Since early publications in the late 1980s and early 1990s, the finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of the method, which can be classified in a variety of ways, such as grid arrangement (cell-centred vs. staggered vs. vertex-centred), solution algorithm (implicit vs. explicit), and stabilisation strategy (Rhie–Chow vs. Jameson–Schmidt–Turkel vs. Godunov upwinding). This article gives an overview, historical perspective, comparison and critical analysis of the different approaches where a close comparison with the de facto standard for computational solid mechanics, the finite element method, is given. The article finishes with a look towards future research directions and steps required for finite volume solid mechanics to achieve more widespread acceptance.

自1980年代末和1990年代初发表以来，有限体积法已被证明适用于固体力学分析。当前，该方法有多种形式，可以以多种方式进行分类，例如网格排列（单元中心vs.交错vs.顶点中心），求解算法（隐式vs.显式）和稳定化。策略（Rhie–Chow对阵Jameson–Schmidt–Turkel对阵Godunov的逆风）。本文给出了不同方法的概述，历史观点，比较和批判性分析，其中与计算固体力学的实际标准（有限元方法）进行了比较。本文以展望未来的研究方向和有限体积固体力学实现更广泛接受所需的步骤为结尾。