Estimates for the elastic moduli of 2D aggregate of hexagonal-shape orthorhombic crystals with in-plane random crystalline orientations

Vuong Thi My Hanh, Le Hoai Chau, Vu Lam Dong, Pham Duc Chinh
Author affiliations

Authors

  • Vuong Thi My Hanh Institute of Mechanics, VAST, Hanoi, Vietnam
  • Le Hoai Chau Institute of Mechanics and Environmental Engineering, Hanoi, Vietnam
  • Vu Lam Dong Institute of Mechanics, VAST, Hanoi, Vietnam
  • Pham Duc Chinh Institute of Mechanics, VAST, Hanoi, Vietnam

DOI:

https://doi.org/10.15625/0866-7136/13183

Keywords:

effective elastic moduli, random cell polycrystal, 2D orthorhombic crystal

Abstract

Numerical finite element simulations on the homogenization problem for large samples of particular 2D hexagonal-shape-geometry random orientation aggregates from the base crystals of orthorhombic symmetry have been performed. At sufficiently large random-aggregate samples, the scatter intervals of the macroscopic 2D bulk and shear elastic moduli converge toward the Voigt-Reuss-Hill bounds, and then our recently constructed theoretical estimates, which have been specified for the aggregates.

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References

R. Hill. The elastic behaviour of a crystalline aggregate. Proceedings of the Physical Society. Section A, 65, (5), (1952), pp. 349–354. https://doi.org/10.1088/0370-1298/65/5/307.

Z. Hashin and S. Shtrikman. A variational approach to the theory of the elastic behavior of polycrystals. Journal of the Mechanics and Physics of Solids, 10, (4), (1962), pp. 343–352. https://doi.org/10.1016/0022-5096(62)90005-4.

J. P. Watt. Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with orthorhombic symmetry. Journal of Applied Physics, 50, (10), (1979), pp. 6290–6295. https://doi.org/10.1063/1.325768.

P. D. Chinh. Elastic moduli of perfectly random polycrystalline aggregates. Philosophical Magazine A, 76, (1), (1997), pp. 31–44. https://doi.org/10.1080/01418619708209960.

G. W. Milton. The theory of composites. Cambridge University Press, UK, (2001).

J. G. Berryman. Bounds and self-consistent estimates for elastic constants of random polycrystals with hexagonal, trigonal, and tetragonal symmetries. Journal of the Mechanics and Physics of Solids, 53, (10), (2005), pp. 2141–2173. https://doi.org/10.1016/j.jmps.2005.05.004.

P. D. Chinh. On the scatter ranges for the elastic moduli of random aggregates of general anisotropic crystals. Philosophical Magazine, 91, (4), (2011), pp. 609–627. https://doi.org/10.1080/14786435.2010.528459.

P. D. Chinh. Bounds on the elastic moduli of statistically isotropic multicomponent materials and random cell polycrystals. International Journal of Solids and Structures, 49, (18), (2012), pp. 2646–2659. https://doi.org/10.1016/j.ijsolstr.2012.05.021.

V. T. M. Hanh, P. D. Chinh, and V. L. Dong. Improved estimates for the effective elastic bulk modulus of random tetragonal crystal aggregates. Vietnam Journal of Mechanics, 38, (3), (2016), pp. 181–192. https://doi.org/10.15625/0866-7136/38/3/6055.

D. C. Pham, C. H. Le, and T. M. H. Vuong. Estimates for the elastic moduli of d-dimensional random cell polycrystals. Acta Mechanica, 227, (10), (2016), pp. 2881–2897. https://doi.org/10.1007/s00707-016-1653-y.

G. Allaire. Shape optimization by the homogenization method. Springer-Verlag, New York, (2012).

M. P. Bendsoe and O. Sigmund. Topology optimization: theory, methods and applications. Springer Science & Business Media, (2003).

C. H. Le. Developments in topology and shape optimization. PhD thesis, University of Illinois at Urbana-Champaign, (2010).

S. J. Hollister and N. Kikuchi. A comparison of homogenization and standard mechanics analyses for periodic porous composites. Computational Mechanics, 10, (2), (1992), pp. 73–95. https://doi.org/10.1007/bf00369853.

P. D. Chinh. Bounds for the effective elastic properties of completely random planar polycrystals. Journal of Elasticity, 54, (3), (1999), pp. 229–251. https://doi.org/10.1023/A:1007623720169.

P. D. Chinh. Bounds on the elastic moduli of completely random two-dimensional polycrystals. Meccanica, 37, (6), (2002), pp. 503–514. https://doi.org/10.1023/A:1020943815452.

D. C. Pham. Revised bounds on the elastic moduli of two-dimensional random polycrystals. Journal of Elasticity, 85, (1), (2006), pp. 1–20. https://doi.org/10.1007/s10659-006-9065-1.

H. H. Landolt and R. Börnstein. Group III: Crystal and solid state physics, Vol. 11. Springer-Verlarg, (1979).

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Published

25-06-2019

Issue

Vol. 41 No. 2 (2019)

Section

Research Article

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This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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