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Any combination of Hookean (linear-response) springs in series or parallel behaves like a single Hookean spring. The formulas for combining their physical attributes are analogous to those that apply to capacitors connected in series or parallel in an electrical circuit .
Materials undergoing strain are often modeled with mechanical components, such as springs (restorative force component) and dashpots (damping component).. Connecting a spring and damper in series yields a model of a Maxwell material while connecting a spring and damper in parallel yields a model of a Kelvin–Voigt material. [2]
The Kelvin–Voigt model, also called the Voigt model, is represented by a purely viscous damper and purely elastic spring connected in parallel as shown in the picture. If, instead, we connect these two elements in series we get a model of a Maxwell material .
Viscoelastic behavior has elastic and viscous components modeled as linear combinations of springs and dashpots, respectively. Each model differs in the arrangement of these elements, and all of these viscoelastic models can be equivalently modeled as electrical circuits.
Diagram of a Maxwell material. The Maxwell model is represented by a purely viscous damper and a purely elastic spring connected in series, [4] as shown in the diagram. If, instead, we connect these two elements in parallel, [4] we get the generalized model of a solid Kelvin–Voigt material.
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Similarly, for a parallel combination of the same elements the strains are equal and the stresses additive. Having said that, the two simplest models that combine more than one element are the following: a spring and dashpot in parallel, called the Voigt (or Kelvin) model; a spring and dashpot in series, called the Maxwell model