General Principles

Abstract

Behaviour of plastic materials resembles the behaviour of both the solids and fluids. Therefore, we consider the theory of plasticity as a part of continuum mechanics. This branch describes the global behaviour of solids, liquids and gases under the influence of external forces. The notions and methods of mathematics are used for the description. In continuum mechanics, we ignore the molecular and atomic structure of real materials and we replace the discontinuous microscopic medium with a set of material particles continuously distributed in the physical space. The physical space is assumed to be the three-dimensional Euclidean space E ³. The set of material particles with a mass attributed to it is called a material body B. Each one-to-one mapping of the body onto E ³ is a configuration of the body. One-parameter family of such configurations is called a motion of the body. The parameter t describing the motion changes in a some interval (t ₀,t ₁) represents the passage of time. From the family of configurations describing the motion we distinguish three: the initial C ₀, the current C _t and the final one C₁. All quantities describing physical properties of the body are introduced as some scalar, vector or tensor fields prescribed on its configurations.