Material Behavior

Abstract

The mechanical behavior of materials depends on the relation between stresses and strains in the material. In the previous chapter stresses and strains have been discussed independently, but in order to represent material behavior, models that relate the stresses and strains must be established. This chapter presents a brief introduction to two aspects of material behavior: elastic behavior typical of working conditions in structures, and criteria describing the states of stress limited by material failure. In both cases a central point is the systematic generalization of the theories beyond the simple uniaxial case. A concise introduction is given to the theory of linear elasticity for a three-dimensional continuum. Simple special cases of this theory form an important tool in structural design, and the general theory constitutes the basis of most Finite Element programs, extensively used for analysis of structures. After a brief general introduction the presentation is specialized to linear elasticity of isotropic materials, i.e. materials with properties that do not depend on the orientation. Typical conditions for yield and failure of metals are discussed. There is a marked difference between the yield and failure of metals and the similar characteristics in materials like concrete and soil. This is primarily due to the fact that while the mean stress has no or at most moderate influence on yield and failure of metals, an additional triaxial compression will lead to a marked increase in the strength of materials like concrete and soil. A simple explanation of this effect is given in the form of the theory of friction materials.