By Gerard A Maugin
This review of the advance of continuum mechanics through the 20th century is exclusive and bold. using a ancient viewpoint, it combines an exposition at the technical development made within the box and a marked curiosity within the position performed via extraordinary members and medical faculties and associations on a speedily evolving social historical past. It underlines the newly raised technical questions and their solutions, and the continued reflections at the bases of continuum mechanics linked, or in festival, with different branches of the actual sciences, together with thermodynamics. The emphasis is put on the advance of a extra reasonable modeling of deformable solids and the exploitation of recent mathematical instruments. The ebook provides a balanced appraisal of advances made in a number of components of the realm. the writer contributes his technical services, own memories, and foreign event to this normal evaluation, that's very informative albeit concise.
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Tresca 1872). C. Barré de Saint– Venant (1797–1886) gave the mathematical formulation of these results (1871). Three important remarks are in order: first, it is noticed that no change in volume (so called isochoric deformation in the modern jargon) is observed during plastic deformation; second, the directions of the principal stresses coincide with those of the principal stresses (this assumes an isotropic response); third, the maximum shearing (or tangential) stress at a point is equal to a specific constant.
This can be written as sM ¼ k. In mathematical terms, we have ð2:1Þ Supa;b ra À rb ¼ 2k; a; b ¼ 1; 2; 3; where the Greek indices label the principal stresses. Introducing the tangential stresses, this can also be expressed by the following set of three inequalities: 2js1 j jr2 À r3 j k; etc; ð2:2Þ by circular permutation. In an astute plane representation this is represented by a hexagon (see Maugin 1992, Fig. 18). The interior domain (a convex domain with angular corners) is the domain of elasticity.
In the theoretical and experimental developments of rubber elasticity, a critical and beneficial role was played in the UK by the British Rubber Producers Research Association (BRPRA) and then the British Rayon Research Association (BRRA). Personal touch: Rivlin was educated at Cambridge (BA in Mathematics in 1937, MA in 1939). After a short stay at General Electric Co and two years as a Scientific Officer with the ministry of Aircraft Production during WWII, he spent nine years at the BRPRA, from 1944 to 1953, doing both seminal theoretical and experimental works with a one-year intermission/visit to the National Bureau of Standards in Washington (1946–1947) and a fruitful stay at the Naval Research Laboratory in Maryland (1952–1953).