Analysis of the isothermal mechanical response of a shape memory polymer rheological model

In this paper, we derive the isothermal mechanical response of a 4-element rheological model for shape memory polymers (SMP) in the context of (i) constant stress, (ii) constant strain, (iii) constant stress rate: (iv) constant strain rate, (v) periodic strain. The effect of shape memory strain (modeled by a friction element) and the temperature dependence of the material properties on the SMP response are examined for a polyurethane shape memory polymer of the polyester polypole series. In particular, it is possible to identify a threshold frequency during periodic loading, near which the damping capacity of the SMP is strongly affected by an increasing shape memory strain. On the other hand, when the applied frequency is much greater than the threshold value, an increasing shape memory strain ceases to have any effect on the damping. It is also shown that at a given frequency (significantly greater than the threshold value), the damping capacity as a function of temperature attains a maximum. While this maximum value is frequency-dependent (being inversely proportional), the temperature at which the maximum is attained is frequency-independent, and is analytically shown to be the glass transition temperature.