Displacement measurements physical time properties

Physical models based on the transport processes, were proposed by Shahinpoor [Shahinpoor (1995)] and Nemat-Nasser et al. [Nemat-Nasser (2002) Nemat-Nasser and Li (2000)]. The models predict the behavior of IPMC accurately, but they require many physical quantities that are not trivial to measure. On the other hand, black-box models such as presented in [Xiao and Bhattacharya (2001)] are simpler and are also able to estimate curvatures and actuation displacements of IPMCs however, they are applicable only to specific shapes and boundary conditions from which the models have been extracted. At the same time, gray-box models that are based on the physics laws, but also depend on some empirical physical properties that are determined by experimental or analytical methods, are easier to apply and are also able to predict behaviors of IPMCs with general shapes and boundary conditions [Kanno et al. (1996) P. G. de Gennes et al. (2000)]. 

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