On The Development Of Finite Volume Methods For Computational Solid Mechanics.

Abstract

Since its initial development as a tool for structural analysis around the mid-fifties the Finite
Element Method (FEM) has evolved to become the most popular and used method in modern Computational
Solid Mechanics. On the other hand, the Finite Volume Method (FVM) born almost at the same
time, has evolved too and become one of the most popular methods in the area of Computational Fluid
Mechanics. Both methods have surpassed the historical finite differences method and other discretization
methods, and nowadays, researchers typically use one or the other to obtain numerical simulations of all
types of physical phenomena. However, although FEM is at present being actively used to solve the
equations of compressible and incompressible flows, there are not many works about the usage of FVM
in solving the equations of solid materials. The physical flavor, the conservation properties and some
properties of reduced integration of the FVM, are advantages that could be very useful in the context
of Computational Solid Mechanics as they are in the context of Computational Fluid Mechanics (CFD).
In the present work we show our first results in our attempt to develop a Finite Volume Method for
Non-linear Solid Mechanics.