Exercise $5$: Viscoelasticity: $(17$ points$)$

Stress$-$relaxation test

$($A$)$

$($B$)$

$($C$)$

Figure $2$: Model of the considered viscoelastic material.

Consider a viscoelastic material whose mechanical behavior can be represented as elements in parallel shown in Figure $2.$

$1.$ Write the general constitute equations relating strain $\backslash (\backslash$epsilon $\backslash )$ and stress $\backslash (\backslash$sigma $\backslash )$ of the material $(5$ points$)$

$2.$ Solving the constitute equation between $0$ and $\backslash ($ t$\_\{1\}\backslash )$ and draw graphically the test result $(($Figure $2-$B$,$ C bottom$)$ for:

$-$ creep test condition $($Figure $2-$B $(6$ points$)$

$-$ stress$-$relaxation condition $($Figure $2-$C$)(6$ points$)$