1. This graph is a stress-strain diagram that is of the type often studied by mechanical engineers to understand the elastic behavior of materials. Given that strain is defined as a fractional deformation or displacement, and stress is defined as a force per unit area, what does the area under this curve represent?

2. Casson model was discussed in class in the context of blood rheology. This phenomenological model is often used to describe the shear stress vs. shear rate relationship in colloidal suspensions where particle aggregation might cause the measured viscosity to increase at low shear rates. In an experiment, data for the shear stress rand the applied shear rate S were fitted to the Casson model written below (in a slightly different form compared to that given in the lecture notes): √t=√₁+√as. (1) The best least square fit parameters to the experimental data were found to be 40 mPa for the yield stress and 2.5 mPas for the parameter a, which is referred to as the plastic viscosity. a. Using Eq. (1), derive an expression for the fluid viscosity u as a function of S. b. Plot the viscosity of the fluid as a function of S for 0.1s¹