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

先进制造（如3D打印）的最新进展允许将复杂的3D微晶格结构实现为锂离子电池材料和单元电池。这些结构具有大的表面积、短的扩散路径和高的应力松弛，提供了显著的性能改善。然而，由于锂化引起的膨胀，梁格的细长韧带容易发生诸如屈曲的机械不稳定性。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理解，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昂贵的实体模型，但基于多物理束公式的有效模拟和优化方案对于不稳定性分析和电极设计都是期望的。该联合提案的目的是通过使用用于作为电池电极材料的微晶格结构的化学机械研究的梁制剂来开发这样的方法。我们计划首先开发多物理束配方和离散耦合力学和瞬态离子扩散。对于诸如锂锰氧化物或钒氧化物之类的受到相对小的弹性应变的材料，几何上精确的共旋转3D束模型将被扩展为离子扩散、膨胀以及材料参数随离子浓度的变化。为了解决横截面扩散，一个简单的启发式模型和一个先进的warping-like模型将开发。对于材料的潜在大变形，如硅，有限应变固体束元素与超弹性材料的法律将被扩展到耦合瞬态离子扩散轴向和通过的横截面。考虑到结构优化，所提出的梁和实体梁单元将使用等几何离散化来实现。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，电池微晶格结构的屈曲和后屈曲行为的可靠的化学力学分析框架将被开发。梁模型的预期效率应允许甚至模拟具有大量单元电池的样品，以展示局部和全局屈曲模式及其对充电速率以及几何和材料参数的依赖性。然后，该框架将用于分析屈曲效应对电池性能的影响，例如容量和充电曲线的电压状态。使用基于梯度的伴随灵敏度优化算法，我们将获得具有空间变化的支柱厚度，材料成分或最佳弯曲支柱的最佳微晶格，这些支柱有助于特定的屈曲行为，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