Gradient theory of thermoelasticity for interface crack problems with a quasicrystal layer. (1st March 2023) - Sladek, Jan; Sladek, Vladimir; Repka, Miroslav; Schmauder, Siegfried
Highlights: The interface crack between two dissimilar quasicrystal materials. The gradient theory of thermoelasticity for quasicrystals. The gradient theory for heat conduction problem. Decagonal quasicrystal properties. The mixed FEM formulation with C 0 continuous finite elements for independent approximations of displacements and strains. Abstract: The interface crack problem between two dissimilar materials under a thermal load is analyzed by the gradient elasticity theory since the size effect is expected in the very thin quasicrystal layer. The uncoupled thermoelasticity is considered here, where the thermal fields are independent on mechanical ones. The thermal transport can't be well described by classical Fourier's law in nano-sized structures. Therefore, a novel gradient theory is developed in such structures, where the second derivatives of temperature in the constitutive equation for the high-order heat flux are considered. Moreover, the phonon strain gradients are incorporated into the higher-grade continuum model. Decagonal quasicrystal material properties are considered here. Governing equations and corresponding boundary conditions are derived from the principle of virtual work. The mixed finite element method (MFEM) is developed for a general 2D boundary value problem. Numerical examples are presented to illustrate the phonon, phason and thermal response to external thermal loading within the considered model.