Modelling of Size Effects with Gradient-Enriched Continuum Theories
Size-dependent mechanical behaviour in simulations with a higher-order continuum material model is studied. It is shown that size effects occur in strain concentrations when a gradient elasticity theory is used. Similarly, size effects in the peak load can be modelled with a gradient damage theory. In both cases, a comparison is made with two scaling laws available in the literature: the Multi-Fractal Scaling Law of Carpinteri and the Size Effect Law of Bažant. Finally, the energy dissipation in Elementary Volumes is shown to be size-dependent, where again a gradient damage theory has been used. This implies that Representative Volumes do not exist when the dissipated energy is considered.
KeywordsGradient elasticity gradient damage length scale strain concentrations peak loads representative volumes
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- 6.C. le Bellégo, J.F. Dubé, G. Pijaudier-Cabot, and B. Gérard. Eur. J. Mech. A/Sol., 22:33–46, 2003.Google Scholar
- 8.A. Carpinteri, editor. Size-scale effects in the failure mechanisms of materials and structures. E. & F.N. Spon, London, 1996.Google Scholar
- 9.G. Efremidis, A. Carpinteri, and E.C. Aifantis. J. Mech. Beh. Mat., 12:95–105, 2001.Google Scholar
- 10.G. Efremidis, A. Carpinteri, and E.C. Aifantis. J. Mech. Beh. Mat., 12:107–120, 2001.Google Scholar
- 12.I.M. Gitman. Representative Volumes and multi-scale modelling of quasi-brittle materials. PhD Thesis, Delft University of Technology, 2006. http://www.library.tudelft.nl.
- 14.B.L. Karihaloo and Q.Z. Xiao. Sadhana, 27:449–459, 2002.Google Scholar
- 15.R.H.J. Peerlings, R. de Borst, W.A.M. Brekelmans, and J.H.P. de Vree. Int. J. Numer. Meth. Engng., 39:3391–3403, 1996.Google Scholar