Plane strain and plane stress elasticity under fractional continuum mechanics

Abstract

In this paper, the application of non-local fractional continuum model for plane strain and plane stress elasticity is presented. The kinematics and stress concepts are discussed, and governing equations in terms of displacements for both plane problems are defined. The numerical implementation utilising generalised finite difference method is shown in detail. Three cases are solved to indicate the role of order of fractional continua and length scale: biaxial tension, pure shear and complex state. Classical (local) solution is obtained as a special case.