Summary
Continuum Damage Mechanics has been applied successfully to technical problems since the idea was introduced by Kachanov almost 40 years ago. In keeping with the traditions of mechanics, the formulation was based on the results of mechanical tests on specimens whose size is measured in centimeters. To model the observations which describe the deterioration of material properties it was found necessary to introduce internal variables referred to as ‘damage’. The approach is phenomenological, with only a minimal attempt to provide a physical interpretation of damage. For this reason the approach has had little appeal to those whose interest is in the physical mechanisms which cause material deterioration. In this presentation a description is given of attempts to develop continuum damage mechanics so that the relationship with the physical mechanism approach is less abrupt. The procedure is illustrated with reference to ceramic matrix composites.
Similar content being viewed by others
References
Kachanov, L. M.: Time of the rupture process under creep conditions. Izv. Akad. Nauk. S.R.S. Odt. Tekh. Nauk. 8 (1958) 26–31
Krajcinovic, D.: Damage mechanics. Mech. Mat. 8 (1989) 117–197
Lemaitre, J.: A course on damage mechanics. Berlin: Springer 1992
Rabotnov, Y. N.: On the equation of state for creep. In Koiter, W. T. (ed) Prager Anniversary Vol. (1963) pp. 307–315, McMillan
Lemaitre, J.: How to use damage mechanics. Nucl. Eng. Design 80 (1984) 233–245
Amar, G.;Dufailly, J.: Identification and validation of viscoplastic and damage constitutive equations. Eur. J. Mech. A/Solids 12 (1993) 197–218
Lemaitre, J.;Dufailly, J.: Damage measurements. Eng. Fract. Mech. 28 (1987) 643–661
Mazars, J.: Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure. Thèse d'état, 1984
Ashby, M. F.; Dyson, B. F.: Creep damage mechanics and micromechanisms. Natl. Phys. Lab. UK 77, 1984
Cocks, A. C. F.;Leckie, F. A.: Creep constitutive equations for damaged materials. Adv. Appl. Mech. 25 (1987) 239–294
Hall, F. R.;Hayhurst, D. R.: Continuum damage mechanics modeling of high temperature deformation and failure in a pipe weldment. Proc. R. Soc. London/A Vol. 433 (1991) 383–403
Evans, A. G.: Perspectives on the development of high-thoughness ceramics. J. Am. Ceram. Soc. 73 (1990) 187–206
Rice, J. R.: Inelastic constitutive relations for solids: An internal variable theory and its application to metal plasticity. J. Mech. Phys. Solids 19 (1971) 433–455
Bataille, J.;Kestin, J.: Irreversible processes and physical interpretations of rational thermodynamics. J. Non Equil. Thermodynamics 4 (1979) 229–258
Germain, P.;Nguyen, Q. S.;Suquet, P.: Continuum thermodynamics. Trans. ASME/J. Appl. Mech. 50 (1983) 1010–1020
Volterra, V.: Sur l'équilibre des corps élastiques multiplement connexes. Annales Scientifiques Ecole Normale Supérieure 24 (1907) 401–518
Love, A. E. H.: The mathematical theory of elasticity. Cambridge: Cambridge University Press 1927
Eshelby, J. D.: The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. R. Soc. London/A 241 (1957) 376–396
Lemaitre, J.;Marquis, D.: Modeling complex behavior of metals by the ‘State-Kinetic Coupling Theory’. J. Eng. Mat. Tech. 114 (1992) 250–254
Budiansky, B.: Thermal and thermoelastic properties of isotropic composites. J. Comp. Mater. 4 (1970) 286
Budiansky, B.;O'Connell, R. J.: Elastic moduli of a cracked system. Int. J. Solids Struct. 12 (1976) 81–97
Lemaitre, J.;Chaboche, J.-L.: Aspect phénoménologique de la rupture par endommagement. J. Mec. Appl. 2 (1978) 317–365
Lemaitre, J.: Sur la détermination des lois de comportement des matériaux élasto-viscoplastiques. Thèse de doctorat d'état, 1971
Chaboche, J.-L.: Description thermodynamique et phénoménologique de la viscoplasticité cyclique avec endommagement. Thèse d'état, 1978
Ladevèze, P.: Sur une théorie de l'endommagement anisotrope. LMT Cachan Report N. 34, 1983
Hill, R.: A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13 (1965) 213–222
Stolz, C.;Zaoui, A.: Combined variational approach and morphological analysis to the behavior of inhomogeneous elastic media. C. R. Acad. Sci. Paris 312 Série II (1991) 143–150
Christensen, R. M.;Lo, K. H.: Solutions for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27 (1979) 315–330
Christensen, R. M.;Lo, K. H.: Solutions for effective shear properties in three phase sphere and cylinder models (erratum). J. Mech. Phys. Solids 34 (1986) 639
Pijaudier-Cabot, G.;Bazant, Z. P.: Nonlocal damage theory. J. Eng. Mech. 113 (1987) 1512–1533
Pijaudier-Cabot, G.;Berthaud, Y.: Damage and interactions in a microcracked medium. Non-local formulation. C. R. Acad. Sci. Paris 310 Série II (1990) 1577–1582
Onat, E. T.;Leckie, F. A.: Representation of mechanical behavior in the presence of changing internal structure. Trans. ASME/J. Appl. Mech. 55 (1988) 1–10
Onat, E. T.: Effective properties of elastic materials that contain penny-shaped voids. Int. J. Eng. Sci. 22 (1984) 1013–1021
Leckie, F. A.; Onat, E. T.: Tensorial nature of damage measuring internal variables. In: Hult, J.; Lemaitre, J. (eds.) Proc. IUTAM Symp. on Physical Nonlinearities in Structures, pp. 140–155. Springer: 1980
Evans, A. G.;Marshall, D. B.: The mechanical behavior of ceramic matrix composites. Acta Metall. 37 (1989) 2567–2583
Cady, C. M.;Makin, T. J.;Evans, A. G.: J. Am. Ceram. Soc. Silicon Carbide Calcium Aluminosilicate-A Notch-Insensitive Ceramic-Matrix Composite, Vol. 18, No. 1, 77–82, 1995
Hutchinson, J. W.;Jensen, H. M.: Models for fiber debonding and fiber pullout in brittle composites with friction. Mech. Mat. 41 (1990) 2365
Evans, A. G.;Domergue, J.-M.;Vagaggini, E.: Methodology for relating the tensile constitutive behavior of ceramic matrix composites to constituent properties. J. Am. Ceram. Soc. 77 (1994) 1425–1435
Allix, O.; Gilletta, D.; Ladeveze, P.: Mechanical behavior of elementary constituents of laminates. Proc. 5th Int. Conf. on Composites Materials (1985) pp. 1039–1057
Jansson, S.;Leckie, F. A.: The mechanics of failure of silicon carbide fiber-reinforced glass-matrix composites. Acta Metall. 40 (1993) 2967–2978
Zienkievicz, O. C.;Taylor, R. L.: The finite element method. London: McGraw-Hill 1989
Hibbitt, H. D.; Karlsson, B. I.; Sorensen, P.: Abaqus, version 5.3, 1993
Chaboche, J.-L.: Le concept de contrainte effective appliquée à l'élasticité et à la viscoplasticité en présence d'un endommagement anisotrope. Colloq. Int. CNRS 295 (1982) 31–43
Hild, F.; Burr, A.; Leckie, F. A.: Matrix cracking and debonding in ceramic-matrix composites, accepted for publication in Int. J. Solids Struct.
Burr, A.; Hild, F.; Leckie, F. A.: Continuum description of damage in ceramic-matrix composites. University of California, Santa Barbara, U.R.I. Report, 1995
Pluvinage, P.: Etude expérimentale et simulation numérique du comportement mécanique de matériaux composites SiC/SiC. Influence des paramètres de stratification et d'élaboration. Thèse d'Université, 1991
Author information
Authors and Affiliations
Additional information
This work was supported by the Defence Advanced Research Project Agency through the University Research Initiative under Office of Naval Research Contract No. N-00014-92-J-1808.
Rights and permissions
About this article
Cite this article
Burr, A., Hild, F. & Leckie, F.A. Micro-mechanics and continuum damage mechanics. Arch. Appl. Mech. 65, 437–456 (1995). https://doi.org/10.1007/BF00835656
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00835656