Abstract.
In classical Lagrangian approaches, e.g. in order to state the constitutive laws, a strain measure (or a metric tensor) is used in an attempt to model, whether intrinsically or relative to a reference state, the current state of stretching at the considered point (the local “metric state”). We will show that, in this manner, a kind of partial linearisation is being performed, thereby leading to an approximate theory: the curved space of all possible local metric states is approximated by one of its linear (or flat) charts. The quality of the approximation is then a function of this chart’s reliability. Some particular charts, associated with more or less classical strain parameters, are studied herein. The chart associated with the logarithmic strain measure would appear as the most satisfactory.
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© 2000 Kluwer Academic Publishers
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Rougée, P. (2000). A Geometrical Interpretation of the Tensorial Characterisations of Finite Strains. In: Lagarde, A. (eds) IUTAM Symposium on Advanced Optical Methods and Applications in Solid Mechanics. Solid Mechanics and its Applications, vol 82. Springer, Dordrecht. https://doi.org/10.1007/0-306-46948-0_13
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DOI: https://doi.org/10.1007/0-306-46948-0_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6604-1
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