Does anyone know if there are some damage models that can be applicated on initial anisotropic materials?
Yes. For instance, many damage models have been proposed for composites. Here is an non-exhaustive list of published papers:
D.H. Allen, C.E. Harris, S.E. Groves, A thermomechanical constitutive theory for elastic composites with distributed damage—I. Theoretical development, International Journal of Solids and Structures, Volume 23, Issue 9, 1987, Pages 1301-1318, ISSN 0020-7683, http://dx.doi.org/10.1016/0020-7683(87)90107-7.
P. Ladeveze, E. LeDantec, Damage modelling of the elementary ply for laminated composites, Composites Science and Technology, Volume 43, Issue 3, 1992, Pages 257-267, ISSN 0266-3538, http://dx.doi.org/10.1016/0266-3538(92)90097-M.
P. Maimí, P.P. Camanho, J.A. Mayugo, C.G. Dávila, A continuum damage model for composite laminates: Part I – Constitutive model, Mechanics of Materials, Volume 39, Issue 10, October 2007, Pages 897-908, ISSN 0167-6636, http://dx.doi.org/10.1016/j.mechmat.2007.03.005.
J.F. Maire, J.L. Chaboche, A new formulation of continuum damage mechanics (CDM) for composite materials, Aerospace Science and Technology, Volume 1, Issue 4, June 1997, Pages 247-257, ISSN 1270-9638, http://dx.doi.org/10.1016/S1270-9638(97)90035-3.
A. Matzenmiller, J. Lubliner, R.L. Taylor, A constitutive model for anisotropic damage in fiber-composites, Mechanics of Materials, Volume 20, Issue 2, April 1995, Pages 125-152, ISSN 0167-6636, http://dx.doi.org/10.1016/0167-6636(94)00053-0.
George Z. Voyiadjis, Babur Deliktas, A coupled anisotropic damage model for the inelastic response of composite materials, Computer Methods in Applied Mechanics and Engineering, Volume 183, Issues 3–4, 17 March 2000, Pages 159-199, ISSN 0045-7825, http://dx.doi.org/10.1016/S0045-7825(99)00218-2.
Hopefully that answers some of your questions.
Thank you very much. I will read these papers. But, just a little question on the application of these models. I work on the single crystal material, so the anisotropy is induced by the crystallographic structure not like the comosite materials, so I don't know if it is appropriate to use the damage models developed from the composite materials. Do you have any idea on this aspect? Thanks a lot.
For continuous fibre reinforced plastics, for instance, the damage mechanisms are mostly dictated by the fibre direction. For Ceramic Matrix Composites, the direction of the loading has to be taken into account. For metals, of course, the mechanisms and their effect are different. You may refer to (CordeBois and Sidoroff)'s pioneering works. Various papers dealing with coupled elasto-visco-plastic damage theories have later been proposed. You may for instance have a look at:
Y.Y. Zhu, S. Cescotto, A fully coupled elasto-visco-plastic damage theory for anisotropic materials, International Journal of Solids and Structures, Volume 32, Issue 11, June 1995, Pages 1607-1641, ISSN 0020-7683, http://dx.doi.org/10.1016/0020-7683(94)00195-3.
Good luck for these readings.
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