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Understanding Strain and Stress in Rheology: A Comprehensive Review

Explore the correlation between strain, stress, and time in rheological models, including elastic, plastic, and viscous behaviors. Learn about Hooke's law, elasticity, recoverability, and the implications of different rheological laws.

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Understanding Strain and Stress in Rheology: A Comprehensive Review

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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 e s In linear elasticity stress is ‘proportional’ to strain

  4. Elastic rheology In linear elasticity stress is ‘proportional’ to stress (‘Hooke’s law’) e s 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 s For Newtonian rheology the strain rate is ‘proportional’ to stress.

  6. Plastic rheology s (e) Plastic ss F t1 t2 NB: The strain evolution depends on the experimental conditions (ex: stiffness of the apparatus) Plastic deformation is non recoverable s ss e For Newtonian viscous rheology the strain rate is ‘proportional’ to stress.

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

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

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