Stress Singularities in Viscoelastic Media 2. Plane-Strain Stress Singularities at Corners

The stress singularities that evolve at the corner of a notchedviscoelastic angular plate subject to mode I deformation isdiscussed when prescribed, but arbitrary, displacements aresymmetrically applied to both radial edges of the sector. Thesolution procedure, based on Laplace and Mellin transforms (withtransform parameters p and s, respectively), leads to an eigenvalueproblem in the complex p-plane, which is dependent on Poisson'sratio and characterizes the singular behaviour of the stressfields. Although simple solutions to the transcendental eigenequationare not available, the real-time evolution of the stress concentrationsis obtained by monitoring a particular branch of the eigenvalueequation as it moves in the complex p-plane. A correspondingpath is traced in an appropriately cut strip in the s-plane,in which solutions to the eigenequation are single-valued. Analyticcontinuation in the p-plane thus allows the Laplace and Mellininversions to be performed and the real-time behaviour of theplane-stress components to be expressed as contour integralswithin the strips in the complex s-plane. Cast in this form,the stress components are evaluated numerically when the viscoelasticmaterial is represented as a standard linear solid. Their dependenceon the angular variation within the plate, the applied load,and the effects of the viscoelastic material properties is exhibitedfor a number of situations, and in each case contrasted withshort- and long-time asymptotic curves based on Tauberian theorems.