General theory of inelastic media
A general approach [1 - 8] for the construction of the theory of inelastic
media is proposed (2001 - 2005). The main attention is given to the clear
introduction of basic concepts: strain measures, internal energy, temperature,
and chemical potential. Polar and non-polar media are considered.
The originality of the suggested approach is in the following. The spatial
description is used. The fundamental laws are formulated for the open systems.
A new handling of the equation of the balance of energy is given, where the
entropy and the chemical potential are introduced by means of purely
mechanical arguments. The internal energy is given in a form, at the same time
applicable for gaseous, liquid, and solid bodies. Phase transitions in the
medium are described without introducing any supplementary conditions;
solid-solid phase transition can also be described in these terms. The
materials under consideration have a finite tensile strength; this means that
the constitutive equations satisfy to the condition of the strong ellipticity.
- Zhilin P.A. Basic equations of the theory of non-elastic media // Proc. of the XXVIII Summer School “Actual Problems in Mechanics”. St. Petersburg. 2001. P. 14-58. (In Russian.)
- 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.
- Altenbach H., Naumenko K., Zhilin P. A micro-polar theory for binary media with application to phase-transitional flow of fiber suspensions // Continuum Mechanics and Thermodynamics, 2003. Vol. 15, N 6. P. 539-570.
- Altenbach H., Naumenko K., Zhilin P.A. A micro-polar theory for binary media with application to flow of fiber suspensions // Proceedings of XXX Summer School - Conference “Advanced Problems in Mechanics”. St. Petersburg, Russia, 2003. P. 39-62.
- Zhilin P.A. Mathematical theory of non-elastic media // Uspehi
mechaniki (Advances in mechanics). Vol. 2. N 4. 2003. P. 3-36. (In Russian.)
- 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.)
- Zhilin P.A. Advanced problems in mechanics. Selection of articles. V. 1. St. Petersburg. Edition of IPME RAS. 2006. 306 p. (In Russian.)
- Zhilin P.A. Advanced problems in mechanics. Selection of articles. V. 2. St. Petersburg. Edition of IPME RAS. 2006. 271 p.
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