  The role of thermodynamics in continuum mechanics and the derivation of the
proper constitutive relations is a discussed subject of Rational Mechanics. The
classical literature did not use the accumulated knowledge of thermostatics and
was very critical with the heuristic methods of irreversible thermodynamics. In
this paper, a small strain gradient elasticity theory is constructed with
memory effects and dissipation. The method is nonequilibrium thermodynamics
with internal variables; therefore, the constitutive relations are compatible
with thermodynamics by construction. Thermostatic Gibbs relation is introduced
for elastic bodies with a single tensorial internal variable. The thermodynamic
potentials are first-order weakly nonlocal, and the entropy production is
calculated. Then the constitutive functions and the evolution equation of the
internal variable is constructed. The second law analysis has shown a
contribution of gradient terms to the stress, also without dissipation.
