Thirty Years of the Finite Volume Method for Solid Mechanics

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, including `cell-centre', `staggered', `vertex-centred', `periodic heterogenous microstructural', `Godunov-type', `matrix-free', `meshless', as well as others. This article gives an overview, historical perspective, comparison and critical analysis of the different approaches, including their relative strengths, weaknesses, similarities and dissimilarities, 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 widespread acceptance.

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