9. Express the main idea of the text in the shortest possible way. Lesson 7

1. Find in the text English equivalents for the following Ukrainian words and word combinations:

текучість металу, теорія, важлива основа, пошкодження, опір, тертя, повзучість металу, критерій утомленості матеріалу, обчислювання, важливість, застосування, завдання, передбачення, взаємозв’язок, використання, структура, дослідження, значення, обстежувати, видатний вчений, здібний до зціплення, умови, дослідник, зріз.

2. Read and translate the text: From the History of Strength Theories

Strength theory deals with the yield and failure of materials under a complex stress state. Strength theory is a general term. It includes yield criteria and failure criteria, as well as multiaxial fatigue criteria, multiaxial creep conditions, and material models in computational mechanics and computer codes. It is an important foundation for research on the strength of materials and structures. Strength theory is widely used in physics, mechanics, material science, earth science, and engineering. It is of great significance in theoretical research and engineering application, and is also very important for the effective utilization of materials. Particularly for design purposes, it is important that a reliable strength prediction be available for various combinations of multiaxial stresses. It is an interdisciplinary field where the physicist, material scientist, earth scientist, and mechanical and civil engineers interact in a closed loop.

Strength theory is a very unusual and wonderful subject. The objective is very simple, but the problem is very complex. It is one of the earliest objectives considered by Leonardo da Vinci -1452-1519, Galileo Galilei -1564-1642, Coulomb -1736-1806, and Otto Mohr -1835-1918, but it is still an open subject. Considerable efforts have been devoted to the formulation of strength theories and to their correlation with test data, but no single model or criterion has emerged which is fully adequate. Hundreds of models or criteria have been proposed. Timoshenko -1878-1972 was an outstanding scientist, distinguished engineer, and a great and inspiring professor. Timoshenko's summers of the years from 1903 to 1906 were spent in Germany where he studied under Foppl, Prandtl, and Klein. After his return from Germany in 1904, he wrote his first paper on the subject of "various strength theories" in 1904. "Strength theories" was also the title of sections in two of his books. Now, "strength theories" is a chapter of most courses of "Mechanics of Materials," sometimes referred to as "Strength of Materials." Moreover, "yield criteria" or "failure criteria" is a chapter of most courses in Plasticity, Geomechanics, Soil Mechanics, Rock Mechanics, and Plasticity of Geomaterials, etc.

This subject, although there are some review articles and books, is difficult and heavy to survey. Some of the surveys were contributed by Mohr, Westergaard , Schleicher, Nadai, Marin, Gensamer, Meldahl, Dorn, and Prager in the first half of the 20th century. It was also reviewed by Freudental and Geiringer, Naghdi, Filonenko-Boroditch, Marin, Paul, Goldenblat and Kopnov, and Taira in the 1960s. The advances in strength theories of materials under complex stress state in the 20th century will be summarized in the framework of continuum and engineering application.

Leonardo da Vinci and Galileo Galilei were among the most outstanding scientists of that period. They may be the earliest researchers of the strength of materials and structures. Da Vinci and Galileo did tensile tests of wire and stone, as well as bending tests. Da Vinci believed that the strength of an iron wire would depend significantly on its length. Galilei believed that fracture occurs when a critical stress was reached.

Coulomb may be the first researcher in the maximum shear stress strength theory. No other scientist of the eighteenth century contributed as much as Coulomb did to the science of mechanics of elastic bodies. Coulomb's Memoir Essay was read by him to the Academy of France on March 10 and April 2, 1773, and published in Paris in 1776. The paper began with a discussion of experiments which Coulomb made for the purpose of establishing the strength of some kind of sandstone; then, Coulomb gave a theoretical discussion of the bending of beams, the compression of a prism, and the stability of retaining walls and arches. Coulomb assumed that fracture is due to sliding along a certain plane, and that it occurs when the component of force along this plane becomes larger than the cohesive resistance in shear along the same plane. To bring the theory into better agreement with experimental results, Coulomb proposed that, not only should cohesive resistance along the shear plane be considered, but also friction caused by the normal force acting on the same plane. This was the first description of the famous Mohr-Coulomb Strength Theory.