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Bodies, Deformations, and Strain Measures

In: Fundamentals of the Mechanics of Solids

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  • Paolo Maria Mariano

    (University of Florence, DICeA)

  • Luciano Galano

    (University of Florence, DICeA)

Abstract

In this chapter we analyze the kinematics of continuous bodies with shape described just by the place they occupy in Euclidean three-dimensional point space. We discuss the large-strain regime and derive small-strain measures and the representation of rigid changes of places as special cases of deformation. We interpret strain measures in terms of spatial and referential metrics and distinguish between contravariant and covariant components of the tensors involved, introducing by stages a language useful to further developments going far beyond the limits of this book. We also discuss motions in actual (Eulerian) and referential (Lagrangian) representations. We include in this chapter several related exercises.

Suggested Citation

  • Paolo Maria Mariano & Luciano Galano, 2015. "Bodies, Deformations, and Strain Measures," Springer Books, in: Fundamentals of the Mechanics of Solids, edition 1, chapter 0, pages 1-67, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4939-3133-0_1
    DOI: 10.1007/978-1-4939-3133-0_1
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