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Excerpt from On Finite Deformations of an Elastic Isotropic Material The proof of (2) is based on the realization that there exist subsets called cores of the domain D which is under going the transformation, in which the relative change in distance of any two points is at most 6. In fact, any convex subset of D whose distance from the boundary of D exceeds a certain amount 6 6(e, d) is such a core. Moreover, 5 tends to 0 for e - e>o. This implies that for convex D and small 6 there are cores of D which fill all of D except for a thin boundary layer. Since in a core the mutual distance between any two points changes by a small amount for small 8, the trans formation of a, core is essentially rigid, which leads to the desired result. Similar estimates can doubtlessly be obtained for D which have shapes differing from square plates. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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