Authors: Abdullah Shafqat, Oliver Weeger, Bai-Xiang Xu

An efficient isogeometric solid-beam finite element for finite strain chemo-mechanical analysis is presented in this work. The formulation is particularly well-suited for simulating diffusion-induced large deformations and buckling of slender micro-lattice structures, such as architectured Li-ion battery electrode materials. This multi-field solid-beam element extends our previous work by fully coupling chemical diffusion, finite volumetric chemical expansion, and large elastic deformations. The mechanics-induced drifting effect on the flux of the chemical species induces higher-order issue. A mixed formulation with displacements, concentration and chemical potential as degrees of freedom is employed. The two-way coupled variational problem is discretized using NURBS basis functions. As with solid finite elements based on Lagrange polynomials, NURBS-based formulations are also affected by the non-physical phenomena of locking. To mitigate such effects in the solid-beam context, the assumed natural strain (ANS) method is employed to alleviate both membrane and transverse shear locking. Additionally, a mixed integration point (MIP) strategy is adopted to enhance computational efficiency and robustness. The proposed element is evaluated through a series of single-patch and multi-patch benchmark problems, and validated against a coupled 3D chemo-mechanical solid element. Results demonstrate that the developed solid-beam element inherits the high accuracy typical of solid elements, along with the computational efficiency and locking-free performance characteristic for analyzing slender beams. This element offers a promising tool for robust simulations of eigenstrain-induced large deformations and buckling of slender structures within a multi-physics framework like chemomechanics and thermomechanics.