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Lie Point Symmetries, Conservation and Balance Laws in Linear Gradient Elastodynamics

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Abstract

The aim of this work is the derivation of Lie point symmetries, conservation and balance laws in linear gradient elastodynamics of grade-2 (up to second gradients of the displacement vector and the first gradient of the velocity). The conservation and balance laws of translational, rotational, scaling variational symmetries and addition of solutions are derived using Noether’s theorem. It turns out that the scaling symmetry is not a strict variational symmetry in gradient elasticity.

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Authors and Affiliations

  1. Emmy Noether Research Group, Department of Physics, Darmstadt University of Technology, Hochschulstr. 6, D 64289, Darmstadt, Germany

    Markus Lazar & Charalampos Anastassiadis

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  1. Markus Lazar
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  2. Charalampos Anastassiadis
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Correspondence to Markus Lazar.

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Lazar, M., Anastassiadis, C. Lie Point Symmetries, Conservation and Balance Laws in Linear Gradient Elastodynamics. J Elasticity 88, 5–25 (2007). https://doi.org/10.1007/s10659-007-9105-5

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  • DOI: https://doi.org/10.1007/s10659-007-9105-5

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