Extended Stroh formalism for plane problems of thermoelasticity of quasicrystal media

Abstract

This study provides a mathematical method for the analysis of plane phonon-phason thermomechanical fields in quasi-crystalline bodies, which was developed based on the complex variable calculus and the Stroh formalism. Constitutive and balance equations of thermoelasticity of quasicrystal solids are written in a generalized form using extended phonon-phason vectors and tensors. Adapting the methods of the Stroh formalism, the formulated general problem is reduced to the search for 7 analytical functions (1 for temperature and 6 for phonon-phason fields). The obtained approach was used to construct the integral equations of the corresponding two-dimensional problems of the thermoelasticity of quasicrystal solids, and on its basis a specific problem for a quasi-crystalline medium with a crack was solved. Distributions of temperature and mechanical fields in the body and functions of asymptotic distributions of phonon-phason fields near the crack tip using intensity coefficients of phonon and phason stresses were obtained.