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REVIEWED BY WILLIAM PRAGER 1THIS IS AN excellent exposition of the mathematical theory of plasticity and its applications to engineering problems in which the plastic strains may be treated as infinitesimal. Accordingly, it is exclusively concerned with the mechanical behavior of structures and machine parts just beyond the elastic range; no applications of plasticity theory to technological forming processes are discussed.

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It has been suggested that optical flashes observed in the upper atmosphere above giant thunderstorms (red sprites) are due to streamers. Such streamers are initiated in the lower ionosphere by electron patches caused by electromagnetic radiation from horizontal intracloud lightning and then develop downward in the static electric field due to the thundercloud. The triggering conditions of streamer development are analysed in the paper. Using similarity relations, known characteristics of streamer tips obtained earlier in laboratory conditions are extended to a description of streamers in rare air. Streamer growth in the nonuniform atmosphere is calculated. It is shown that streamers first appear at a height of about 80 km and then grow downward to slightly below 50 km, where they are terminated. This is in agreement with red sprite observations. An altitude distribution of the streamer generated plasma is obtained. The simple models of streamer development presented in this paper could be applied for computations of streamers growing in various other conditions.

The initiation and development of a leader is theoretically studied by considering an electrode which is embedded in a cloud of space charge injected by a corona discharge. The focus is on the initiation of upward lightning from a stationary grounded object in a thundercloud electric field. The main results are also applicable to the leader process in long laboratory air gaps at direct voltage. Simple physical models of non-stationary coronae developing in free space near a solitary stressed sphere and of a leader propagating in the space charge cloud of coronae are suggested. It is shown that the electric field redistribution due to the space charge released by the long corona discharge near the top of a high object hinders the initiation and development of an upward leader from the object in a thundercloud electric field. The conditions for the formation of corona streamers that are required to initiate a leader are derived. The criteria are obtained for a leader to be initiated and propagate in the space charge cloud. A hypothesis is proposed that the streamers are never initiated near the top of a high object under thunderstorm conditions if at ground level there is only a slowly-varying electric field of the thundercloud. The streamers may be induced by the fast-rising electric field of distant downward leaders or intracloud discharges.

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