Rheological‐Model Concept

The theory of rheological models considers series and parallel combinations of lumped elements that are assumed to behave mechanically like the constituent phases of a material, but that, apart from this mechanical behavior, have nothing in common with the real medium. Usually, the elements are elastic springs, viscous dashpots, and dry‐friction bodies. The behavior of real materials can be described only approximately by models. However, in principle, any degree of approximation can be achieved by an indefinite number of model elements. Models subjected to impressed harmonic forces are represented by complex constants that, for linear models, are mechanical impedances, dependent upon frequency, with the element characteristics as parameters. Nonlinear models result from the inclusion of dry‐friction bodies that are approximated by viscous dashpots that absorb the same energy per cycle. For these cases, the model constants are again defined as mechanical impedances but differ from those for linear models in the sense that they are dependent upon driving‐force amplitude as well as frequency. The use of a generalized model constant gives generality to equations of motion and adds no complications to the mathematics. Applications can be made for lumped and continuous media, both solid and fluid. For generalized forces, models are represented by real‐time‐dependent operators.