Temperature field and heat flux that do not induce stress and electric displacement in a free thermoelectroelastic anisotropic solid

•We consider a thermoelectroelastic solid free of mechanical and electric load.•We seek for the temperature field that does not induce electric displacement.•There is a sole direction of a heat flux that does not induce electric displacement.

The paper derives the equations, which should be satisfied by the temperature field that does not induce stress and electric displacement in an anisotropic thermoelectroelastic solid. It is shown that these equations are satisfied identically only if the pyroelectric solid is heated or cooled by a constant temperature. Due to the tertiary pyroelectric effect a free thermoelectroelastic solid, which temperature is a linear function of spatial coordinates, can undergo nonzero internal stress and electric displacement. Sufficient conditions are obtained, which satisfaction vanishes stress and electric displacement in a free pyroelectric solid under the action of a steady-state uniform heat flow.