https://scholars.lib.ntu.edu.tw/handle/123456789/80551
Title: | Noncanonical Poisson brackets for elastic and micromorphic solids | Authors: | Chen, Kuo-Ching | Keywords: | Continuum mechanics; Lagrangian-to-Eulerian transformation; Microcontinuum; Noncanonical Poisson bracket | Issue Date: | 2007 | Journal Volume: | 44 | Journal Issue: | 24 | Start page/Pages: | 7715-7730 | Source: | International Journal of Solids and Structures | Abstract: | This paper investigates the Lagrangian-to-Eulerian transformation approach to the construction of noncanonical Poisson brackets for the conservative part of elastic solids and micromorphic elastic solids. The Dirac delta function links Lagrangian canonical variables and Eulerian state variables, producing noncanonical Poisson brackets from the corresponding canonical brackets. Specifying the Hamiltonian functionals generates the evolution equations for these state variables from the Poisson brackets. Different elastic strain tensors, such as the Green deformation tensor, the Cauchy deformation tensor, and the higher-order deformation tensor, are appropriate state variables in Poisson bracket formalism since they are quantities composed of the deformation gradient. This paper also considers deformable directors to comprise the three elastic strain density measures for micromorphic solids. Furthermore, the technique of variable transformation is also discussed when a state variable is not conserved along with the motion of the body. © 2007 Elsevier Ltd. All rights reserved. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/119636 https://www.scopus.com/inward/record.uri?eid=2-s2.0-35148862714&doi=10.1016%2fj.ijsolstr.2007.05.005&partnerID=40&md5=a6ec2d650b6f8c2ab0362e7811e6095b |
ISSN: | 00207683 | DOI: | 10.1016/j.ijsolstr.2007.05.005 | SDG/Keyword: | Density measurement (specific gravity); Euler equations; Function evaluation; Green's function; Hamiltonians; Lagrange multipliers; Lagrangian-to-Eulerian transformation; Micromorphic solids; Poisson brackets; Poisson distribution |
Appears in Collections: | 應用力學研究所 |
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