Modelling of Size Effects with Gradient-Enriched Continuum Theories

  • Harm Askes
  • Inna M. Gitman
  • Angelo Simone
  • Lambertus J. Sluys
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)


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.


Gradient elasticity gradient damage length scale strain concentrations peak loads representative volumes 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Harm Askes
    • 1
  • Inna M. Gitman
  • Angelo Simone
  • Lambertus J. Sluys
  1. 1.Department of Civil and Structural EngineeringUniversity of SheffieldUnited Kingdom

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