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A review of finite-element modelling in snow mechanics

机译：雪力学中的有限元建模研究述评

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The finite-element method (FEM) is one of the main numerical analysis methods in continuum mechanics and mechanics of solids (Huebner and others, 2001). Through mesh discretization of a given continuous domain into a finite number of sub-domains, or elements, the method finds approximate solutions to sets of simultaneous partial differential equations, which express the behavior of the elements and the entire system. For decades this methodology has played an accelerated role in mechanical engineering, structural analysis and, in particular, snow mechanics. To the best of our knowledge, the application of finite-element analysis in snow mechanics has never been summarized. Therefore, in this correspondence we provide a table with a detailed review of the main FEM studies on snow mechanics performed from 1971 to 2012 (40 papers), for facilitating comparison between different mechanical approaches, outlining numerical recipes and for future reference. We believe that this kind of compact review in a tabulated form will produce a snapshot of the state of the art, and thus become an appropriate, timely and beneficial reference for any relevant follow-up research, including, for example, not only snow avalanche questions, but also modeling of snow microstructure and tire-snow interaction. To that end, this correspondence is organized according to the following structure. Table 1 includes all essential information about previously published FEM studies originally developed to investigate stresses in snow with all corresponding mechanical and numerical parameters. Columns in Table 1 provide references to particular studies, placed in chronological order. Rows correspond to the main model parameters and other details of each considered case.
机译：有限元方法（FEM）是连续介质力学和固体力学中的主要数值分析方法之一（Huebner等，2001）。通过将给定连续域的网格离散化为有限数量的子域或元素，该方法找到了表示部分元素和整个系统行为的同时偏微分方程组的近似解。几十年来，这种方法在机械工程，结构分析，尤其是雪力学中起了加速作用。据我们所知，有限元分析在雪力学中的应用从未被总结过。因此，在此通信中，我们提供了一张表格，其中详细介绍了1971年至2012年进行的关于雪力学的主要有限元研究（40篇论文），以促进不同机械方法之间的比较，概述数值配方并供将来参考。我们认为，以表格形式进行的这种紧凑回顾将提供最新技术的概况，从而成为任何相关后续研究（包括例如雪崩）的适当，及时和有益的参考问题，还包括雪的微观结构和轮胎-雪地相互作用的建模。为此，根据以下结构来组织该对应关系。表1包含有关先前发布的FEM研究的所有基本信息，这些研究最初是为研究雪中的应力以及所有相应的力学和数值参数而开发的。表1中的列提供了按时间顺序排列的特定研究的参考。各行对应于主要模型参数以及每种情况的其他详细信息。

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