Finite element modeling of frequency-dependent and temperature-dependent dynamic behavior of viscoelastic materials in simple shear

Material dynamic mechanical behavior can depend strongly on frequency and temperature. This dependence is especially significant for elastomers and polymers, such as those used in bearings and damping treatments. Previous research has yielded a time-domain model of linear viscoelastic material and structural behavior that captures characteristic frequency-dependent behavior; continuing research has addressed the accommodation of temperature dependence as well. The resulting approach is based on the notion of time-temperature superposition for thermorheologically-simple materials. In such materials, temperature effects are experienced primarily through a temperature-dependent factor multiplying the time scale. The phenomenon of "thermal runaway", observed in some tests of helicopter elastometric dampers, motivates a numerical example of forced vibration of a 40 × 16 × 5 mm elastomeric test specimen in simple shear. For forcing at 1500 N and 4 Hz, and the temperature on one face held constant, the temperature at the thermally free face increases by about 3 K. For forcing at 3000 N, the temperature rapidly increases more than 35 K, and displacement amplitudes increase by more than a factor of 4. The coupled-field finite element simulation evidently captures the key features of observed material response, including a rapidly increasing rate of temperature change and an accompanying stiffness reduction.