Deriving and numerically solving the weak form equation of a continuum field model for an electro-elastic-diffusive system



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Rash utilization of conventional means of energy generation has forced many to acknowledge the perturbing foreshadowing of the emerging energy crisis and the dearth of viable energy sources. In recent years, conscious efforts have been made to address this reckless use of readily available energy resources and to foster energy conservation. Traditional non-replenishable means of energy generation and inefficient energy storage solutions are being discarded in favor of cleaner and more efficient energy storage devices like batteries. Solid state batteries have favorable characteristics that make them ideal for portable stretchable electronics. However, these still incur substantial energy losses during energy storage and tend to have less ionic conductivity when compared to their liquid electrolyte counterparts. Still, advancements have been made recently by proposing a homogenized continuum field model for an electro-elastic-diffusive system for solid polymer electrolyte batteries to address the issue of ionic conductivity. This work builds upon the theoretical framework discussed in one such research paper. The governing equations for this electro-elastic-diffusive system are the non-linear partial differential equations governing linear elasticity, steady state diffusion of ions, and Maxwell’s equation of electrostatics. In this document, we derive the weak form for this amalgamated problem, consisting of elasticity, diffusion of ions at steady state, and electrostatics, using the technique of Galerkin formulation. We then implement the weak form for this electro-elastic-diffusive system and develop a computational model, to obtain numerical solutions for displacement, chemical, and electric potential. We utilize the solutions fields to learn and report the behavior of chemical potential difference and concentration of ions at steady state under the application of external traction.



Continuum field theory for electro-elastic-diffusive system, Stretchable electronics, Energy harvesters, Weak form of coupled systems