An effective strategy to transform second-gradient equilibrium equations from the Eulerian to the Lagrangian configuration

An effective strategy to transform second-gradient equilibrium equations from the Eulerian to the Lagrangian configuration

Roberto Fedele, Francesco dell’Isola, Pierre Seppecher, Simon R. Eugster

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Abstract. In this communication the problem of transforming the equilibrium equations from the Eulerian to the Lagrangian form is discussed with reference to materials governed by second-gradient energy densities. In particular, novel theoretical achievements are outlined, which represent intermediate steps to attain the purpose: the transformation of edge vectors and of complementary orthogonal projectors over the boundary surface; a novel formula based on the divergence theorem for curved surfaces with boundary, relating material and spatial expressions; a remarkable relationship between Lagrangian and Eulerian (hyper-)stress tensors of different orders.

Keywords
Continuum Mechanics, Second-Gradient Materials, Nonstandard Boundary Conditions, Variational Approach

Published online 3/17/2022, 5 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Roberto Fedele, Francesco dell’Isola, Pierre Seppecher, Simon R. Eugster, An effective strategy to transform second-gradient equilibrium equations from the Eulerian to the Lagrangian configuration, Materials Research Proceedings, Vol. 26, pp 627-631, 2023

DOI: https://doi.org/10.21741/9781644902431-101

The article was published as article 101 of the book Theoretical and Applied Mechanics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

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