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Understanding Strain and Stress in Rheology: A Review of Simple Models

Explore the relationship between strain, stress, and time in rheology through simple rheological models like perfect plastic and elasto-plastic systems. Discover how elastic and viscous deformations differ and how they influence material behavior. Learn about coupled rheological models and the effects of recoverable and non-recoverable deformations.

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Understanding Strain and Stress in Rheology: A Review of Simple Models

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  1. III. Strain and Stress • Strain • Stress • Rheology A rheological law relates strain to stress and time.

  2. A review of simple rheological models… (e) Perfect plastic (f) Elasto-plastic F F

  3. Elastic rheology Elastic deformation is recoverable σ ε In linear elasticity stress is ‘proportional’ to strain

  4. Elastic rheology In linear elasticity stress is ‘proportional’ to stress (‘Hooke’s law’) σ ε is the elasticity tensor. It is a symmetric tensor (21 elasticity coefficients) For an isotropic linear elastic medium there are only 2 elasticity coefficients , e.g.: the Young modulus and Poisson ratio: Young Modulus Poisson ratio From a uniaxial stress experiment:

  5. Viscous rheology Viscous deformation is non recoverable σ For Newtonian rheology the strain rate is ‘proportional’ to stress.

  6. Plastic rheology σ (e) Plastic σc F t1 t2 NB: The strain evolution depends on the experimental conditions (ex: stiffness of the apparatus) Plastic deformation is non recoverable σ σc ε

  7. Coupled rheological models… Non-recoverable Recoverable, with hysteresis loop

  8. …Coupled rheological models (f) Elasto-plastic σ σ F ε t1 t2 ε Non-recoverable

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