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Ionic Polymer Metal Composite is a well-known soft electroactive polymer composite that it's promising features tell us that it has adequate potential to be a utilizable and applicative soft actuator in the practical applications, especially in the small size applications. But this smart material is still immature, and one of the reasons that lead to its immaturity is lack of a valid and proper physics-based model for large deformation situations. In practical online and large deformation applications, the inverse non-autoregressive identification based models are the proper choices but if we want to know how IPMC works and what is the physics of its behavior in the large deformation situation the inverse identification based models are deeply blind, and we have to use physical and multi-physical approaches. It is our main aim in this paper, and for the first time, we want to present a fully analytical and physics-based ion transport 3D and non-Linear model for large deformable IPMC. In this direction, based on three dimensional Nernst-Plank PDE we will find a well-defined and valid relationship between input voltage and output tip displacement of IPMC for large deformation situation and with four provable pieces of evidence it will be proven that proposed model has chosen a proper way and it is more complete than previous benchmark and well-known physics-based models for IPMC, and also it is valid and accurate enough for large deformation modeling of IPMC.