Diffusion Rate for Stress in Orthotropic Materials

Abstract

Axial rates of diffusion of the symmetrical state of stress caused by equal but opposed normal forces acting on opposite sides of an indefinitely long strip or plate, are examined in the context of orthotropic elastic materials. To obtain the stress components for this boundary value problem, the imposed surface tractions are represented by a Fourier integral. At distances larger than one quarter of the thickness, the normal stress on the middle surface is closely represented by the sum of eigenfunctions for this problem, up to, and including the first complex eigenfunction as well as its conjugate. Each eigenfunction is a product of exponentially decreasing and oscillatory terms. The exponential term is more significant for determining the rate of diffusion of stress in materials with a large ratio of axial to transverse Young’s moduli Ex/Ey ⩾ 3; this term shows a strong dependence on the ratio of transverse Young’s modulus to shear modulus Ey/G.