The thermoelastic response of cracked polycrystals with hexagonal symmetry

References

• F. Cormery and H. Welemane, A critical review of some damage models with unilateral effect, Mech. Res. Comm. 29 (2002), pp. 391–395. doi: 10.1016/S0093-6413(02)00262-8
   Web of Science ®Google Scholar
• R. Bargellini, D. Halm and A. Dragon, Modelling of quasi-brittle behaviour: A discrete approach coupling anisotropic damage growth and frictional sliding, Eur. J. Mech. A/Solids 27 (2008), pp. 564–581. doi: 10.1016/j.euromechsol.2007.11.003
   Web of Science ®Google Scholar
• F. Cormery and H. Welemane, A stress-based macroscopic approach for microcracks unilateral effect, Comput. Mat. Sci. 47 (2010), pp. 727–738. doi: 10.1016/j.commatsci.2009.10.016
   Web of Science ®Google Scholar
• N. Challamel, A variationally based nonlocal damage model to predict diffuse microcracking evolution, Int. J. Mech. Sci. 52 (2010), pp. 1783–1800. doi: 10.1016/j.ijmecsci.2010.09.012
   Web of Science ®Google Scholar
• B. Budiansky and R.J. O'Connell, Elastic moduli of a cracked solid, Int. J. Solids. Struct. 12 (1976), pp. 81–97. doi: 10.1016/0020-7683(76)90044-5
   Web of Science ®Google Scholar
• H. Horii and S. Nemat-Nasser, Overall moduli of solids with microcracks: Load-induced anisotropy, J. Mech. Phys. Solids 31 (1983), pp. 155–171. doi: 10.1016/0022-5096(83)90048-0
   Web of Science ®Google Scholar
• S. Andrieux, Y. Bamberger and J. Marigo, Un modèle de matériau microfissuré pour les bétons et les roches, J. Méca. Théor. Appl. 5 (1986), pp. 471–513.
   Google Scholar
• D. Krajcinovic, Damage mechanics, Mech. Mat. 8 (1989), pp. 117–197. doi: 10.1016/0167-6636(89)90011-2
   Web of Science ®Google Scholar
• M. Kachanov, Effective elastic properties of cracked solids: Critical review of some basic concepts, Appl. Mech. Rev. 45 (1992), pp. 304–335. doi: 10.1115/1.3119761
   Google Scholar
• V. Pensée and D. Kondo, Micromechanics of anisotropic brittle damage: Comparative analysis between a stress based and a strain based formulation, Mech. Mat. 35 (2003), pp. 747–741. doi: 10.1016/S0167-6636(02)00203-X
   Web of Science ®Google Scholar
• L. Dormieux and D. Kondo, Stress-based estimates and bounds of effective elastic properties: The case of cracked media with unilateral effects, Comput. Mat. Sci. 46 (2009), pp. 173–179. doi: 10.1016/j.commatsci.2009.02.027
   Web of Science ®Google Scholar
• Q.Z. Zhu, J.F. Shao and D. Kondo, A micromechanics-based thermodynamic formulation of isotropic damage with unilateral and friction effects, Eur. J. Mech. A/Solids 30 (2011), pp. 316–325. doi: 10.1016/j.euromechsol.2010.12.005
   Web of Science ®Google Scholar
• V. Monchiet, C. Gruescu, O. Cazacu and D. Kondo, A micromechanical approach of crack-induced damage in orthotropic media: Application to a brittle matrix composite, Engrg. Fract. Mech. 83 (2012), pp. 40–53. doi: 10.1016/j.engfracmech.2011.11.011
   Web of Science ®Google Scholar
• S. Levasseur, H. Welemane and D. Kondo, A microcracks-induced damage model for initially anisotropic rocks accounting for microcracks closure, Int. J. Rock Mech. Mining Sci. 77 (2015), pp. 122–132. doi: 10.1016/j.ijrmms.2015.03.011
   Web of Science ®Google Scholar
• M. Ortiz, A constitutive theory for the inelastic behavior of concrete, Mech. Mater. 4 (1985), pp. 67–93. doi: 10.1016/0167-6636(85)90007-9
   Web of Science ®Google Scholar
• G. Pijaudier-Cabot and Z.P. Bažant, Nonlocal damage theory, J. Engrg. Mech. 113 (1987), pp. 1512–1533. doi: 10.1061/(ASCE)0733-9399(1987)113:10(1512)
   Web of Science ®Google Scholar
• R.G. Naum and C.K. Jun, Thermal expansion of polycrystalline graphite, J. Appl. Phys. 41 (1970), pp. 5092–5095. doi: 10.1063/1.1658613
   Web of Science ®Google Scholar
• L. Delannay, P. Yan, J.F.B. Payne and N. Tzelepi, Predictions of inter-granular cracking and dimensional changes or irradiated polycrystalline graphite under plane strain, Comput. Mater. Sci. 87 (2014), pp. 129–137. doi: 10.1016/j.commatsci.2014.02.008
   Web of Science ®Google Scholar
• J.R. Kolb and H.F. Rizzo, Growth of 1,3,5-Triamino-2,4,6-Trinitrobenzene (TATB). I. anisotropic thermal expansion, Propellants Explos. Pyrotech. 4 (1979), pp. 10–16. doi: 10.1002/prep.19790040104
   Google Scholar
• A. Ambos, F. Willot, D. Jeulin and H. Trumel, Numerical modeling of the thermal expansion of an energetic material, Int. J. Solids. Struct. 60–61 (2015), pp. 125–139. doi: 10.1016/j.ijsolstr.2015.02.025
   Web of Science ®Google Scholar
• Y. Huang and K.X. Hu, Elastic moduli of a microcracked composite with spherical inclusions of cubic anisotropy, Compos. Sci. Technol. 50 (1994), pp. 149–156. doi: 10.1016/0266-3538(94)90136-8
   Web of Science ®Google Scholar
• N. Laws, A note on penny-shaped cracks in transversely isotropic materials, Mech. Mater. 4 (1985), pp. 209–212. doi: 10.1016/0167-6636(85)90017-1
   Web of Science ®Google Scholar
• C. Gruescu, V. Monchiet and D. Kondo, Eshelby tensor for a crack in an orthotropic elastic medium, Comptes Rendus Mecanique 333 (2005), pp. 467–473. doi: 10.1016/j.crme.2005.04.005
   Web of Science ®Google Scholar
• J.R. Bristow, Microcracks, and the static and dynamic elastic constants of annealed and heavily cold-worked metals, Br. J. Appl. Phys. 11 (1960), pp. 81. doi: 10.1088/0508-3443/11/2/309
   Web of Science ®Google Scholar
• R. Hill, A self-consistent mechanics of composite materials, J. Mech. Phys. Solids. 13 (1965), pp. 213–222. doi: 10.1016/0022-5096(65)90010-4
   Web of Science ®Google Scholar
• I. Sevostianov, N. Yilmaz, V. Kushch and V. Levin, Effective elastic properties of matrix composites with transversely-isotropic phases, Int. J. Solids. Struct. 42 (2005), pp. 455–476. doi: 10.1016/j.ijsolstr.2004.06.047
   Web of Science ®Google Scholar
• T. Mura, Micromechanics of Defects in Solids, Martinus Nijhoff Publishers, The Hague, 1982.
   Google Scholar
• V.M. Levin, M.I. Rakovskaja and W.S. Kreher, The effective thermoelectroelastic properties of microinhomogeneous materials, Int. J. Solids. Struct. 36 (1999), pp. 2683–2705. doi: 10.1016/S0020-7683(98)00131-0
   Web of Science ®Google Scholar
• I. Sevostianov and M. Kachanov, Explicit cross-property correlations for anisotropic two-phase composite materials, J. Mech. Phys. Solids. 50 (2002), pp. 253–282. doi: 10.1016/S0022-5096(01)00051-5
   Web of Science ®Google Scholar
• Wolfram Research, Inc., Mathematica software version 10.2. Champaign, IL,2015.
   Google Scholar
• Y. Benveniste, Universal relations in piezoelectric composites with eigenstress and polarization fields, Part 2: Multiphase media–effective behavior, J. Appl. Mech. 60 (1993), pp. 270–274. doi: 10.1115/1.2900789
   Web of Science ®Google Scholar
• J.G. Berryman, Bounds and self-consistent estimates for elastic constants of random polycrystals with hexagonal, trigonal, and tetragonal symmetries, J. Mech. Phys. Solids. 53 (2005), pp. 2141–2173. doi: 10.1016/j.jmps.2005.05.004
   Web of Science ®Google Scholar
• Z. Hashin, Thermal expansion of polycrystalline aggregates: I. Exact analysis, J. Mech. Phys. Solids. 32 (1984), pp. 149–157. doi: 10.1016/0022-5096(84)90016-4
   Web of Science ®Google Scholar
• Z. Hashin, Analysis of composite materials–a survey, J. Appl. Mech. 50 (1983), pp. 481–505. doi: 10.1115/1.3167081
   Web of Science ®Google Scholar
• G.W. Milton, The Theory of Composites, Cambridge University Press, Cambridge, 2002.
   Google Scholar
• M. Avellaneda, Iterated homogenization, differential effective medium theory and applications, Commun. Pure. Appl. Math. 40 (1987), pp. 527–554. doi: 10.1002/cpa.3160400502
   Web of Science ®Google Scholar
• E. Kröner, Bounds for effective elastic moduli of disordered materials, J. Mech. Phys. Solids. 25 (1977), pp. 137–155. doi: 10.1016/0022-5096(77)90009-6
   Web of Science ®Google Scholar
• J.G. Berryman, Long-wavelength propagation in composite elastic media ii. ellipsoidal inclusions, J. Acoust. Soc. Am. 68 (1980), pp. 1820–1831. doi: 10.1121/1.385172
   Web of Science ®Google Scholar
• P.N. Sævik, M. Jakobsen, M. Lien and I. Berre, Anisotropic effective conductivity in fractured rocks by explicit effective medium methods, Geophys. Prospect. 62 (2014), pp. 1297–1314. doi: 10.1111/1365-2478.12173
   Web of Science ®Google Scholar
• P.N. Sævik, I. Berre, M. Jakobsen and M. Lien, A 3d computational study of effective medium methods applied to fractured media, Transp. Porous. Media. 100 (2013), pp. 115–142. doi: 10.1007/s11242-013-0208-0
   Web of Science ®Google Scholar
• E.H. Saenger, O.S. Krüger and S.A. Shapiro, Effective elastic properties of randomly fractured soils: 3d numerical experiments, Geophys. Prospect 52 (2004), pp. 183–195. doi: 10.1111/j.1365-2478.2004.00407.x
   Web of Science ®Google Scholar
• R. Rosenzweig, V.V. Mourzenko, J.F. Thovert and P.M. Adler, Solid matrix partition by fracture networks, Phys. Rev. E 90 (2014), pp. 022407. doi: 10.1103/PhysRevE.90.022407
   Web of Science ®Google Scholar
• Y.B. Yi and K. Esmail, Computational measurement of void percolation thresholds of oblate particles and thin plate composites, J. Appl. Phys. 111 (2012), pp. 124903.
   Web of Science ®Google Scholar
• T. Bretheau and D. Jeulin, Caractéristiques morphologiques des constituants et comportement à la limite élastique d'un matériau biphasé fe/ag, Revue de Physique Appliquée 24 (1989), pp. 861–869. doi: 10.1051/rphysap:01989002409086100
   Google Scholar
• Y.B. Yi and E. Tawerghi, Geometric percolation thresholds of interpenetrating plates in three-dimensional space, Phys. Rev. E 79 (2009), pp. 041134.
   Web of Science ®Google Scholar
• Y. Benveniste, A new approach to the application of Mori-Tanaka's theory in composite materials, Mech. Mater. 6 (1987), pp. 147–157. doi: 10.1016/0167-6636(87)90005-6
   Web of Science ®Google Scholar
• P. Ponte Castañeda and J.R. Willis, The effect of spatial distribution on the effective behavior of composite materials and cracked media, J. Mech. Phys. Solids. 43 (1995), pp. 1919–1951. doi: 10.1016/0022-5096(95)00058-Q
   Web of Science ®Google Scholar
• F. Willot and Y.P. Pellegrini, Fast Fourier transform computations and build-up of plastic deformation in 2D, elastic-perfectly plastic, pixelwise-disordered porous media, in Continuum Models and Discrete Systems CMDS 11, D. Jeulin and S. Forest eds., Paris. École des Mines, 2008, pp. 443–449, online Available at https://arxiv.org/abs/0802.2488
   Google Scholar
• F. Willot, Fourier-based schemes for computing the mechanical response of composites with accurate local fields, Comptes Rendus Mécanique 343 (2015), pp. 232–245. doi: 10.1016/j.crme.2014.12.005
   Web of Science ®Google Scholar
• J.B. Gasnier, F. Willot, H. Trumel, Thermoelastic properties of microcracked polycrystals. Part I: Adequacy of Fourier-based methods for cracked elastic bodies. International Journal of Solids and Structures 155 (2018), pp. 248–256. doi: 10.1016/j.ijsolstr.2018.07.024
   Web of Science ®Google Scholar
• F. Willot, Y.P. Pellegrini, M. Idiart and P. Ponte Castañeda, Effective-medium theory for infinite-contrast two-dimensionally periodic linear composites with strongly anisotropic matrix behavior: dilute limit and crossover behavior, Phys. Rev. B 78 (2008), pp. 104111. doi: 10.1103/PhysRevB.78.104111
   Web of Science ®Google Scholar
• J.B. Gasnier, F. Willot, H. Trumelet al., Thermoelastic properties of microcracked polycrystals. Part II: The case of jointed polycrystalline TATB. International Journal of Solids and Structures 155 (2018), pp. 257–274. doi: 10.1016/j.ijsolstr.2018.07.025
   Web of Science ®Google Scholar