On the material symmetry group for micromorphic media with applications to granular materials - Publication - Bridge of Knowledge

Search

On the material symmetry group for micromorphic media with applications to granular materials

Abstract

Within the framework of the theory of nonlinear elastic micromorphic continua we introduce the new definition of the local material symmetry group. The group consists of ordered triples of second- and third-order tensors describing such changes of a reference placement that cannot be recognized with any experiment. Using the definition we characterize the micromorphic isotropic media, micromorphic fluids, solids and special intermediate cases called micromorphic subfluids or micromorphic liquid crystals. We demonstrate that some typical behaviour of such complex media as granular materials can be described within the micromorphic subfluids mechanics.

Citations

  • 3 0

    CrossRef

  • 0

    Web of Science

  • 3 0

    Scopus

Cite as

Full text

download paper
downloaded 32 times
Publication version
Accepted or Published Version
License
Creative Commons: CC-BY-NC-ND open in new tab

Keywords

Details

Category:
Articles
Type:
artykuł w czasopiśmie wyróżnionym w JCR
Published in:
MECHANICS RESEARCH COMMUNICATIONS no. 94, pages 8 - 12,
ISSN: 0093-6413
Language:
English
Publication year:
2018
Bibliographic description:
Eremeev V.: On the material symmetry group for micromorphic media with applications to granular materials// MECHANICS RESEARCH COMMUNICATIONS. -Vol. 94, (2018), s.8-12
DOI:
Digital Object Identifier (open in new tab) 10.1016/j.mechrescom.2018.08.017
Bibliography: test
  1. K. Hutter, K. R. Rajagopal, On flows of granular ma- terials, Continuum Mechanics and Thermodynamics 6 (2) (1994) 81-139. open in new tab
  2. P. G. de Gennes, Reflections on the mechanics of granular matter, Physica A: Statistical Mechanics and its Applications 261 (3) (1998) 267-293. open in new tab
  3. P. G. de Gennes, Granular matter: a tentative view, Rev. Mod. Phys. 71 (1999) S374-S382. open in new tab
  4. R. M. Nedderman, Statics and Kinematics of Gran- ular Materials, Cambridge University Press, Cam- bridge, 1992. open in new tab
  5. A. Castellanos, The relationship between attractive interparticle forces and bulk behaviour in dry and uncharged fine powders, Advances in Physics 54 (4) (2005) 263-376. open in new tab
  6. R. D. Mindlin, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis 16 (1) (1964) 51-78. open in new tab
  7. A. C. Eringen, E. S. Suhubi, Nonlinear theory of sim- ple micro-elastic solids-I, International Journal of En- gineering Science 2 (2) (1964) 189-203. open in new tab
  8. A. C. Eringen, Microcontinuum Field Theory. I. Foundations and Solids, Springer, New York, 1999. open in new tab
  9. S. Forest, Micromorphic media, in: H. Altenbach, V. A. Eremeyev (Eds.), Generalized Continua from the Theory to Engineering Applications, Vol. 541 of CISM International Centre for Mechanical Sciences, Springer Vienna, 2013, pp. 249-300. open in new tab
  10. G. A. Maugin, Non-Classical Continuum Mechanics: A Dictionary, Springer Singapore, Singapore, 2017. open in new tab
  11. A. Misra, P. Poorsolhjouy, Granular micromechanics based micromorphic model predicts frequency band gaps, Continuum Mechanics and Thermodynamics 28 (1-2) (2016) 215. open in new tab
  12. A. Misra, P. Poorsolhjouy, Elastic behavior of 2d grain packing modeled as micromorphic media based on granular micromechanics, Journal of Engineering Mechanics 143 (1) (2016) C4016005. open in new tab
  13. A. Misra, P. Poorsolhjouy, Grain-and macro-scale kinematics for granular micromechanics based small deformation micromorphic continuum model, Me- chanics Research Communications 81 (2017) 1-6. open in new tab
  14. T. Dillard, S. Forest, P. Ienny, Micromorphic con- tinuum modelling of the deformation and fracture behaviour of nickel foams, European Journal of Mechanics-A/Solids 25 (3) (2006) 526-549. open in new tab
  15. A. Madeo, P. Neff, I.-D. Ghiba, G. Rosi, Reflection and transmission of elastic waves in non-local band- gap metamaterials: a comprehensive study via the relaxed micromorphic model, Journal of the Mechan- ics and Physics of Solids 95 (2016) 441-479. open in new tab
  16. A. Sridhar, V. G. Kouznetsova, M. G. Geers, Homog- enization of locally resonant acoustic metamaterials towards an emergent enriched continuum, Computa- tional mechanics 57 (3) (2016) 423-435. open in new tab
  17. R. Jänicke, S. Diebels, H.-G. Sehlhorst, A. Düster, Two-scale modelling of micromorphic continua, Con- tinuum Mechanics and Thermodynamics 21 (4) (2009) 297-315. open in new tab
  18. S. Forest, Micromorphic approach for gradient elas- ticity, viscoplasticity, and damage, Journal of Engi- neering Mechanics 135 (3) (2009) 117-131. open in new tab
  19. H.-J. Chang, N. M. Cordero, C. Déprés, M. Fivel, S. Forest, Micromorphic crystal plasticity versus dis- crete dislocation dynamics analysis of multilayer pile- up hardening in a narrow channel, Archive of Applied Mechanics 86 (1-2) (2016) 21-38. open in new tab
  20. F. J. Vernerey, W. K. Liu, B. Moran, G. Olson, A mi- cromorphic model for the multiple scale failure of het- erogeneous materials, Journal of the Mechanics and Physics of Solids 56 (4) (2008) 1320-1347. open in new tab
  21. C.-C. Wang, A general theory of subfluids, Archive for Rational Mechanics and Analysis 20 (1) (1965) 1-40. open in new tab
  22. C. Truesdell, W. Noll, The Non-linear Field Theories of Mechanics, 3rd Edition, Springer, Berlin, 2004. open in new tab
  23. G. de Gennes, P., J. Prost, The Physics of Liq- uid Crystals, 2nd Edition, Clarendon Press, Oxford, 1993.
  24. S. Chandrasekhar, Liquid Crystals, Cambridge Uni- versity Press, Cambridge, UK, 1977.
  25. J. G. Simmonds, A Brief on Tensor Analysis, 2nd Edition, Springer, New Yourk, 1994. open in new tab
  26. L. P. Lebedev, M. J. Cloud, V. A. Eremeyev, Ten- sor Analysis with Applications in Mechanics, World Scientific, New Jersey, 2010. open in new tab
  27. C. Truesdell, Rational Thermodynamics, 2nd Edi- tion, Springer, New York, 1984. open in new tab
  28. V. A. Eremeyev, W. Pietraszkiewicz, Material sym- metry group of the non-linear polar-elastic contin- uum, International Journal of Solids and Structures 49 (14) (2012) 1993-2005. open in new tab
  29. V. A. Eremeyev, W. Pietraszkiewicz, Material sym- metry group and constitutive equations of micropolar anisotropic elastic solids, Mathematics and Mechan- ics of Solids 21 (2) (2016) 210-221. open in new tab
  30. A. I. Murdoch, H. Cohen, Symmetry considerations for material surfaces, Archive for Rational Mechanics and Analysis 72 (1) (1979) 61-98. open in new tab
  31. V. A. Eremeyev, W. Pietraszkiewicz, Local symmetry group in the general theory of elastic shells, Journal of Elasticity 85 (2) (2006) 125-152. open in new tab
  32. A. Bertram, Compendium on Gradient Materials, Otto von Guericke University, Magdburg, 2017.
  33. J. C. Reiher, A. Bertram, Finite third-order gradi- ent elasticity and thermoelasticity, Journal of Elas- ticitydoi:10.1007/s10659-018-9677-2. open in new tab
  34. N. Auffray, H. Le Quang, Q.-C. He, Matrix repre- sentations for 3D strain-gradient elasticity, Journal of the Mechanics and Physics of Solids 61 (5) (2013) 1202-1223. open in new tab
  35. N. Auffray, J. Dirrenberger, G. Rosi, A complete de- scription of bi-dimensional anisotropic strain-gradient elasticity, International Journal of Solids and Struc- tures 69 (2015) 195-206. open in new tab
  36. N. Auffray, B. Kolev, M. Olive, Handbook of bi- dimensional tensors: Part I: Harmonic decomposition and symmetry classes, Mathematics and Mechanics of Solids 22 (9) (2017) 1847-1865. open in new tab
  37. P. Neff, I.-D. Ghiba, A. Madeo, L. Placidi, G. Rosi, A unifying perspective: the relaxed linear micromor- phic continuum, Continuum Mechanics and Thermo- dynamics 26 (5) (2014) 639-681. open in new tab
  38. F. dell'Isola, D. Steigmann, A two-dimensional gradient-elasticity theory for woven fabrics, Journal of Elasticity 118 (1) (2015) 113-125.
  39. F. dell'Isola, I. Giorgio, M. Pawlikowski, N. Rizzi, A C C E P T E D M A N U S C R I P T Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenisation, ex- perimental and numerical examples of equilibrium, Proceedings of the Royal Society of London. Series A. 472 (2185) (2016) 20150790.
  40. L. Placidi, E. Barchiesi, E. Turco, N. L. Rizzi, A re- view on 2D models for the description of pantographic fabrics, Zeitschrift für angewandte Mathematik und Physik 67 (5) (2016) 121. open in new tab
  41. P. Seppecher, Moving contact lines in the Cahn- Hilliard theory, International Journal of Engineering Science 34 (9) (1996) 977-992. open in new tab
  42. N. Auffray, F. dell'Isola, V. A. Eremeyev, A. Madeo, G. Rosi, Analytical continuum mechanicsà la Hamilton-Piola least action principle for second gra- dient continua and capillary fluids, Mathematics and Mechanics of Solids 20 (4) (2015) 375-417. open in new tab
  43. G. Sciarra, F. dell'Isola, O. Coussy, Second gradient poromechanics, International Journal of Solids and Structures 44 (20) (2007) 6607-6629. open in new tab
  44. G. Sciarra, F. dell'Isola, N. Ianiro, A. Madeo, A vari- ational deduction of second gradient poroelasticity. Part I: General theory, Journal of Mechanics of Ma- terials and Structures 3 (3) (2008) 507-526. open in new tab
Verified by:
Gdańsk University of Technology

seen 82 times

Recommended for you

Meta Tags