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III. Strain and Stress. Strain Stress Rheology. A rheological law relates strain to stress and time. A review of simple rheological models…. (e) Perfect plastic. (f) Elasto-plastic. F. F. Elastic rheology. Elastic deformation is recoverable. σ. ε.

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## III. Strain and Stress

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**III. Strain and Stress**• Strain • Stress • Rheology A rheological law relates strain to stress and time.**A review of simple rheological models…**(e) Perfect plastic (f) Elasto-plastic F F**Elastic rheology**Elastic deformation is recoverable σ ε In linear elasticity stress is ‘proportional’ to strain**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:**Viscous rheology**Viscous deformation is non recoverable σ For Newtonian rheology the strain rate is ‘proportional’ to stress.**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**Coupled rheological models…**Non-recoverable Recoverable, with hysteresis loop**…Coupled rheological models**(f) Elasto-plastic σ σ F ε t1 t2 ε Non-recoverable

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