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

A finite volume formulation for determining small strain deformations in in compressible materials is presented in detail. The formulation includes dis placement and hydrostatic pressure variables. The displacement field varies linearly along and across each cell face. The hydrostatic pressure field a ssociated with each face is uniform. The cells that discretize the structur e are geometrically unrestricted, each cell can have an arbitrary number of faces. The formulation is tested on a number of linear elastic plane strai n benchmark problems. This testing reveals that when meshes of multifaceted cells are employed to represent the structure then locking behaviour is ex hibited, but when triangular cells are used then accurate predictions of th e displacement and stress fields are produced. Copyright (C) 1999 John Wile y & Sons, Ltd.