Journal of Materials Science

, Volume 46, Issue 18, pp 6158–6161 | Cite as

Comments on “Model and analysis of size-stiffening in nanoporous cellular solids” by Wang and Lam [J. Mater. Sci. 44, 985–991 (2009)]

  • Harm AskesEmail author
  • Elias C. Aifantis


The mechanical response of microstructured materials can be modelled with sufficient accuracy and efficiently through gradient elasticity. Compared to classical elasticity, the governing equations of gradient elasticity are equipped with additional spatial gradients of relevant variables (such as strains and/or accelerations). Through the inclusion of these additional gradients, phenomena that are dominated by microstructural influences can be modelled accurately and realistically, such as stress and strain concentrations around crack tips [2, 3, 4, 5] or dislocation cores [6, 7, 8], and the size-dependent mechanical behaviour of specimens [4, 9, 10]. For a more recent account on the use of gradient theory to eliminate elastic singularities in dislocation lines and crack tips, as well as to interpret size effects, one may consult [11]. In dynamics, there is the additional motivation of simulating dispersive wave propagation, but this is beyond the scope of this short note.


Couple Stress Gradient Elasticity Classical Elasticity Standard Finite Element Finite Element Implementation 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Civil and Structural EngineeringUniversity of SheffieldSheffieldUK
  2. 2.Polytechnic School, Laboratory of Mechanics and MaterialsAristotle University of ThessalonikiThessalonikiGreece

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