Analysis of the crack problem under unified generalized thermoelasticity

Abstract

The present article aims to manifest a two-dimensional dynamical problem based on a unified way of dual-phase lags generalized thermoelasticity. The problem deals with finite mode-I crack due to tensile force in an unbounded linear thermoelastic space under a specified stress distribution and temperature. Here the governing equations are constructed for a homogenous and isotropic medium. Boundary conditions convert the problem into four dual integral equations, whose solution corresponds to the solution of Fredholm’s integral equation of first order. The integral transform methods are applied to obtain the solution to a problem. An inversion of the Laplace transform using the Bellman method is applied to determine the numerical value of the components of temperature, stress, and displacement for copper material, which are interpreted graphically. Moreover, the stress intensity factor (SIF) near the crack center is calculated and shown graphically.