A stress-strain relation on the basis of a homogenized continuum is devel oped from a potential energy function for an elastic material with anisotropic damage. It is assumed that the influence of the state of damage can be represented by a vector-valued function, resulting from an array of surface discontinuities with coinciding orientation such as disk-like, parallel cracks. Usually, only low-order polynomial expansions in terms of the damage variable have been considered in the literature, limiting the results to non- interacting microcracks. In this paper, a complete polynomial expansion of the potential function with respect to the damage variable is developed and the general form of the con stitutive tensor for the damaged material is derived. This allows account to be taken of nonlinear dependencies of the effective elastic properties on the damage variable in the case of interacting microcracks.
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References
1.
Betten, J.1982. "Net-Stress Analysis in Creep Mechanics," Ingenieur-Archiv, 52:405-419.
2.
Betten, J.1983. "Damage Tensors in Continuum Mechanics," Journal de Mechanique Théorique et Appliquée, 2:13-32.
3.
Betten, J.1986. 'Applications of Tensor Functions to the Formulation of Constitutive Equations Involving Damage and Initial Anisotropy," Engng. Frac. Mech. , 25:573-584.
4.
Costin, L.S.1985. "Damage Mechanics in the Post-Failure Regime," Mechanics of Materials, 4:149-160.
5.
Davison, L. and A.L. Stevens.1973. "Thermomechanical Constitution of Spalling Elastic Bodies," J. Appl. Phys. , 44(2).
6.
Gottesman, T., Z. Hashin and M.A. Brull.1980. "Effective Elastic Moduli of Cracked Fiber Composites," in Advances in Composite Material, Proc. 3rd. Int. Conf. Composite Materials, Paris, 1980, A. R. Bunsell et al., eds., Pergamon Press, pp. 749-758.
7.
Green, A.E. and P.M. Naghdi.1979. "A Note on Invariance under Superimposed Rigid Body Motion," J. Elasticity, 9(1):1-8.
8.
Herakovich, C.T., J. Aboudi, S.W. Lee and E.A. Strauss.1988. "Damage in Composite Laminates : Effects of Transverse Cracks," Mechanics of Materials , 7:91-107.
9.
Hibbs, M.F. and W.L. Bradley.1987. "Correlations between Micromechanical Failure Processes and the Delamination Toughness of Graphite/Epoxy Systems," in Fractography of Modern Engineering Materials, Composites and Metals, ASTM STP 948, J. E. Masters et al., eds., Philadelphia : ASTM, pp. 68-97.
10.
Highsmith, A.L. and K.L. Reifsnider.1982. "Stiffness-Reduction Mechanisms in Composite Laminates," in Damage in Composite Materials, ASTM STP 775, K. L. Reifsmder, ed., pp. 103-117.
11.
Kachanov, L.M.1958. "Time of Rupture Process under Creep Conditions," Izv. Akad. Nauk S.S.S.R., Otd. Tekh. Nauk, 8:26-31.
12.
Kachanov, M.1980. "Continuum Model of Medium with Cracks," J Eng. Mech. Div., ASCE106 (EM5), pp. 1039-1051.
13.
Kachanov, M.1987. "On Modelling of Anisotropic Damage in Elastic-Brittle Materials-A Brief Review," in Damage Mechanics in Composites, AD-Vol. 12, A. S. D. Wang et al., eds., New York : ASME, pp. 99-105.
14.
Kachanov, M.1987. "Elastic Solids with Many Cracks: A Simple Method of Analysis," Int. J. Solids Structures , 23(1):23-43.
15.
Krajcinovic, D. and G.U. Fonseka.1981. "The Continuous Damage Theory of Brittle Materials, Part I and II,"J. of Appl. Mech. , 48:809-824.
16.
Krajcinovic, D.1989. "Damage Mechanics," Mechanics of Materials, 8:117-197.
17.
Laws, N., G.J. Dvorak and M. Hejazi.1983. "Stiffness Changes in Umdirectional Composites Caused by Crack Systems," Mechanics of Materials , 2:123-137.
18.
Laws, N. and G.J. Dvorak.1987. "Transverse Matrix Cracking in Composite Laminates," in Composite Material Response: Constitutive Relations and Damage Mechanisms, G. E. Smith, ed., Elsevier Applied Science.
19.
Nuismer, R.J.1980. "Predicting the Performance and Failure of Multidirectional Polymenc Matnx Composite Laminates: A Combined Micro-Macro Approach," in Advances in Composite Material, Proc. 3rd Int. Conf Composite Materials, Pans1980, A. R. Bunsell et al., eds., Pergamon Press, pp. 436-452.
20.
Onat, E.T.1984. "Effective Properties of Elastic Materials that Contam Penny Shaped Voids," Int. J. Engng. Sci., 22(8)-(10):1013-1021.
21.
Rabotnov, Y.N.1969. Creep Problems in Structural Members, (engl. transl. of Polzuchest Elementov Konstruktsu. North-Holland, Amsterdam.
22.
Spencer, A.J.M.1971. "Theory of Invariants," in Continuum Physics, Vol. I, A. C. Enngen, ed., Academic Press.
23.
Spencer, A.J.M.1972. Deformations of Fiber-Reinforced Materials. Oxford University Press.
24.
Spencer, A.J.M.1982. "The Formulation of Constitutive Equations for Amsotropic Solids," in Mechanical Behavior of Anisotropic Solids , J. P. Boehler, ed., Paris: Nijhoff, The Hague and Editions du CNRS, pp. 2-26.
25.
Spencer, A J. M.1984. "Constitutive Theory for Strongly Amsotropic Solids," in Continuum Theory of the Mechanics of Fiber-Reinforced Composites, A. J. M. Spencer, ed., Springer Verlag.
26.
Smith, G.F.1982. "On Transversely Isotropic Functions of Vectors, Symmetric Second-Order Tensors and Skew-Symmetric Second-Order Tensors," Quart. Appl. Math. , 39:509-516.
27.
Talreja, R.1985. "A Continuum Mechanics Characterization of Damage in Composite Materials," Proc. R. Soc. Lond. Ser. A. , 399:195-216.
28.
Talreja, R.1985. "Transverse Cracking and Stiffness Reduction in Composite Laminates," J. of Composite Materials, 19:355-373.
29.
Talreja, R.1990. "Internal Variable Damage Mechanics of Composite Materials," in Yielding, Damage and Failure of Anisotropic Solids, Proc. of the IUTAM/ICM Symp , J. P. Boehler, ed., Mechanical Engineering Publ.
30.
Weitsman, Y.1987. "Coupled Damage and Moisture-Transport in Fiber-Reinforced, Polymeric Composites,"Int. J. Solids Structures, 23(7):1003-1025.
