In recent times, there has been a growing interest in ionic electroactive polymer-based artificial muscle owing to their capacity to operate effectively with low-voltage input. Conducting polymer (CP)-based soft actuators exhibit functionality akin to natural muscles, enabling multi-modal actuation by applying voltage within the range of 1-5 V \cite{chen2022low}. On applying a potential difference, the redox reaction initiates the charge transport across the actuator, resulting in its mechanical deformation. The complex multi-physics phenomena involved in actuation make its accurate modeling interesting to study. The existing models of CP actuators approximate the charge transport through a lumped parameter electrical circuit model that requires parameter estimation through experiments \cite{ghosh2022nonlinear}. Consequently, developing the charge transport equations from the first principles is imperative. A trilayer bending CP actuator has been developed that uses Nernst-Planck-Poisson (NPP) equations and a linear mechanical deformation model \cite{price2013unified}. However, the stress-strain behavior of CPs as a material is found to be nonlinear \cite{ghosh2022nonlinear}. Therefore, a coupled electro-chemo-mechanics deformation model needs to be developed from the first principle. In the present study, a physics-based electrochemomechanical (ECM) deformation model is formulated to predict the response of the CP actuator. The model predicts the actuator's mechanical deformation due to ions' diffusion from the surrounding electrolyte. The electrochemical model depicts charge transport using the NPP-coupled equation. Further, the charge stored in CP is coupled to a nonlinear mechanical deformation model using the free-energy density function. The free-energy density function includes a combination of energy functions due to the stretching of the network and chemomechanical coupling, including ion mixing and the interaction between ion concentration and mechanical deformation. The derived model is validated with existing experimental results for a trilayer bending CP actuator.