Fracture Properties of Concrete Band on Principles of Damage, (Matematisk Modellering av Betongens Deformasjons-og Bruddegenskaper Basert Pa Skademekaniske Prinsipper), University of Trondheim, Rapport BML 81. 101.

    Google Scholar 

  43. Margolin L. G., (1983), Elastic Moduli of a Cracked Body, International Journal of Fracture, 22, p. 65–79.

    Article  Google Scholar 

  44. Mazars J., (1981), Mechanical Damage and Fracture of Concrete Structures, in Advances in Fracture Research (Fracture 81) ed. Francois D., Vol. 4, p. 1499–1506.

    Google Scholar 

  45. Mazars J., (1984), Application of the Damage Mechanics in Non-linear Response and Rupture of Concrete Structures, (Application de la Mecanique de l’Endommagement au Comportment Non Lineare to a la Rupture du Baton de Structure), These de Doctorat d’Etat, Universite Pierre et Marie Curie, Paris 6.

    Google Scholar 

  46. McHugh S. L., Curan D. R., Seaman L., (1980), The NAG-FRAG Computational Fracture Model and its Use for Simulating Fragmentation and Fracture, SESA meeting, Fort Lauerdale FL.

    Google Scholar 

  47. Mroz Z., Angellilo M., (1982), Rate-Dependent Degradation Model for Concrete and Rock, in Numerical Models in Geomechanics, ed. Dungar R., A. A. Balkema, Roterdam.

    Google Scholar 

  48. Murakami S., Ohno N., (1981), A Continuum Theory of Creep and Creep Damage, in Creep in Structures, ed. Pouter A.R.S. Pouter, Springer-Verlag.

    Google Scholar 

  49. Nemat-Nasser S., (1975), On Nonequilibrium Thermo-Dynamics of Viscoelasticity: Inelastic Potentials and Normality Conditions, in Mechanics of Visco-Elastic Media and Bodies, ed. Hult J., Springer-Verlag.

    Google Scholar 

  50. Nicholson D. W., (1981), Constitutive Model for Rapidly Damaging Structural Materials, Acta Mechanica, 39, p. 195–205.

    Article  MathSciNet  MATH  Google Scholar 

  51. Ouchterlony F., (1983), A Distributed Damage Approach to Combined Bending and Axial Loading of Rock Beams, in Mechanical Behavior of Materials, ed. Carlsson I., Ohlson N. G., Volume 2, Pergamon Press.

    Google Scholar 

  52. Pak A. P., Trapeznikov L. P., (1981), Experimental Investigations Based on the Griffith-Irwin Theory Processes of the Crack Development in Concrete, in Advances in Fracture Research (Fracture 81), Vol. 4, ed. Francois D., p. 1531–1539.

    Google Scholar 

  53. Passwan S. L., Grady D. E., Rundle J. B., (1980), The Role of Inertia in the Fracture of Rock, Journal of Applied Physics, 51, p. 4070–4075.

    Article  ADS  Google Scholar 

  54. Peirce D., Asaro R. J., Needleman A., (1982), An Analysis of Nonuniform and Localized Deformation in Ductile Single Crystals, Acta Metallurgica, 30, p. 1087–1119.

    Article  Google Scholar 

  55. Rice J. R., (1971), Inelastic Constitutive Relations f or Solids: An Internal Variable Theory and its Application to Metal Plasticity, Journal of Mechanics and Physics of Solids, 19, p. 433–455.

    Article  ADS  MATH  Google Scholar 

  56. Rice J. R., (1975), Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms, in Constitutive Equations in Plasticity, ed. Argon A. S., the MIT Press.

    Google Scholar 

  57. Rusinko K. N., (1981), Theory of Plasticity and Nonstationary Creep, Lvov (in Russian).

    Google Scholar 

  58. Shah S. P., Chandra S., (1968), Critical Stress, Volume Change and Microcracking of Concrete, Journal of the American Concrete Institute, 65, p. 770–781.

    Google Scholar 

  59. Spencer A. J. M., (1971), Theory of Invariants, in Continuum Physics, Vol. I, ed. Eringen A. C., Academic Press.

    Google Scholar 

  60. Suaris W., Shah S. P., (1984), Rate-Sensitive Damage Theory for Brittle Solids, Journal of Engineering Mechanics, ASCE, 110, p. 985–997.

    Article  Google Scholar 

  61. Tapponier P., Brace W. F., (1976), Development of Stress-Induced Microcracks in Westerly Granite, International Journal of Rock Mechanics and Mineral Science, 13, p. 103–112.

    Article  Google Scholar 

  62. Vakulenko A. A., Wachanov M. L., (1971), Continuum Theory of Cracked Media, Mekhanika Tverdogo Tela, 6, p. 159–166.

    Google Scholar 

  63. Wong T. F., (1982), Micramechanics of Faulting in Westerly Granite, International Journal of Bock Mechanics and Mineral Sciences, 19, p. 49–64.

    Article  Google Scholar 

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© 1985 Martinus Nijhoff Publishers, Dordrecht

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Krajcinovic, D. (1985). Mechanics of Solids with a Progressively Deteriorating Structure. In: Shah, S.P. (eds) Application of Fracture Mechanics to Cementitious Composites. NATO ASI Series, vol 94. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-5121-1_15

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  • DOI: https://doi.org/10.1007/978-94-009-5121-1_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8764-3

  • Online ISBN: 978-94-009-5121-1

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