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Second-gradient continua: From Lagrangian to Eulerian and back

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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… Click to show full 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.

Keywords: lagrangian eulerian; continua lagrangian; eulerian back; gradient continua; second gradient

Journal Title: Mathematics and Mechanics of Solids
Year Published: 2022

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