Analysis of Stress

Abstract

In this section we analyze inner forces in a deformable body. A deformable body could be solid or fluid. We do not go into the mathematical definition of a solid and fluid body¹ (for such a definition, see Truesdell and Noll (1965)). We define a solid as a deformable body that possesses shear strength, i.e., a solid body can support shearing forces (forces that are directed parallel to the material surface on which they act) over the time scale of some natural process or technological application of interest. The fluid body does not have shear strength (cannot sustain shear stresses). In the analysis of stress we are concerned with the study of inner forces and couples that hold a solid body in the shape that it has in the undeformed and deformed states. On the atomic level, those forces are ionic, metallic, and van der Waals forces that act between individual atoms. They hold the atoms in their positions. Such forces could be studied by the methods of solid-state physics. The notion of stress is introduced in continuum mechanics to analyze integrated effects of atomic forces. This is the so-called macroscopic view of the solid body. In it we ignore the discrete nature of the body and assume that the mass of the body is continuously distributed in part of three-dimensional Euclidean space. Therefore when we say point C of a body we are sure that we did not specify the point in the interatomic space and that there is part of the body at this point.