Viscoelastic Behavior Models: Maxwell vs Voigt

What are the fundamental differences between the Maxwell and Voigt models in describing viscoelastic behaviors?

Explore the formation, stress-strain curve patterns for creep and relaxation, and the roles of spring and dashpot components in both models.

Answer:

The Maxwell model and the Voigt model are two essential models used in explaining the viscoelastic behavior of materials. Let's dive into the distinct characteristics of each model.

The Maxwell model comprises a spring and a dashpot connected in series. The spring signifies the elastic behavior, while the dashpot signifies the viscous behavior of the material. When a constant force is applied, both components deform simultaneously. In creep, the stress-strain curve showcases an initial rapid increase in strain, followed by a gradual rise as the material continues to deform over time. Whereas in relaxation, the curve demonstrates an initial rapid decrease in stress, followed by a gradual decline as the material relaxes.

On the other hand, the Voigt model involves a spring and a dashpot connected in parallel, with both components deforming simultaneously under a constant force. In creep, the stress-strain curve exhibits a gradual increase in strain as the material deforms progressively. Conversely, in relaxation, the curve shows a gradual decrease in stress as the material unwinds over time.

Both models emphasize the distinction between the elastic spring component, responsible for energy storage and release, and the viscous dashpot component, responsible for energy dissipation. It is essential to understand that the stress-strain curves for creep and relaxation may vary depending on the material being modeled. These models present simplified representations of viscoelastic behavior, acting as a foundational framework for more intricate models and experiments.