13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- shaped particles or blocks to ensure the desirable properties of the hybrid not achievable otherwise. In particular, according to Fig. 3 the presence of rotating non-spherical particles in a matrix can either increase or decrease the effective shear modulus depending upon the magnitude of applied compressive stress. This suggests a method of designing materials whose moduli can be controlled by applied load without the creation of additional internal damage. Acknowledgements The authors acknowledge the financial support through the ARC Discovery grant DP120102434. References [1] H-B. Mühlhaus, I. Vardoulakis, The thickness of shear bands in granular materials, Géotechnique 37 (1987) 271-283. [2] H.-B. Mühlhaus, R. de Borst, E.C. Aifantis, Constitutive models and numerical analyses for inelastic materials with microstructure, in: G., Beer, et al (Eds.) Computing Methods and Advances in Geomechanics (1991) pp. 377-385. [3] C.S. Chang, L. Ma, Elastic material constants for isotropic granular solids with particle rotation, Int. J. Solids Structures 29 (1992) 1001-1018. [4] H.-B. Mühlhaus,. Continuum models for layered and blocky rock. In: Comprehensive Rock Eng., Invited Chapter for Vol. II: Analysis and Design Methods, Pergamon Press (1993) pp. 209-230. [5] H-B. Mühlhaus, F. Oka, Dispersion and wave propagation in discrete and continuous models for granular materials, Int. J. Solids Structures 33 (1996) 2841-2858. [6] E. Pasternak, H.-B. Mühlhaus, A.V. Dyskin, On the possibility of elastic strain localisation in a fault, Pure Appl. Geophys. 161 (2004) 2309-2326. [7] E. Pasternak, H.-B. Mühlhaus, Generalised homogenisation procedures for granular materials. Eng Math, 52 (2005) 199-229. [8] D.M. Mueth, G.F. Debregeas, G.S. Karczmar, P.J. Eng, S.R. Nagel, H.M. Jaeger, Signatures of granular microstructure in dense shear flows. Nature 406 (2000), 385. [9] J. Desrues, G. Viggiani, Strain localization in sand: an overview of the experimental results obtained in Grenoble using stereophotogrammetry. Int. J. Numer. Anal. Meth. Geomech. 28 (2004) 279–321. [10] A. Rechenmacher, S. Abedi, O. Chupin, Evolution of force chains in shear bands in sands. Geotechnique, 60 (2010) 343–351. [11] H.J. Herrmann, Physics of granular media. Chaos, Solitons and Fractals, 6 (1995) 203-212. [12] Y. Kishino, C. Thornton, Discrete element approaches, in: M. Oda, K. Iwashita (Eds.), Mechanics of Granular Materials. An introduction. Balkema. Rotterdam, Brookfield (1999) 147-223. [13] K. Bagi, M.R. Kuhn, Different rolling measures for granular assemblies. In: Vermeer, Ehlers, Herrmann and Rahmm (Eds.) Modelling of Cohesive-Frictional Materials, Taylor and Francis Group, London (2004) pp. 3-12. [14] F. Allonso-Marroquin, I. Vardoulakis, H.J. Herrmann, D. Weatherley, P. Mora, Effect of rolling on dissipation in fault gouge. Phys. Rev. E, 74 (2006). [15] P.W. Cleary, M.L. Sawley, DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Applied Mathematical Modelling 26 (2002) 89-111. [16] A.V. Dyskin, Y. Estrin, A.J. Kanel-Belov, E. Pasternak, Topological interlocking of platonic solids: A way to new materials and structures, Phil. Mag. Lett. 83(2003) 197-203.
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