1.2 Nanoscale Actors and Their Properties

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Figure 1.24: Mathematical models of viscoelasticity to predict stress and strain in materials based on

springs and dashpots.

filled damper) represents viscosity. A Newtonian, i. e. a laminar, ideal flow is assumed.

These two models can be combined mathematically in a variety of ways, the most com-

mon and simple of which are the Maxwell element (spring and dashpot in series) and the

Voigt element (spring and dashpot in parallel) (Figures 1.23 and 1.24). In these models,

the equations for stress and strain become mathematical combinations of the equations

for ideal elasticity and ideal viscosity.

More complicated combinations of several Maxwell and/or Voigt elements have

been proposed. These models are still approximations; stress strain curves of real poly-

mers are more complicated (Figure 1.25). Therefore, in mechanical engineering error