On higher gradients in continuum-atomistic modelling

By R. Sunyk, Paul Steinmann. 2003

153 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/87aa0cb691ea921dce023133f0bd18115cf94662

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert” (2012, unknown): “, [43–49,55,76,81,87,103,120,121]).”
Geometrically nonlinear higher-gradient elasticity with energetic boundaries (2013, background): “…“microscopical” structure may produce at a macroscopic level general- ized continuum theories: Forest et al. (2000, 2001); Tenek and Aifantis (2001); Sunyk and Steinmann (2003); Forest and Sievert (2003); Maranganti and Sharma (2007); Nikolov et al. (2007); Pozrikidis (2008); Sun et al.…”
At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola (2013, methodology): “From the mathematical point of view this procedure is applicable when the searched solution has a stronger regularity than the one strictly needed to formulate the basic variational principle.”
Variational Foundations and Generalized Unified Theory of RVE-Based Multiscale Models (2016, background): “Multiscale formulations have proved useful also in deriving higher order constitutive models [58,59,65,66, 114].”
Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids (2013, background): “In our opinion models for surface phenomena in presence of thermodynamical phenomena and diffusion or phase transitions in solids developed, e.g., by McBride et al. [126, 127], Steeb and Diebels [128] and Steinmann et al. [129] or for growth phenomena in living tissues such as those presented by [13”
Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua (2012, unknown): “[52], [95], [94], [69], [100], [3], [54], [55], [57], [59], [56], [58], [101]), [93].”