GRADELA is a simple gradient elasticity model involving one internal length in addition to the two

Lamé parameters In continuum mechanics, Lamé parameters (also called the Lamé coefficients, Lamé constants or Lamé moduli) are two material-dependent quantities denoted by λ and μ that arise in strain- stress relationships. In general, λ and μ are ind ...

. It allows to eliminate elastic singularities and discontinuities and to interpret elastic size effects. This model has been suggested by Elias C. Aifantis. The main advantage of GRADELA over Mindlin's elasticity models (which contains five extra constants) is the fact that solutions of boundary value problems can be found in terms of corresponding solutions of classical elasticity by

operator splitting This is a list of operator splitting topics. General *Alternating direction implicit method — finite difference method for parabolic, hyperbolic, and elliptic partial differential equations * GRADELA — simple gradient elasticity model * Matrix ...

method. In 1992-1993 it has been suggested by Elias C. Aifantis a generalization of the linear elastic

constitutive relations In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and app ...

by the gradient modification that contains the

Laplacian In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \nabla is the ...

in the form :

\sigma_ = \Bigl( \lambda  \varepsilon_ \delta_ + 2 \mu \varepsilon_ \Bigr) - l^2_s \, \Delta \, \Bigl( \lambda  \varepsilon_ \delta_ + 2 \mu \varepsilon_{ij} \Bigr) ,

where

l_s

is the scale parameter.

References

* E. C. Aifantis
"On the role of gradients in the localization of deformation and fracture" International Journal of Engineering Science Volume 30, Issue 10, October 1992, Pages 1279–1299
* E. C. Aifantis
"On non-singular GRADELA crack fields" Theor. Appl. Mech. Lett. 2014, Vol. 4 Issue (5): 5-051005
DOI: 10.1063/2.1405105 * E. C. Aifantis
"On the gradient approach – Relation to Eringen’s nonlocal theory" International Journal of Engineering Science Volume 49, Issue 12, December 2011, Pages 1367–1377
* C. Q. Ru, E. C.Aifantis
"A simple approach to solve boundary value problems in gradient elasticity. Acta Mechanica, 1993, Volume 101, Issue 1-4, pp 59-68.

References

See also