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

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

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

4. In linear elasticity stress is ‘proportional’ to stress (‘Hooke’s law’)   is the elasticity tensor. It is a symmetric tensor (21 elasticity coefficients) Elastic rheology 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  For Newtonian rheology the strain rate is ‘proportional’ to stress. Viscous deformation is non recoverable

6. Plastic rheology  For Newtonian viscous rheology the strain rate is ‘proportional’ to stress. Plastic deformation is non recoverable (e) Plastic F   t1t1 t2t2 NB: The strain evolution depends on the experimental conditions (ex: stiffness of the apparatus) ss ss

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

8.   F t1t1 t2t2  …Coupled rheological models (f) Elasto-plastic Non-recoverable