Engineering Transactions, 2, 1, pp. 71-141, 1954

Podstawy Teorii Plastyczności (I).

J. Nowiński
Instytut Matematyczny

These lectures were held by the author at the Institute of Mathematics of the Polish Academy of Sciences in 1953. They are based on the well
known manuals by Bezukhov, Iliushin, Nádai, Soko-Filonenko-Boroditsh, Goldenblat and others (see list of references).
 Lecture I contains fundamental notions of the state of stress and strain from the point view of the requirements of the theory of plasticity. The state of stress at a point is discussed, as well as the principal and the octahedral stresses.
In lecture II the principal values of shear stresses (on the walls of the principal rhombic dodecahedron) are discussed, as well as the state of deformation at a point, the law of linear elasticity in the form depending on the intensity of stress and deformation and the laws of change of volume and shape.
In Lecture III the conditions of plasticity (strength theories) are discussed.
Lecture IV brings a short account of a new paper by W. W. Novozhilov (Prikl. Math. Mech. 5, 1952) in which a definition of stress intensity is given. Next, the basic principles of the theory of small deformations are explained in the form developed by Soviet scientists.
In Lecture V a discusion of the theorem of  Iliushin, concerning the so-called simple loading and unloading, and the basic equations of elastic-plastic bodies are given.
Lecture VI is illustrated by examples of application of the theory, discussed in the foregoing lectures. The problems considered are: a thick-walled tube subjected to internal and external pressures and the problem of pure bending. In Lecture VII relations - between the strength phenomena and the structure of matter are considered.
Monocrystalline, amorphous and polycrystalline bodies are discussed on the basis of [6]. Finally, the author expresses the opinion that further development of the theory of plasticity should be based chiefly on the phenomenological approach to the considered problems, without deeper consideration of submicroscopic structure.

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N. I. Biezuchow, Wwiedienje w tieorju uprugosti i plasticznosti, Moskwa-Leningrad 1950.

A. A. Iljuszin, Ptasticznost, Gostiechizdat 1948.

Nádai, The Theory of Flow and Fractures of Solids, t. 1, New York

W. W. Sokołowski, Tieorja plasticznosti, Moskwa-Leningrad 1950.

M. M. Filonienko-Borodicz i inni, Kurs soprotiwlenja, matierialow, t. 1, Moskwa-Leningrad 1949.

I. I. Goldienbtat, Wwiedienje w tieorju polzuczesti stroitielnych matierialow, Moskwa 1952.

A. D. Tomlenow, Tieorja plasticzeskich dieformacij mietallow, Moskwa 1951,

L. M. Kaczano w, Miechanika ptasticzeskich sried, Leningrad-Moskwa 1948.

J. Nowiński i W. Olszak, O podstawach teorii ciał sprężystych fizykalnie nieliniowych, Arch. Mech. Stos., t. 6, 1 (1954).

W. W. Nowożniłow, Prikl. Mat. Miech., 5 (1952).