Constitutive modeling of thermal actuation

While extensive modeling work has been done, this chapter intends to provide a brief overview to help point the reader in the right direction.

Thermoviscoelasticity modeling approach for amorphous SMP networks

Thermoviscoelastic modeling approaches have been developed for SMPs in which the mobility of polymer chains can be correlated with viscosity or relaxation time of a Maxwell element [60,76—81]. The viscous strain developed at temperatures above Tg is restricted at temperatures below Tg for temporary shape-fixing [60]. Reheating above Tg will reduce the viscosity, reactivate the dashpot, and allow the structure to relax to its equilibrium configuration, which leads to shape-recovery. With this modeling concept, comprehensive 3D thermoviscoelastic models have been developed with the merits in capturing various polymer behaviors in addition to the SME, such as finite-deformation, entropic elasticity of the rubbery network, nonlinear thermal expansion, structural relaxation, and viscoplastic flow below Tg [76—79]. In order to describe the glass transition behavior of SMPs across broad temperature range, two modeling strategies can be applied. The first one is based on a modified standard linear solid (SLS) model with Kohlrausch—Williams—Watts (KWW) stretched exponential function, where the regular material relaxation is mapped into a new timing space in describing the material clock. In the second modeling strategy, the multibranched models resembling the generalized viscoelastic model or Prony series are applied [60,82—84]. A unified theory to predict the shape- memory behavior of amorphous SMPs have been developed based on the one-dimensional (1D) multibranched model [85].

 
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