Plane strain gradient elastic rectangle in tension

Abstract

In the present work, the simplest version of Mindlin’s theory is employed for the analytical solution of a strain gradient elastic rectangle subjected to plane strain tensional conditions. The employed plane strain theory is explained, and the classical and non-classical boundary conditions valid for a 2D structure with corners are described. Expressions for all types of stresses and boundary conditions in a Cartesian co-ordinate system are explicitly provided. A simple solution procedure for the aforementioned strain gradient elastic boundary value problem is proposed. Results that reveal a significant diversification from the classical elasticity theory and assign these modifications appropriately to the specific features of the underlying microstructure are provided and discussed.