A mixed finite volume formulation for determining the small strain deformation of incompressible materials

A Þnite volume formulation for determining small strain deformations in incompressible materials is presented in detail. The formulation includes displacement and hydrostatic pressure variables. The displacement Þeld varies linearly along and across each cell face. The hydrostatic pressure Þeld associated with each face is uniform. The cells that discretize the structure are geometrically unrestricted, each cell can have an arbitrary number of faces. The formulation is tested on a number of linear elastic plane strain benchmark problems. This testing reveals that when meshes of multifaceted cells are employed to represent the structure then locking behaviour is exhibited, but when triangular cells are used then accurate predictions of the displacement and stress Þelds are produced. Copyright