Abstract
Definitions of the Lagrangian stretch and wryness tensors in the non-linear Cosserat continuum are discussed applying three different methods. The resulting unique strain measures have several distinguishing features and are called the natural ones. They are expressed through the translation vector and either the rotation tensor or various finite rotation vector fields. The relation of the natural strain measures to those proposed in the representative literature is reviewed.
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References
Bauchau, O.A., Trainelli, L., The vectorial parameterization of rotation. Nonlinear Dyn. 32, 71–92 (2003)
Cosserat, E., Cosserat, F., Théorie des corps déformables. Hermann et Fils, Paris (1909)
Gibbs, J.W., Vector Analysis. Yale University Press, New Haven (1901)
Kafadar, C.B., Eringen, A.C., Micropolar media—I. The classical theory. Int. J. Eng. Sci. 9, 271–305 (1971)
Pietraszkiewicz, W., Eremeyev, V.A., On natural strain measures of the non-linear micropolar continuum. Int. J. Solids Struct. 46(34), 774–787 (2009)
Pietraszkiewicz, W., Eremeyev, V.A., On vectorially parameterized natural strain measures the non-linear Cosserat continuum. Int. J. Solids Struct. 46(11–12), 2477–2480 (2009)
Reissner, E., On kinematics and statics of finite-strain force and moment stress elasticity. Stud. Appl. Math. 52, 93–101 (1973)
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Pietraszkiewicz, W., Eremeyev, V.A. (2010). Natural Lagrangian Strain Measures of the Non-Linear Cosserat Continuum. In: Maugin, G., Metrikine, A. (eds) Mechanics of Generalized Continua. Advances in Mechanics and Mathematics, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5695-8_9
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DOI: https://doi.org/10.1007/978-1-4419-5695-8_9
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