Two dimensional transient analysis of coupled non-Fick diffusion–thermoelasticity based on Green–Naghdi theory using the meshless local Petrov–Galerkin (MLPG) method

• 2D non-Fick diffusin-thermoelasticity based on GN theory is studied in details.
• Meshless local Petrov–Galerkin (MLPG) is employed to solve the problem.
• The governing equations are derived in meshless local integrals (LIEs) forms.
• The propagation of molar concentration wave are observed with finite speed.
• Displacements and temperature wave fronts can be tracked using the presented method.

This work deals with the application of meshless local integral equations (LIEs) based on the meshless local Petrov–Galerkin (MLPG) method to two dimensional coupled non-Fick diffusion-thermoelasticity analysis, based on Green–Naghdi theory of generalized coupled thermoelasticity without energy dissipation. The molar concentration diffuses through the analyzed 2D domain with a finite speed similar to thermoelastic waves. The propagation of mass diffusion, temperature and elastic waves are obtained and discussed with showing the profiles of molar concentration, temperature and displacements in two orthogonal directions at various time instants. The MLPG method has a high capability to track the diffusion, elastic and thermal wave fronts at arbitrary time instants in 2D domain.