Stress singularities in angular sectors of viscoelastic media

Abstract

Concentrations of stress and associated singularities which develop at re-entrant corners and notches deforming viscoelastically are discussed for plane strain situations when mixed boundary conditions are imposed on the sector flanks. Laplace and Mellin transforms are used to establish that the corner singularity is characterised by a transcendental eigenequation identical in form to that of the corresponding elastic problem, but is a function of the Laplace transform parameter p and time transform of Poisson's ratio. To effect the real time evolution of the stress concentrations at the notch tip requires that specific branches of the eigenequation be monitored as a function of p. The process of analytic continuation is used to this end and permits the components of stress and displacement in real time to be formulated as complex integrals. Numerical integration completes the inversion process. Stress vs time curves for material behaviour based on the standard linear solid are given for different situations and the manner in which they depart from and tend towards their respective instantaneous and long time limits of the corresponding planar elasticity problem is noted.