Generalized continua and non‐homogeneous boundary conditions in homogenisation methods

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A unifying perspective: the relaxed linear micromorphic continuum (2013, unknown): “However, mixed terms may appear if homogenization techniques are used, see [53,54,58].”
Evaluation of generalized continuum substitution models for heterogeneous materials (2012, methodology): “Such a procedure has been proposed in Forest and Trinh (2011) and will be used in the present contribution.”
Computational second-order homogenization of materials with effective anisotropic strain-gradient behavior (2020, methodology): “Despite its appealing simplicity, as shown in [26,63,10], the method has two major flaws: (a) the effective strain-gradient properties remain non zero either when the scale are separated or when the material is homogeneous [26] which induces a contradiction with the local Cauchy behavior of the phas”
Mindlin second-gradient elastic properties from dilute two-phase Cauchy-elastic composites Part I: Closed form expression for the effective higher-order constitutive tensor (2013, background): “…(theoretical considerations were developed by Achenbach and Herrmann (1968), Beran and McCoy (1970), Boutin (1996), Dal Corso and Deseri (2013), Forest and Trinh (2011), Li (2011), Pideri and Seppecher (1997), and Wang and Stronge (1999); numerical approaches were given by Auffray et al.…”