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Journal Articles Mathematics and Mechanics of Solids Year : 2022

Second-gradient continua: From Lagrangian to Eulerian and back

Abstract

In this paper, we represent second-gradient internal work functionals in Lagrangian (referential) and Eulerian (spatial) descriptions, and we deduce the corresponding expressions for the Piola transformations of stress and double-stress tensors and of external forces and double-forces. We also derive, in both the Eulerian and Lagrangian description, the expression of surface and edge contact interactions (which include forces and double-forces) for second-gradient continua in terms of the normal and the curvature of contact boundary surfaces and edge shapes.
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Dates and versions

hal-03606801 , version 1 (12-03-2022)

Identifiers

  • HAL Id : hal-03606801 , version 1

Cite

Francesco Dell'Isola, Simon Eugster, Roberto Fedele, Pierre Seppecher. Second-gradient continua: From Lagrangian to Eulerian and back. Mathematics and Mechanics of Solids, 2022. ⟨hal-03606801⟩

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