Abstract
In this work, the concept of a linearized damage variable is introduced within the framework of continuum damage mechanics. Instead of considering one single fictitious undamaged configuration, a number n of smaller fictitious undamaged configurations are utilized. Thus, a smaller and linearized damage variable can be defined for each individual fictitious undamaged configuration. Additionally, the equations of damage evolution are formulated with respect to each individual fictitious undamaged configuration. Some interesting and surprising results are obtained. In this regard, a new result is obtained for the strain energies with respect to the n fictitious undamaged configurations. The linearized damage variable can be used for states of damage where the damage is small. The formulation is linear elastic based on linear superposition and should be applicable to many high-cycle fatigue problems.
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References
Celentano D.J., Tapia P.E., Chaboche J-L.: Experimental and numerical characterization of damage evolution in steels. In: Buscaglia, G., Dari, E., Zamonsky, O. (eds) Mecanica Computacional, vol. XXIII, Bariloche, Argentina (2004)
Doghri I.: Mechanics of Deformable Solids: Linear and Nonlinear, Analytical and Computational Aspects. Springer, Germany (2000)
Hansen N.R., Schreyer H.L.: A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. Int. J. Solids Struct. 31(3), 359–389 (1994)
Kachanov, L.: On the Creep Fracture Time. Izv Akad, Nauk USSR Otd Technical, vol. 8, pp. 26–31 (1958) (in Russian)
Kattan P.I., Voyiadjis G.Z.: A plasticity-damage theory for large deformation of solids–part II: applications to finite simple shear. Int. J. Eng. Sci. 31(1), 183–199 (1993)
Kattan P.I., Voyiadjis G.Z.: Decomposition of damage tensor in continuum damage mechanics. J. Eng. Mech. ASCE 127(9), 940–944 (2001)
Kattan P.I., Voyiadjis G.Z.: Damage Mechanics with Finite Elements: Practical Applications with Computer Tools. Springer, Germany (2001)
Ladeveze, P., Poss, M., Proslier, L.: Damage and fracture of tridirectional composites. In: Progress in Science and Engineering of Composites. Proceedings of the Fourth International Conference on Composite Materials, vol. 1, pp. 649–658. Japan Society for Composite Materials (1982)
Ladeveze, P., Lemaitre, J.: Damage effective stress in quasi-unilateral conditions. In: The 16 International Congress of Theoretical and Applied Mechanics. Lyngby, Denmark (1984)
Lubineau G.: A pyramidal modeling scheme for laminates—identification of transverse cracking. Int. J. Damage Mech. 19(4), 499–518 (2010)
Lubineau G., Ladeveze P.: Construction of a micromechanics-based intralaminar mesomodel, and illustrations in ABAQUS/standard. Comput. Mater. Sci. 43(1), 137–145 (2008)
Lee H., Peng K., Wang J.: An anisotropic damage criterion for deformation instability and its application to forming limit analysis of metal plates. Eng. Fract. Mech. 21, 1031–1054 (1985)
Rabotnov, Y.: Creep rupture. In: Hetenyi, M., Vincenti, W.G. (eds.) Proceedings, Twelfth International Congress of Applied Mechanics, Stanford, 1968, pp. 342–349. Springer, Berlin, (1969)
Sidoroff, F.: Description of anisotropic damage application in elasticity. In: IUTAM Colloquium on Physical Nonlinearities in Structural Analysis, pp. 237–244, Springer, Berlin (1981)
Voyiadjis G.Z., Kattan P.I.: A plasticity-damage theory for large deformation of solids—part I: theoretical formulation. Int. J. Eng. Sci. 30(9), 1089–1108 (1992)
Voyiadjis G.Z., Kattan P.I.: Damage Mechanics. CRC Press, Taylor and Francis (2005)
Voyiadjis G.Z., Kattan P.I.: Advances in Damage Mechanics: Metals and Metal Matrix Composites with an Introduction to Fabric Tensors. Elsevier, Oxford (2006)
Voyiadjis G.Z., Kattan P.I.: A comparative study of damage variables in continuum damage mechanics. Int. J. Damage Mech. 18(4), 315–340 (2009)
Voyiadjis G.Z., Kattan P.I.: Mechanics of damage processes in series and in parallel: a conceptual framework. Acta Mech. 223(9), 1863–1878 (2012)
Kachanov L.M.: Introduction to Continuum Damage Mechanics. Martinus Nijhoff Publishers, Dordrecht (1986)
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Voyiadjis, G.Z., Kattan, P.I. Linearized damage mechanics for states of small damage. Acta Mech 226, 3707–3715 (2015). https://doi.org/10.1007/s00707-015-1446-8
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DOI: https://doi.org/10.1007/s00707-015-1446-8