We develop a variationally consistent framework for chemo-elastic special Cosserat rods that incorporates a two-way chemo-mechanical coupling to accurately model large deformations in slender rods. This two-way coupling is particularly important to model stress-assisted diffusion for various metamaterial-based battery electrodes and soft robotics applications. Using the virtual power and energy minimization approach, we first derive coupled equilibrium equations in Lagrangian formulation applicable to three-dimensional chemo-elastic solids. Upon utilizing these equations, we subsequently establish the one-dimensional equilibrium equations for the chemo-elastic special Cosserat rod through dimensional reduction. Later, we formulate the constitutive relations and determine work conjugates for chemo-elastic rods coherent with our dimensional reduction approach. Using these constitutive relations, we develop closed-form solutions for the chemo-elastic rod subjected to extension. We present a benchmark result from our theoretical model that shows an excellent agreement with experimental observations for the stress-assisted diffusion case, wherein the concentration increases with the applied load. Such a phenomenon is important in lithium-ion batteries, wherein stress alters lithium diffusion patterns, and this can be captured by our two-way coupling model. Finally, the nonlinear coupled differential equations for chemo-elastic rods are solved numerically, and interestingly, we found the contrasting chemo-mechanical response under displacement and force boundary conditions for varying concentration and concentration gradient.
This article has been accepted in IJSS. You can enjoy reading it here: https://www.researchgate.net/publication/397070059_A_variationally_consistent_chemo-elastic_theory_for_special_Cosserat_rods