Finite element analysis with staggered gradient elasticity
Document Type
Article
Publication Date
6-1-2008
Abstract
In this article, staggered gradient elasticity formulations are studied. Firstly, the standard equations of classical elasticity are considered. Afterwards, a set of Helmholtz equations associated with the theory of gradient elasticity is solved to handle the gradient dependence. Due to the two-step nature of the algorithms, C0-continuous interpolation functions suffice and finite element discretisations are straightforward and efficient. Different versions of staggered gradient elasticity are treated, whereby the Helmholtz equations operate on the displacements, on the strain tensor, on the stress tensor or on a strain invariant. The governing equations are given with their consistent boundary conditions. The formulations are tested against two criteria: whether all singularities are removed from the strain field, and whether the models are capable of describing size effects. © 2007 Elsevier Ltd. All rights reserved.
Publication Title
Computers and Structures
Recommended Citation
Askes, H.,
Morata, I.,
&
Aifantis, E.
(2008).
Finite element analysis with staggered gradient elasticity.
Computers and Structures,
86(11-12), 1266-1279.
http://doi.org/10.1016/j.compstruc.2007.11.002
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/6161