Cardiff, PhilipPhilipCardiffDemirdžić, IsmetIsmetDemirdžić2024-06-042024-06-042021 CIMNE2021-02-02Archives of Computational Methods in Engineering1134-3060http://hdl.handle.net/10197/26133Since 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.enThis is a post-peer-review, pre-copyedit version of an article published in Archives of Computational Methods in Engineering. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11831-020-09523-0.Fluid structure interactionHigher-order theoryRapid crack-propagationStress-wave-propagationFunctionally graded materialsFidelity generalized methodCentered Lagrangian schemeDynamic fracture phenomenaPetrov-Galerkin methodMicromechanical analysisJournal Article283721378010.1007/s11831-020-09523-02021-05-0516/RC/3872IRCLA/2017/4516/RC/3872https://creativecommons.org/licenses/by-nc-nd/3.0/ie/