For passive (classical) materials, stress and strain are used to extract the material behavior from the sample behavior in a tensile test. In analogy, the actuation behavior of active (smart) materials can be normalized. In the present research, we show the normalization using the example of hydrogels that react with a volume change (swelling and deswelling) when exposed to stimulus-changes like temperature, chemical concentrations, pH or light intensity changes. The normalized behavior can then be implemented with the Temperature-Expansion-Model which is based on the analogy of active behavior with thermal expansion. This allows the simulation of arbitrary active structures and the extraction of the sensitivity measure to a stimulus.
Active behaviorThe actuation behavior of active (smart) materials is still very difficult to grasp by engineers who are not familiar with the multi-physics backgrounds: These are for example electro-activity in Dielectric Elastomers, phase transitions in hydrogels, combined electro-chemical interactions in conductive polymers or phase transitions in shape memory alloys [1][2][3]. In the current work, we provide a concept based on the normalization and general representation of active behavior using the concept of analogies: Different phenomena can be described as analog if they can be represented by the same macroscopic model, i.e. mathematical representation. Well-known analogies are for example between electric and hydraulic circuits or between the thermal and chemical field. In the current work, we present how the active equilibrium behavior of different smart materials can be described in analogy to thermal expansion.
Description of the Temperature-Expansion-ModelThe approach of representing the isotropic swelling of the hydrogel poly(N-isopropylacrylamide) (PNiPAAm) with thermal expansion was called Temperature-Expansion-Model (TEM) [4,5] in order to avoid confusion with thermal expansion which is a physical process. The TEM is a phenomenological approach to represent the active behavior using the same mathematical description, which is also done in various actuator equations. Table 1: Equations for the Temperature-Expansion-Model (TEM), the extended (nonlinear) and the normalized version.