Mathematical modeling and numerical simulation are integral components in enabling the understanding the underlying physical and/or chemical mechanisms governing the vast array of complex material behaviors. This is especially so in advanced biomaterials such as bio-stimuli responsive hydrogels, which are widely used in BioMEMS devices. In these applications, multi-physics and multi-phase phenomena are commonly encountered. In the published studies on stimuli-responsive hydrogels, the literature clearly indicates that the vast majority of works in this area are experimental-based. The rest are predominantly ad-hoc studies of these hydrogel materials usually conducted by trial and error. This is a very time-consuming and inefficient process, and certain aspects of fundamental knowledge can often be missed or overlooked, resulting in off-tangent research directions. Thus it is absolutely necessary in the analysis of bio-stimuli-responsive hydrogels to first establish a sound theoretical platform by developing the correct mathematical models. Thereafter, powerful numerical techniques also have to be developed to solve these challenging models, which are often highly-coupled, nonlinear, and involve moving boundaries.
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