Phase Transitions and General Theory of Elasto-Plastic Bodies

The new theory of elasto-plastic bodies is developed (2002). The theory is based on the description of the nonelastic properties by the phase transitions in the materials [1 - 3]. The definition of the phase transition is given in the following way. Two material characteristics are related to the density of material: solid fraction, defined as multiplication of number of particles in a unit volume on the particle volume, and porosity (void fraction), defined as unit minus solid fraction. A solid has several stable states, corresponding to different values of solid fraction. Transition from one stable state to another is a typical phase transition. The constitutive equation describing the solid fraction change near the phase transition point is suggested.

The constitutive equation for elastic pressure is proposed [1]. This equation describes well not only gases and liquids, but also solids with phase transitions. The limited tensile strength is taken into account. The difference between solids and liquids mainly is in their reaction on the shape change. This reaction can be described only if the stress tensor deviator is taken into account. For the classical approach the deviator of the elastic stress tensor, which is independent of velocities by definition, is ignored for description of inelastic properties of materials. For solids this is unacceptable. One of the problems of the theory is the definition of the internal energy structure in a way that would make possible the existence of several solid phases. The constitutive equations for the stress tensor deviator are suggested [1], where the shear modulus depends on the state parameters (temperature, mass density, deformation).

  1. Zhilin P.A. Phase Transitions and General Theory of Elasto-Plastic Bodies // Proceedings of XXIX Summer School - Conference “Advanced Problems in Mechanics”. St. Petersburg, Russia. 2002. P. 36-48.
  2. Zhilin P.A. Mathematical theory of non-elastic media // Uspehi mechaniki (Advances in mechanics). Vol. 2. N 4. 2003. P. 3-36. (In Russian.)
  3. Zhilin P.A. On the general theory of non-elastic media // Mechanics of materials and strength of constructions. Proc. of St. Petersburg State Polytechnical University. N 489. 2004. P. 8-27. (In Russian.)