A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics

A vertex-based nite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and in nitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and threedimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational e ciency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted