Semi-inverse method for a plane strain gradient orthotropic elastic rectangle in tension

Abstract

Considering a simple form of the strain energy functional for anisotropic elastic materials as proposed with Lazar and Kirchner (Int J Solids Struct 44(7–8):2477–2486, 2007), Lazar and Po (Eur J Mech A Solids 50:152–162, 2015a), (Phys Lett A 379:1538–1543, 2015b), depending on the strain tensor and its derivatives. The field equations, boundary conditions and technique solution are listed in Placidi and El Dhaba (Math Mech Solids 22:5, 2017), a two-dimensional problem is solved for a rectangle fixed at one side and subjected to two different displacement fields at the opposite side. The analytical solution is obtained using the semi-inverse method. The physical quantities are plotted and the numerical results are discussed.