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.

Inelasticity: the important experimental facts

A behavior of solid structures under an external loading has been studied during several centuries. However intensive and task-oriented investigations had begun in XIX century and are carried out till the present time. All known materials can be separated on two different classes: elastic materials and all others. In general, the fundamentals of the nonlinear theory of elasticity may be considered as completely developed. For inelastic materials the situation is quite different. There exists a huge massive of experimental data. This data is widely used for practical purposes and normative documents for the engineering projects, but as a rule this data is not used in theoretical investigations. A lot of established experimental facts cannot be described by the existing theories of the elastoplastic bodies till now. Let us point out some of them:

1. Under sufficiently high pressure all materials experience irreversible strains (Bridgman), which can be considered as phase transitions. The rate of these transitions is determined by the properties of the material and do not depend on the rate of change of the external loads.

2. At sufficiently high pressure all rigid bodies flow similarly to a fluid (Tresca, Bridgman). For example, the classical experiment by H. Tresca on extrude of lead shows absence of the stagnant zones in the material. On contrary, from any existing theory of plasticity it follows that the bands of the 'dead' material should be present. Thus we see a serious qualitative discrepancy between the theory and experiment.

3. The experiments on large inelastic deformation show essential influence of the size effect.

4. In all experiments with a smooth loading the Savart - Masson effect is exhibited clearly.

5. Experiments with bulk materials show the necessity of taking into account the dry friction between particles of the medium.

All these facts are of great importance because they are observed practically in all experiments. Nevertheless, the existing theories of plasticity are not able to explain these facts. Moreover, the most of the known theories of plasticity are based on the yield criterions either by Saint-Venant - Tresca or by Mises. Both criterions were never strictly confirmed by experiments. While the existing theories cover almost all practical needs and extremely useful, nevertheless they are not able to explain some features of the material behavior.