Higher Gradient Theories and Their Foundations

Francesco Dell'Isola (1, 2) , Pierre Seppecher (1, 3) , Alessandro Della Corte (1, 4)

1 MEMOCS - International Research Center for the Mathematics & Mechanics of Complex Systems
2 DISG - Dipartimento di Ingegneria Strutturale e Geotecnica
3 IMATH - Institut de Mathématiques de Toulon - EA 2134
4 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]

Continuum mechanics always supplies approximate models for physical systems, in which a more fundamental (possibly discrete or inhomogeneous) microstructure may be somehow neglected. Indeed, Cauchy (or Cauchy-Navier) continuum theory describes efficiently, at a macroscopic level, the behavior of a mechanical system only when the inhomogeneities which the model does not take into account have a characteristic length scale much smaller than the macroscale where phenomena are observed. Therefore, it is now widely accepted that in some circumstances, it is necessary to add to the placement field some extra kinematical fields, to take into account, at a macroscopic level, some aspects of the mechanical behavior of materials having complex microscopic...

Domaines: Physique mathématique [math-ph]

Francesco Dell'Isola, Pierre Seppecher, Alessandro Della Corte. Higher Gradient Theories and Their Foundations. Encyclopedia of Continuum Mechanics (2020 EDITION), pp.1090-1099, 2020. ⟨hal-02918379v2⟩