Abstract
In this work we derive conservation and balance laws in the context of linear, anisotropic elasticity of grade three including cohesive forces. More particularly, for a homogeneous medium without external forces we derive the conservation laws of translation and addition of solutions as well as the balance laws that stem from the rotation and scaling transformations. The Eshelby stress tensor of such a gradient theory of higher order is determined. On the other hand, we calculate all the corresponding balance laws for an inhomogeneous medium in the presence of external forces. The dynamical reciprocal theorem for anisotropic elasticity of grade three is derived and its relationship to the balance law of addition of solutions is examined.
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Agiasofitou, E., Lazar, M. (2009). Anisotropic Elasticity of Grade Three: Conservation and Balance Laws. In: Steinmann, P. (eds) IUTAM Symposium on Progress in the Theory and Numerics of Configurational Mechanics. IUTAM Bookseries, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3447-2_17
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DOI: https://doi.org/10.1007/978-90-481-3447-2_17
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3446-5
Online ISBN: 978-90-481-3447-2
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