Mixed finite element formulations of strain-gradient elasticity problems

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Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results (2011, background): “…certain authors have focussed on implementing the more complete (and more complicated) theories of the 1960s, see for instance (Shu et al., 1999; Amanatidou and Aravas, 2002; Zervos, 2008; Papanicolopulos et al., 2009), some others have exploited the simplicity offered by the Aifantis theory…”
Computational homogenization for the multi-scale analysis of multi-phase materials (2002, background): “Recently also Amanatidou and Aravas (2002) and Matsushima et al. (2002) presented various types of mixed formulations and elements for the second gradient continuum.”
On deformational and configurational mechanics of micromorphic hyperelasticity – Theory and computation (2007, background): “As examples for such formulations of the gradient elasticity serve for instance the following contributions: Shu et al. [25] and Amanatidou and Aravas [1] for small deformations, as well as, extended to large deformations, Shu and Barlow [24] and – in the context of a homogenisation procedure [14– 1”