Continuum modeling of electrochemomechanical phenomena by a variational approachwith application to all solid state batteries

全固态锂离子电池是一种很有前途的电池设计，它比基于液体电解质的锂离子电池具有几个优点。然而，预计需要大量的努力来解决几个问题，如机械退化和所有固态锂离子电池的倍率能力不足。在这种情况下，相关现象的建模可以帮助充分理解和减少/消除这些问题。本研究的目的是在适当的电化学力学连续建模方法，这是适用于宏观尺度以及微观尺度上的发展和数值评价。该模型将表示在一个率型变分原理，从而使一个相当紧凑的，一致的配方。此外，变分原理允许应用程序的强大和有效的数值求解方案，这也将被开发。所得到的空间-时间离散配方将被应用到所有固态锂离子电池的背景下发生的情况代表的问题的建模。这旨在为未来系统研究和优化所有固态锂离子电池的性能提供基础。

All solid state lithium-ion batteries are a promising battery design, which has several advantages over liquid electrolyte based lithium-ion batteries. However, significant effort is expected to be required to solve several issues like mechanical degradation and insufficient rate capability of all solid state lithium-ion batteries. In this context, modeling of the relevant phenomena can help to fully understand and reduce/eliminate these problems. The present research aims at the development and numerical evaluation of an appropriate electrochemomechanical continuum modeling approach, which is applicable on the macro-scale as well as on the micro-scale. The model will be stated in terms of a rate-type variational principle, thereby enabling for a rather compact, thermodynamically consistent formulation. Moreover, the variational principle allows for the application of robust and efficient numerical solution schemes, which will likewise be developed. The resulting space-time discrete formulation will be applied to the modeling of problems representative of situations occurring in the context of all solid state lithium-ion batteries. This is intended to provide the basis for future systematic studies and optimization of the properties of all solid state lithium-ion batteries.