2020
DOI: 10.2140/memocs.2020.8.153
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The method of virtual power in the mechanics of continuous media, I: Second-gradient theory

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Cited by 74 publications
(72 citation statements)
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“…The strain gradient tensor is adopted to model size and non-local effects observed in the considered continuum system [ 39 , 40 , 41 , 42 , 43 , 44 ]. The presence of in the list of meaningful variables follows the suggestion by Biot [ 32 ] and Cowin [ 45 ] to model porous materials.…”
Section: The Model Employed To Describe Bone Remodelingmentioning
confidence: 99%
“…The strain gradient tensor is adopted to model size and non-local effects observed in the considered continuum system [ 39 , 40 , 41 , 42 , 43 , 44 ]. The presence of in the list of meaningful variables follows the suggestion by Biot [ 32 ] and Cowin [ 45 ] to model porous materials.…”
Section: The Model Employed To Describe Bone Remodelingmentioning
confidence: 99%
“…The used heuristic procedure will lead to a formal expression of the work functional for externally applied loads: it is proven that together with standard volume forces and surface contact forces, dilatational strain gradient continua can support, on edges already present in the reference configuration, externally applied edge forces. Moreover, see [63], one can apply on contact surfaces also external double forces, that it interactions that expend work on normal (to the contact surface) derivative of virtual displacement. Rather interestingly it has been presented a reasoning which indicates that one can apply, on the regular parts of the boundary (i.e on the boundary faces) of the considered dilatational strain gradient continua, external forces concentrated on curves that are not already edges, in the reference configuration.…”
Section: Conclusion and Research Perspectivesmentioning
confidence: 99%
“…After works by Korteweg [71], Cahn and Hilliard [15,16] dealing with so-called capillary fluids, by Mindlin [87][88][89] and Toupin [128,129] dealing with more general continua, including elastically deformable solids, and after the more general approaches proposed by Germain [62,63] and Sedov [113], who considered microstructured generalized continua, see also [39], the second gradient elasticity was discussed and enlarged in many works, e.g. [7,12,32,54,134,138].…”
Section: Introductionmentioning
confidence: 99%
“…Later, Le Roux and other scholars see, e.g. [21,51,52] and the reference therein, continued the line of thought started by Piola and, more recently, also by using the by using a more modern formalism and the powerful tools given by functional analysis, Paul Germain gave a further impulse to generalised continuum mechanics, see [28,42,43].…”
Section: Introductionmentioning
confidence: 96%
“…This special case of second gradient continuum models have a peculiarity which made them more acceptable by those who want to postulate continuum mechanics on the primitive concept of "balance laws" for forces and couples (or torques). In facts, [21] in the framework of couple-stress theories, the admissible boundary conditions (naturally deduced from the adapted variational principle) assume a particular for which double-forces are vanishing, see [28,43] for a detailed discussion of the concept of double force and Alibert et al [5] for its interpretation at micro-scales. Let us also note that the concept of double forces and other hypermoments are known in structural mechanics, see comments in [31, pp.…”
Section: Introductionmentioning
confidence: 99%