Existence of minimizers for a finite-strain micromorphic elastic solid

By Patrizio Neff. Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 2006

133 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/36e51d491fb791b51f14a1fdfceada1133aeb544

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Citations in the corpus

Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements (2015, background): “…et al. (2011) or in Porfiri et al. (2004), Rosi et al. (2010), Porfiri et al. (2005)) ! well-posedness properties (e.g. of the kind studied in Jeong and Neff (2010) and Neff (2006)) for the class of nonstandard deformation energies arising in the class of generalized continua we introduced here.”
A Geometrically Exact Micromorphic Model for Elastic Metallic Foams Accounting for Affine Microstructure. Modelling, Existence of Minimizers, Identification of Moduli and Computational Results (2007, background): “Since the two-field variational problem is only conditionally coercive we need to introduce a modification for the applied loads as given in [57, 58] in order to ensure first that the functional to be minimized is bounded below and second that the curvature contribution can be controlled.”
A unifying perspective: the relaxed linear micromorphic continuum (2013, unknown): “There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke.”
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, result): “Some examples of mathematical results which exploit in an efficient way the power of variational methods are those presented in Neff [74–76].”