Abstract
An ‘incremental form’ of anisotropic damage constitutive equation is proposed both for brittle and ductile materials. Based on the concept of irreversible thermodynamics that damage processes are history independent coupled with irreversible energy dissipation, two types of definition for damage representation are established, known as damage tensor D and damage strain tensor εd, to describe constitutive responses of damaged materials. A state variable coupled with damage and other observable state variables, i.e. εd, is formulated separately from other internal variables and defined as an equivalent damage variable. A constitutive relation due to damage is finally formulated by introducing ‘damage flow potential function’ employing the theory of irreducible integrity bases. A clear physical representation based on theoretical foundations and rigorous mathematical arguments of the conventional damage models defined in terms of ‘damage effect tensor M(D)’ is also elucidated. Validity of the proposed model is verified by comparing with the formulations of conventional damage effect tensor. A plastic potential function coupled with damage is also introduced by employing the anisotropic plastic flow theory, so that the proposed damage model can be applied to characterize a wide range of damage problems of practical engineering interest.
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References
S. Murakami, in Continuum Damage Mechanics: Theory and Applications, D. Krajcinovic and J. Lemaitre (eds.) (1987) 91–115.
L.M. Kachanov, Izvestiya Akademii Nauk SSR, Otd Tech Nauk, no. 8 (1958) 26–31.
J. Lemaitre, in Proceedings ICM 1, Kyoto, Japan (1971).
J. Lemaitre and J.L. Chaboche, in Proceedings of IUTAM Symposium on Mechanics of Visco-elastic Media and Bodies, Springer-Verlag, Gothenburg, Sweden (1974).
D. Krajcinovic, Applied Mechanics Review 37, no.1 (1984) 1–6.
J. Lemaitre, Journal of Engineering Materials and Technology 107 (1985) 83–89.
S. Murakami, JSME International Journal 30, no 263 (1987) 701–710.
J.L. Chaboche, in 2nd International Seminar on Incl. Analysis and Life Prediction in High Temperature Environment (1979) 9–14.
J.L. Chaboche, in Mechanical Behavior of Anisotropic Solids, J.P. Bocher (ed.) (1982) 737–760.
F. Sidoroff, in Symposium IUTAM, Physical Non-linearities in Structural Analysis, SENLTS Mai (1980).
L.M. Kachanov, Introduction to Continuum Damage Mechanics 8 Nijhoff, The Netherlands (1986)
C.L. Chow and J. Wang, International Journal of Fracture 33 (1987) 3–16.
C.L. Chow and J. Wang, Engineering Fracture Mechanics 30, No. 5 (1988) 547–563.
C.L. Chow and J. Wang, Engineering Fracture Mechanics 32 no. 4 (1989) 601–612.
C.L. Chow and J. Wang, Engineering Fracture Mechanics 33, no. 2 (1989) 309–317.
C.L. Chow and T.J. Lu, Engineering Fracture Mechanics 34, no. 3 (1989) 679–701.
J.E. Masters and K.L. Reifsnider, Damage in Composite Materials, ASTM STP 775, K.L. Reifsnider (ed.) (1982) 40–62.
A.A. Vakulenko and L.M. Kachanov, Mech. Tverdogo Tiela, no. 4 (1971) 159–166.
D. Krajcinovic and G.U. Fonseka, Journal of Applied Mechanics 48 (1981) 809–815.
R. Alreja, Proceedings, Royal Society London A399 (1985) 195–216.
D.H. Allen and C.E. Harris, International Journal of Solids and Structures 23, No. 9 (1987) 1301–1318.
H. Lee, K. Peng and J. Wang, Engineering Fracture Mechanics 21, no. 5 (1985) 1031–1054.
A.J.M. Spencer, in Continuum Physics Vol. 1, part III, A.C. Eringen (ed.) (1971) 240–355.
R. Talreja, in Yielding, Damage and Failure of Anisotropic Solids, EGF5, J.P. Boechler (ed.) Mechanical Engineering Publications, London (1989) 509–533.
J.W. Ju, International Journal of Solids and Structures 25 no. 7 (1989) 803–833.
C.L. Chow and Y. Wei, International Journal of Fracture 50 (1991) 301–316.
C.L. Chow and T.J. Lu, Theoretical and Applied Fracture Mechanics 14 (1990) 187–218.
R. Hill, The Mathematical Theory of Plasticity, Clarendon Press, Oxford (1950).
W. Olszak and J. Ostrowska-Maciejewska, Engineering Fracture Mechanics 21 no. 4 (1985) 625–632.
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Chow, C.I., Liu, Y.J. & Asundi, A. An incremental stress-based constitutive modeling on anisotropic damaged materials. Int J Fract 64, 299–319 (1993). https://doi.org/10.1007/BF00017847
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DOI: https://doi.org/10.1007/BF00017847