ABSTRACT
In Section 2.4 we consider a body subjected to external loads and we define certain quantities (the components of strain) which specify completely the deformation of its particles. In Section 2.6 we consider a body subjected to external loads and we define certain quantities (the components of stress) which specify completely the internal forces acting on its particles. In this chapter we present relations among the components of strain and stress of a particle of a body subjected to external loads. These relations represent properties of the material from which the body is made and they are known as its constitutive equations. They are based on experimental observations of the macroscopic phenomenological behavior of bodies of simple geometry subjected to such loads that the distribution of the components of stress acting on their particles can be easily established. The constitutive equations of materials are classified into two groups — time independent and time dependent. Those belonging to the second group include first and possibly higher time derivatives of stress and/or strain, and are sensitive to the rate and history of loading. For instance, the stress-strain relations of metals at high temperatures and of certain non-metallic materials, such as plastics, ceramics and rubbers at room temperature are affected appreciably by the rate of loading.
