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By Baracco L., Zaitsev D., Zampieri G.

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Appl. Polym. , 7, 1867 (1963); J. L. White, J. Appl. Polym. , 8, 2339 (1964); Rubber Chem. , 42, 257 (1969). A. J. B. de St. Venant, Mémoire sur équilibre des corps solides, dous les limits de leur élasticité, et sur les conditions de lèur resistance quond es désplacements êpouvés par leurs points ne sont par trés petit, C. R. Acad. , Paris, 24, 1847. J. Finger, Acad. Wiss. Wien Sitzungsberichte, (IIa), 103 (1884). S. Zaremba, Bull. Int. Acad. , Cracovie, 594, 614 (1903). F. Cosserat, Thèorie des corps deformable, Paris, 1909.

4] where the first line includes derivatives of the u1-component of displacement along three coordinate axis, the second line is the same for the u2-component, and the third, for the u3-component of the vector u. It is quite evident that the tensors dij and gij are not equivalent. 5] The first, so-called symmetrical, part of the tensor gij coincides with the deformation tensor dij, but gij ≠ dij Then, we need to understand the physical meaning of this difference or the meaning of the second, so-called antisymmetrical, part of the displacement tensor.

Ya. 1. Displacement of two points in a body and appearance of deformation. The result of action of outer forces can be either movement of a body in space or change of its shape. Here, we are interested in describing the changes occurring inside a body. The change of a shape of a body is essentially the change of distances between different points on its surface. Thus, change of shape can only occur if there are changes of distances between different sites inside a material, and this phenomenon is called deformation.

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A Burns-Krantz type theorem for domains with corners by Baracco L., Zaitsev D., Zampieri G.


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