Microlattice structures for lithium-ion battery electrodes: Chemo-mechanical beam modeling of diffusion-induced instabilities and optimal design

3D打印等先进制造技术的最新进展使复杂的3D微晶格结构可以作为锂离子电池材料和单元电池实现。这些结构具有较大的表面积、较短的扩散路径和较高的应力松弛，可显著提高性能。然而，由于锂离子诱导的膨胀，梁格子的细长韧带容易发生屈曲等力学不稳定性。这种化学诱导的非线性不稳定性及其对电极电化学性能的影响还没有得到充分的了解，更不用说电极微晶格的优化设计了。虽然目前锂离子电池的多物理模拟主要基于计算代价高昂的实体模型，但基于多物理束流公式的高效模拟和优化方案对于稳定性分析和电极设计都是可取的。这项联合提案的目的是通过使用束流公式来开发这种方法，用于作为电池电极材料的微晶格结构的化学机械研究。我们计划首先开发多物理束公式和离散化，耦合力学和瞬变离子扩散。对于具有相对较小弹性应变的材料，如锂锰氧化物或五氧化二钒，几何精确、共旋转的3D梁模型将扩展到离子扩散、膨胀和材料参数随离子浓度的变化。为了处理横截面扩散，将开发一个简单的启发式模型和一个高级的类似翘曲的模型。对于像硅这样具有潜在大变形的材料，具有超弹性材料定律的有限应变固体梁单元将被扩展，以耦合轴向和横截面上的瞬时离子扩散。在结构优化方面，建议的梁单元和实体梁单元将采用等几何离散。为了确保这些模型的可靠性和评估效率，将通过化学机械三维实体有限元模拟对其进行验证。基于这些梁公式，将建立电池微晶格结构屈曲和后屈曲行为的可靠化学力学分析框架。梁模型的预期效率应该允许对具有大量单胞的样品进行模拟，以演示局部和全局屈曲模式及其对充电率以及几何和材料参数的依赖关系。然后，该框架将用于分析屈曲效应对电池性能的影响，如容量和充电电压-状态曲线。使用具有伴随灵敏度的基于梯度的优化算法，我们将获得具有空间变化的支撑厚度、材料组成或优化弯曲的支撑的最佳微晶格，以促进特定的屈曲行为以提高性能

Recent progress in advanced fabrication such as 3D printing allows implementation of complex 3D microlattice structures as lithium-ion battery materials and unit cells. With large surface area, short diffusion paths and high stress relaxation, these structures offer significant performance improvement. However, due to lithiation-induced expansion, the slender ligaments of beam-lattices are prone to mechanical instabilities such as buckling. Such chemically induced nonlinear instabilities and their impact on the electrochemical performance of the electrode are insufficiently understood, let alone the optimal design of electrode microlattices. While current multi-physical simulation of lithium-ion batteries is mainly based on computationally expensive solid models, efficient simulation and optimization schemes based on multi-physical beam formulations are desirable for both instability analysis and electrode design. The objective of this joint proposal is to develop such methods by using beam formulations for the chemo-mechanical study of microlattice structures as battery electrode materials. We plan to first develop multi-physical beam formulations and discretizations coupling mechanics and transient ion diffusion. For materials subject to relatively small elastic strains such as Lithium manganese oxide or Vanadiumpentoxid, a geometrically exact, co-rotational 3D beam model will be extended with ion diffusion, swelling, and variation of material parameters with ion concentration. To address cross-sectional diffusion, both a simple heuristic model and an advanced warping-like model will be developed. For materials subject to potentially large deformations such as Silicon, a finite strain solid beam element with hyperelastic material laws will be extended to couple transient ion diffusion both axially and through the cross-sections. In view of structural optimization, the proposed beam and solid-beam elements will be implemented using isogeometric discretizations. To ensure the reliability and assess the efficiency of these models, they will be verified by chemo-mechanical 3D solid finite element simulations. Based on these beam formulations, a framework for the reliable chemo-mechanical analysis of buckling and post-buckling behavior of battery microlattice structures will be developed. The expected efficiency of the beam models should allow even simulations of samples with large numbers of unit cells to demonstrate both local and global buckling patterns and their dependency on charging rates, as well as geometric and material parameters. The framework will then be used to analyze the impact of buckling effects on battery performance such as capacity and voltage-state of charge curves. Using gradient-based optimization algorithms with adjoint sensitivities, we will obtain optimal microlattices with spatially varying strut thickness, material composition, or optimally curved struts that facilitate specific buckling behaviors to enhance performance