Singular stress behavior in a bonded hereditarily-elastic aging wedge. Part I: Problem statement and degenerate case

Abstract

Stress singularity is investigated in a plane problem for a bonded isotropic hereditarily elastic (viscoelastic) aging infinite wedge. The general solution of the operator Lamb equations, which are partial differential equations in space co-ordinates and integral equations in time, respectively, is represented in terms of one-parametric holomorphic functions (the Kolosov-Muskhelishvili complex potentials depending on time) in weighted Hardy-type classes. After application of the Mellin transform with respect to the radial variable, the problem is reduced to a system of linear Volterra integral equations in time. By using the residue theory for the inverse Mellin transform, the stress asymptotics and strain estimates near the singular point are presented here for non-hereditary Dundurs parameters. The general case of the hereditary Dundurs operators is considered in Part 11 (see [21]).