Question

Among the viscoelastic models:

• A. Voigt model behaves as a viscoelastic solid
• B. Kelvin model behaves as a viscoelastic fluid
• C. Maxwell model behaves as a viscoelastic fluid
• D. Maxwell model behaves as a viscoelastic solid

Hint:

Viscoelastic Models Summary: - Maxwell Model (Series): Continuous deformation path under constant stress $\rightarrow$ Behaves like a Viscoelastic Fluid. - Kelvin-Voigt Model (Parallel): The internal spring caps maximum deformation and enables full shape recovery $\rightarrow$ Behaves like a Viscoelastic Solid. [Image comparing Maxwell series model vs Kelvin-Voigt parallel model structures]

Answer 1

The Correct Option is C

Concept: Biological tissues exhibit viscoelasticity, meaning they display a combination of elastic solid characteristics (storing energy like a spring) and viscous fluid characteristics (dissipating energy over time like a dashpot). Mechanical engineers model this behavior using idealized lump networks of linear elastic springs (stiffness $E$) and viscous fluid dashpots (viscosity $\eta$). The two fundamental two-element configurations are:
• Maxwell Model: Formed by arranging a spring and a dashpot in a series configuration.
• Kelvin-Voigt Model: Formed by arranging a spring and a dashpot in a parallel configuration.

Step 1: Testing the Maxwell Model under sustained load.
In the series Maxwell model, the total displacement is the sum of the individual component extensions ($\varepsilon_{total} = \varepsilon_{spring} + \varepsilon_{dashpot}$). If you apply a constant stress ($\sigma_0$) to this system over a long period:
• The spring stretches instantly to a fixed value.
• The viscous dashpot continues to slide and extend at a constant rate indefinitely ($\frac{d\varepsilon}{dt} = \frac{\sigma_0}{\eta}$), showing no mechanical limit to its deformation. Because it flows continuously under a sustained load and cannot return to its original shape once the stress is removed, the Maxwell model acts fundamentally as a viscoelastic fluid. This matches statement (C).

Step 2: Testing the Kelvin-Voigt Model under sustained load.
In the parallel Kelvin-Voigt model, the spring and dashpot are locked together, meaning they must undergo identical displacements ($\varepsilon_{total} = \varepsilon_{spring} = \varepsilon_{dashpot}$). When a sustained stress is applied, the viscous dashpot slows down the initial deformation, but over time, the spring takes on the entire mechanical load. This causes the system to reach a stable, finite deformation equilibrium. When the load is removed, the spring pulls the dashpot back to its original position, achieving full shape recovery. This ability to maintain structural shape under long-term loads classifies the Kelvin-Voigt model as a viscoelastic solid. This means statements (A) and (B) are incorrect. Thus, Option (C) stands as the accurate mechanical statement.