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On nonlinear dilatational strain gradient elasticity

Abstrakt

We call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the only second gradient effects are due to the inhomogeneous dilatation state of the considered deformable body. The dilatational second gradient continua are strictly related to other generalized models with scalar (one-dimensional) microstructure as those considered in poroelasticity. They could be also regarded to be the result of a kind of “solidification” of the strain gradient fluids known as Korteweg or Cahn–Hilliard fluids. Using the variational approach we derive, for dilatational second gradient continua the Euler–Lagrange equilibrium conditions in both Lagrangian and Eulerian descriptions. In particular, we show that the considered continua can support contact forces concentrated on edges but also on surface curves in the faces of piecewise orientable contact surfaces. The conditions characterizing the possible externally applicable double forces and curve forces are found and examined in detail. As a result of linearization the case of small deformations is also presented. The peculiarities of the model is illustrated through axial deformations of a thick-walled elastic tube and the propagation of dilatational waves.

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Creative Commons: CC-BY otwiera się w nowej karcie

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Kategoria:
Publikacja w czasopiśmie
Typ:
artykuły w czasopismach
Opublikowano w:
CONTINUUM MECHANICS AND THERMODYNAMICS nr 33, strony 1429 - 1463,
ISSN: 0935-1175
Język:
angielski
Rok wydania:
2021
Opis bibliograficzny:
Eremeev V., Cazzani A., Dell'Isola F.: On nonlinear dilatational strain gradient elasticity// CONTINUUM MECHANICS AND THERMODYNAMICS -Vol. 33,iss. 4 (2021), s.1429-1463
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1007/s00161-021-00993-6
Weryfikacja:
Politechnika Gdańska

wyświetlono 33 razy

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