Identities in Finite Strain |
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Authors: | P Boulanger M Hayes |
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Institution: | (1) Département de Mathématique, Université Libre de Bruxelles, Campus Plaine C.P. 218/1, 1050 Bruxelles, Belgium;(2) School of Electrical, Electronic and Mechanical Engineering, University College Dublin, Belfield, Dublin, 4, Ireland |
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Abstract: | First of all the deformation is considered of two infinitesimal material line elements lying along vectors M,N emanating from a particle at X in a body. For all M,N lying in a given plane, an identity is derived relating the stretches along M,N and the angles of the pair of infinitesimal material line elements before and after deformation. Then, the deformation is
considered of three non-coplanar infinitesimal material line elements lying along vectors M,N,P emanating from a particle at X in a body. An identity is derived relating the stretches along M,N,P and the angles between the three pairs of infinitesimal material line elements before and after deformation. The identity
is factored leading to easy interpretation. The special case of infinitesimal strain is considered.
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Keywords: | Strain tensor Material line element Stretch Shear |
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