Engineering Transactions, 66, 4, pp. 461–470, 2018
10.24423/EngTrans.942.20181113

A Theory of Undamageable Graphene

George Z. VOYIADJIS
Louisiana State University
United States

Peter Issa KATTAN
Petra Books
Jordan

It is the aim of this work to develop and extend the theory of undamageable materials to graphene. An undamageable material is a material where the value of the damage variable remains zero throughout the deformation process. It is anticipated that the constitutive equations for undamageable graphene can be modeled with differential equations for the case of graphene. The equations are solved for three cases: n = 1, n = 2, and the general case of n. It is hoped that undamageable graphene can be achieved in the laboratory in the near future when the manufacturing technology advances so as to produce such materials.
Keywords: undamageable material; graphene; strain energy equivalence; continuum damage mechanics; elastic stiffness degradation.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

Basaran C., Nie S., An irreversible thermodynamic theory for damage mechanics of solids, International Journal of Damage Mechanics, 13(3): 205–224, 2004.

Basaran C., Yan. C.Y., A Thermodynamic Framework for Damage Mechanics of Solder Joints, Trans. of ASME, Journal of Electronic Packaging, 120: 379–384, 1998.

Cai M., Horii H., A constitutive model of highly jointed rock masses, Mechanics of Materials, 13(3): 217–246, 1992.

Cauvin A., Testa R.B., Damage mechanics: basic variables in continuum theories, International Journal of Solids and Structures, 36: 747–761, 1999.

Celentano D.J., Tapia P.E., Chaboche J.-L., Experimental and numerical characterization of damage evolution in steels, Mecanica Computacional, XXIII(2): 45–58, 2004.

Chaboche J.L., On some modifications of kinematic hardening to improve the description of ratcheting effects, International Journal of Plasticity, 7: 661–678, 1991.

Chaboche J.L., Thermodynamic formulation of constitutive equations and applications to the viscoplasticity and viscoelasticity of metals and polymers, International Journal of Solids and Structures, 34: 2239–2254, 1997.

Chow C.L., Jie M., Anisotropic damage-coupled sheet metal forming limit analysis, International Journal of Damage Mechanics, 18: 371–392, 2009.

Doghri I., Mechanics of deformable solids: linear and nonlinear, analytical and computational aspects, Springer-Verlag, Germany, 2000.

Hansen N.R., Schreyer H.L., A thermodynamically consistent framework for theories of elastoplasticity coupled with damage, International Journal of Solids and Structures, 31(3): 359–389, 1994.

Ju J.W., Chen T.M., Effective elastic moduli of two-dimensional brittle solids with interacting microcracks. Part I: Basic formulations, ASME Journal of Applied Mechanics, 61: 349–357, 1994.

Ju J.W., Chen T.M., Effective elastic moduli of two-dimensional brittle solids with interacting microcracks. Part II: Evolutionary damage models, ASME Journal of Applied Mechanics, 61: 358–366, 1994.

Kachanov L., On the creep fracture time [in Russian], Izv Akad, Nauk USSR Otd Tech., 8: 26–31, 1958.

Kattan P.I., Voyiadjis G.Z., A coupled theory of damage mechanics and finite strain elasto-plasticity. Part I: Damage and elastic deformations, International Journal of Engineering Science, 28(5): 421–435, 1990.

Kattan P.I., Voyiadjis G.Z., A plasticity-damage theory for large deformation of solids. Part II: Applications to finite simple shear, International Journal of Engineering Science, 31(1): 183–199, 1993.

Kattan P.I., Voyiadjis G.Z., Damage mechanics with finite elements: practical applications with computer tools, Springer-Verlag, Germany, 2001.

Kattan P.I., Voyiadjis G.Z., Decomposition of damage tensor in continuum damage mechanics, Journal of Engineering Mechanics, ASCE, 127(9): 940–944, 2001.

Krajcinovic D., Damage Mechanics, North Holland, 1996.

Ladeveze P., Lemaitre J., Damage effective stress in quasi-unilateral conditions, The 16th International Cogress of Theoretical and Applied Mechanics, Lyngby, Denmark, 1984.

Ladeveze P., Poss M., Proslier L., Damage and fracture of tridirectional composites, [in:] Progress in Science and Engineering of Composites. Proceedings of the 4th International Conference on Composite Materials, Japan Society for Composite Materials, Vol. 1, pp. 649–658, 1982.

Lee C., Wei X, Kysar J. W., Hone J., Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science, 321(5887): 385–388, 2008.

Lee H., Peng K., Wang J., An anisotropic damage criterion for deformation instability and its application to forming limit analysis of metal plates, Engineering Fracture Mechanics, 21: 1031–1054, 1985.

Lemaitre J., Coupled elastoplasticity and damage constitutive equations, Computer Methods in Applied Mechanics and Engineering, 51: 31–49, 1985.

Lemaitre J., How to use damage mechanics, Nuclear Engineering and Design, 80: 233–245, 1984.

Lemaitre J., Chaboche J.L., Mechanics of solid materials, Cambridge University Press, Cambridge, 1990.

Lubarda V.A., Krajcinovic D., Damage tensors and the crack density distribution, International Journal of Solids and Structures, 30: 2859–2877, 1993.

Lubineau G., A pyramidal modeling scheme for laminates – identification of transverse cracking, International Journal of Damage Mechanics, 19(4): 499–518, 2010.

Lubineau G., Ladeveze P., Construction of a micromechanics-based intralaminar mesomodel, and illustrations in ABAQUS/Standard, Computational Materials Science, 43(1): 137–145, 2008.

Luccioni B., Oller S., A directional damage model, Computer Methods in Applied Mechanics and Engineering, 192: 1119–1145, 2003.

Rice J.R., Inelastic Constitutive Relations for Solids: An Internal Variable Theory and its Application to Metal Plasticity, Journal of the Mechanics and Physics of Solids, 19: 433–455, 1971.

Sidoroff F., Description of anisotropic damage application in elasticity, [in:] IUTAM Colloqium on Physical Nonlinearities in Structural Analysis, pp. 237–244, Springer-Verlag, Berlin, 1981.

Voyiadjis G.Z., Degradation of elastic modulus in elastoplastic coupling with finite strains, International Journal of Plasticity, 4: 335–353, 1988.

Voyiadjis G.Z., Kattan P.I., A comparative study of damage variables in continuum damage mechanics, International Journal of Damage Mechanics, 18(4): 315–340, 2009.

Voyiadjis G.Z., Kattan P.I., A coupled theory of damage mechanics and finite strain elasto-plasticity. Part II: Damage and finite strain plasticity, International Journal of Engineering Science, 28(6): 505–524, 1990.

Voyiadjis G.Z., Kattan P.I., A plasticity-damage theory for large deformation of solids.– Part I: Theoretical formulation, International Journal of Engineering Science, 30(9): 1089–1108, 1992.

Voyiadjis G.Z., Kattan P.I., Advances in damage mechanics: metals and metal matrix composites with an introduction to fabric tensors, 2nd Ed., Elsevier, 2006.

Voyiadjis G.Z., Kattan P.I., Damage Mechanics, Taylor and Francis (CRC Press), 2005.

Voyiadjis G.Z., Kattan P.I., Decomposition of elastic stiffness degradation in continuum damage mechanics, Journal of Engineering Materials and Technology, ASME, 139(2): 021005-1–021005-15, 2017, doi: 10.1115/1.4035292.

Voyiadjis G.Z., Kattan P.I., Elasticity of damage graphene: a damage mechanics approach, International Journal of Damage Mechanics, 25(8): 1184–1213, 2017, doi: 10.1177/1056789516656747.

Voyiadjis G.Z., Kattan P.I., Governing differential equations for the mechanics of undamageable materials, Engineering Transactions, 62(3): 241–267, 2014.

Voyiadjis G.Z., Kattan P.I., Healing and super healing in continuum damage mechanics, International Journal of Damage Mechanics, 23(2): 245–260, 2014, doi: 10.1177/1056789513491773.

Voyiadjis G.Z., Kattan P.I., Introducing damage mechanics templates for the consistent and systematic formulation of holistic material damage models, Acta Mechanica, 228(3): 951–990, 2017, doi: 10.1007/s00707-016-1747-6.

Voyiadjis G.Z., Kattan P.I., Introduction to the mechanics and design of undamageable materials, International Journal of Damage Mechanics, 22(3): 323–335, 2013, doi: 10.1177/1056789512446518.

Voyiadjis G.Z., Kattan P.I., Mechanics of damage, healing, damageability, and integrity of materials: a conceptual framework, International Journal of Damage Mechanics, 26(1): 50–103, 2017, doi: 10.1177/1056789516635730.

Voyiadjis G.Z., Kattan P.I., On the theory of elastic undamageable materials, ASME Journal of Materials and Technology, 135(2): 021002, 2012c (6 pages), Paper No: MATS-12-1107; doi: 10.1115/1.4023770.

Voyiadjis G.Z., Shojaei A., Li G., Kattan P.I., A theory of anisotropic healing and damage mechanics of materials, Proceedings of the Royal Society A, 468(2137): 163–183, 2012, doi: 10.1098/rspa.2011.0326.

Voyiadjis G.Z., Shojaei A., Li G., Kattan P.I., Continuum damage-healing mechanics with introduction to new healing variables, International Journal of Damage Mechanics, 21(3): 391–414, 2012.

Voyiadjis G.Z., Yousef M.A., Kattan P.I., New tensors for anisotropic damage in continuum damage mechanics, ASME Journal of Engineering Materials and Technology, 134(2): 021015, 1–10, 2012.




DOI: 10.24423/EngTrans.942.20181113