Interface corners in linear anisotropic viscoelastic materials

Abstract

In this study, an extended Stroh formalism for two-dimensional linear anisotropic viscoelasticity is developed for the problems of interface corners between two dissimilar viscoelastic materials. In this formalism, the solutions for the displacements and stress functions in the time domain can be written in the form of a matrix function using complex variables. The correspondence relations for viscoelastic analysis are then obtained and verified for material eigenvectors, displacement and stress eigenfunctions, singularity orders of stresses, and stress intensity factors. Explicit solutions for the material eigenvector matrices in the Laplace domain are also obtained for standard linear and isotropic linear viscoelastic solids. To calculate the singularity orders and stress intensity factors of the interface corners, four different approaches are proposed. Through numerical examples on cracks, interface cracks, and interface corners, an approach using the path-independent H-integral in the Laplace domain with an elastic near-tip solution, which takes the correspondence relations for singularity orders and stress intensity factors, is demonstrated to be better than the other three approaches.