A note on the quasi-static problem of periodic linearized thermoviscoelasticity.

*(English)*Zbl 0719.73015This paper is concerned with a linear theory of quasi-static thermoviscoelasticity, with constitutive equations of Maxwell type. The theory is uncoupled in the sense that the temperature field can be found independently of the mechanical fields. The stiffness and the viscosity tensor are assumed to be temperature dependent. First, the author establishes the existence of a periodic solution without assuming that the viscosity tensor is uniformly coercive. The case where the viscosity field varies smoothly on time and is not invertible is also studied. Then, the stability of the periodic stress is established. The thermal effect is not discussed.

Reviewer: D.Ieşan (Iaşi)

##### MSC:

74D99 | Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) |

74A15 | Thermodynamics in solid mechanics |