Return your solutions by Thursday 10.3 on MyCourses (single PDF format, deadline at 13:45). 1. The relation between the stres o(t) and strain (t) of a material is often represented by the mechanical models shown in Fig. 1. The models consist of elastic elements represented by springs in which o(t) and (t) are related by a = G) (Fig. 1(a)), and a viscous elements represented by dashpots in which o =rry (Fig. 1(b). Answer the following questions www (a) spring o=G (c) Maxwell model mo 1 (d) Voigt model (b) dash pot arri Figure 1: Doi, Fig. 9.17. (a) Consider the model shown in Fig. 1(c) in which the spring and the dashpot are connected in series. This model is called the Maxwell model. Show that o(t) and (t) are related by the following differential equation: = 1. 7 (1) (b) Calculate the relaxation modulus G(t) for the Maxwell model. (c) For the Maxwell model, calculate (t) when o(t) is changed as follows: 0. (t) = . if t 0 (2) ) 0. 1 (d) Consider the model shown in Fig. 1(d) in which the spring and the dashpot are connected in parallel. This model is called the (Kelvin-) Voigt model. Calculate the relaxation modulus G(t) of the Voigt model. Also calculate the strain y(t) when the stress is changed as in Eq. (2) (e) Construct the mechanical model which gives the relaxation modulus of Eq. (9.17): G(0) G. + Ge-t/T