Discretization of Gradient Elasticity Problems Using C1 Finite Elements

  • Stefanos-Aldo Papanicolopulos
  • A. Zervos
  • Ioannis Vardoulakis
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)


Strain-gradient theories have been used to model a variety of problems (such as elastic deformation, fracture behavior and plasticity) where size effect is of importance. Their use with the finite element method, however, has the drawback that specially designed elements are needed to obtain correct results.

This work presents an overview of the use of elements with C 1 continuous interpolation for strain-gradient models, using gradient elasticity as an example. After showing how the C 1 requirement arises and giving details concerning the implementation of specific elements, a theoretical comparison is made between elements based on this approach and elements resulting from the use of some alternative formulations.


Lagrange Multiplier Strain Gradient Mixed Formulation Gradient Elasticity Quadratic Interpolation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Stefanos-Aldo Papanicolopulos
    • 1
  • A. Zervos
    • 2
  • Ioannis Vardoulakis
  1. 1.Department of MechanicsNational Technical University of AthensZografouGreece
  2. 2.School of Civil Engineering and the EnvironmentUniversity of SouthamptonSouthamptonUK

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