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Mechanical Models

Mechanical Models. Approaches to Viscoelaticity. The viscoelastic properties of foods may be difficult to describe. Three approaches have been developed: Creep/Stress Relaxation experiments Mechanical analogies Dynamic testing. Mechanical Models.

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Mechanical Models

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  1. Mechanical Models

  2. Approaches to Viscoelaticity • The viscoelastic properties of foods may be difficult to describe. Three approaches have been developed: • Creep/Stress Relaxation experiments • Mechanical analogies • Dynamic testing

  3. Mechanical Models • Viscoelastic behavior can be modeled as a combination of springs and dashpots • Spring: stretches or compresses instantly under a stress; holds stress indefinitely; once stress removed, system recovers • Dashpot: cup with viscous liquid through which a plunger is driven; rate increases with stress, decreases with viscosity; system does not recover.

  4. Maxwell Model • Maxwell Model: a spring with elastic modulus E1 in series with a dashpot with viscosity 1 • Both spring and dashpot experience same stress but exhibit different deformations (strains)

  5. Kelvin Model • Kelvin Model (Voight element): a spring with elastic modulus E1 in parallel with a dashpot of viscosity 1. • The deformation on each element is the same, but each experiences different stresses

  6. Response under constant stress

  7. Maxwell: spring stretches immediately in accordance with Hooke’s law  =E • The dashpot pulls out over time; the greater 1, the slower it responds • Both elasticity and flow

  8. Kelvin: spring and dashpot respond together. The spring cannot instantaneously stretch. • The spring bears more and more stress as the element is extended

  9. Other Models • The Maxwell and Kelvin models are usually too simplistic to describe real foods. Several extensions have been made. • Three element models • Four element models

  10. Three Element Models • Used to describe bread dough • Extra viscous element allows additional deformation over time • Strain does not plateau as with Kelvin model

  11. Four Element Model • Burger model: Kelvin element in series with a Maxwell element • Simplest model that exhibits all features of viscoelasticity

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