Experimental Investigation and Numerical Treatment of Viscoelastic Materials

Visoelastic material behavior is characterized by creep and relaxation processes for static loadings and damping in the case of dynamic harmonic loading. These phenomena are observed for all engineering materials to some extent. This paper gives an overview of classical linear viscoelastic material models and their limitations. The respective constitutive equations are first expressed as differential equations in time and are then generalized by the concept of fractional derivatives. This approach overcomes the disadvantages of classical models, leads to causal material behavior, and fulfills the second law of thermodynamics. As an example, experimental investigations conducted on an engineering plastic material yield its temperature und frequency dependent material properties. Based on the principle of thermorheologic simple material behavior, a so-called master curve is identified which maps the elastic and the dissipative properties of the material over an extensive frequency range. Finally, the material behavior is efficiently modeled with few material parameters through the use of fractional derivatives. The resulting constitutive equation is then used for further numerical calculations.