Section 1.1 - Background on Modeling

Abstract

This chapter provides an overview of modeling. Modeling in mechanics is considered as a science or a technique or an art. In mechanics of materials, a model does not exist for itself; it exists in connection with a purpose. If it is the macroscopic behavior of mechanical components of structures that is being considered, the basic tool is the mechanics of continuous media, which deals with the following: (1) strain, a second-order tensor related to the displacement of two points and stress, (2) a second-order tensor dual of the strain tensor; (3) and its contracted product by the strain rate tensor is the power involved in the mechanical process. From the mathematical point of view, strains and stresses are defined on a material point, but the real materials are not continuous. Physically, strain and stress represent averages on a fictitious volume element called the representative volume element (RVE) or mesoscale. All variables which define the internal state of the RVE are called internal variables. The process is not finished until the model is applied and compared to special tests which are not used for the identification.