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.