A Geometrically Exact Micromorphic Model for Elastic Metallic Foams Accounting for Affine Microstructure. Modelling, Existence of Minimizers, Identification of Moduli and Computational Results

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On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush (2016, unknown): “Incidentally, this postulate is automatically satisfied in classical elasticity, Cosserat and micromorphic models [32], since the possible variations of the field variables are independent anyway.”
A unifying perspective: the relaxed linear micromorphic continuum (2013, unknown): “Moreover, in [128] the authors proved the existence of minimizers, and they identified the relevant effective material parameters.”
Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements (2015, background): “…continua, multipolar continua, enhanced continuum models and so on (see e.g. dell’Isola et al., in press; Pideri and Seppecher, 1997; Camar-Eddine and Seppecher, 2002, 2003; Bouchet and Brechet, 2009; Auffray et al., 2010; Auffray et al., in press; Svendsen et al., 2009; Neff and Forest, 2007).”
Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps (2013, unknown): “also [55]): μ = μh, λ = λh, b1 = λe+λh, b2 = μe+μh +μc, b3 = μe + μh − μc, g1 = −λh, g2 = −μh, (7) a10 = αc, a14 = −αc, a1 = a2 = a3 = a4 = a5 = a8 = a11 = a13 = a15 = 0, (8) we are able to recover that our relaxed model can be obtained as a particular case of Mindlin’s one.”