Numerical modeling of size effects with gradient elasticity - Formulation, meshless discretization and examples

A theory of gradient elasticity is used and numerically implemented by a meshless method to model size effects. Two different formulations of this model are considered, whereby the higher-order gradients are incorporated explicitly and implicitly, respectively. It turns out that the explicit gradient dependence leads to a straightforward spatial discretization, while use of the implicit gradient dependence can result in an awkward form of the stiffness matrix. For the numerical analyses the Element-Free Galerkin method has been used, due to its ability to incorporate higher-order gradients in a straightforward manner. Two boundary value problems have been considered, which show the capability of the gradient elasticity theory to capture size effects. In a follow-up paper, the formulation developed herein will be used to analyze additional configurations with attention to comparison with available experimental data on size effects and verification of available scaling laws for structural components.