Viscoelastic behavior of organic materials: consequences of a logarithmic dependence of force on strain rate

The viscoelastic and -plastic behavior of organic materials like bone, tendon or wood, as well as technical polymers, is amply documented. It is usually modeled using linear “Newtonian” friction, i.e., a viscous force proportional to the deformation rate. If the experimental results cannot be fitted with the resulting exponential “Debye” curves, a multitude of relaxation mechanisms or a spectrum of relaxation times is invoked. In this contribution experimental evidence is compiled which indicates that for polymers and organic materials a logarithmic dependence of the deformation force on the deformation rate is more appropriate. The corresponding equation of motion is solved in the quasi-static approximation and the solutions display just the typical deviations from the Debye behavior found experimentally, without any complications from multi-mechanism relaxation.