A micromorphic computational homogenization framework for auxetic tetra-chiral structures

Multiscalar DIC analyses of granular string under stretch reveal non-standard deformation mechanisms

“…On the other hand, experimental results have suggested the use of generalized continuum theories to correctly predict chirality. This observation has led several researchers to describe the complex deformation of chiral materials adopting generalized continuum theories (e.g., see (Spadoni et al, 2009;Liu et al, 2011Liu et al, , 2012Chen et al, 2014;Frenzel et al, 2017;Duan et al, 2018;Poncelet et al, 2018;Reasa and Lakes, 2019;Wu et al, 2019;Biswas et al, 2020;Chen et al, 2020) to name a few).…”

Buckling and postbuckling of architectured materials: A review of methods for lattice structures and metal foams

“…82,89 For complex microstructures and especially if material nonlinearities of the parent material are involved, computational homogenization schemes can be employed. 85,[90][91][92] Other concepts falling within the scope of continuum modelling of archimats are the quasi-continuum theory proposed in Phlipot and Kochmann 93 or the non-linear constitutive models proposed by Vigliotti et al 94,95 Alternatively, multilevel schemes can be used to study localization phenomena originating from sharp edges/cracks or local buckling in heterogeneous materials. 93,96,97 Within these schemes, the archimat is resolved in its full complexity around the localization zones, whereas far away from these 'hot spots', a macroscale continuum model is used.…”

“…To overcome this issue, generalized continua have been used as they introduce a material length scale into the constitutive relations. Micropolar, [78][79][80][81][82] strain-gradient [82][83][84] or micromorphic 85 continua have been employed to describe the effective behaviour of archimats. For a general review and classification of the various generalized continuum theories, the reader is referred to Noor, 86 Fatemi et al, 87 Forest and Sievert, 88 and references therein.…”

“…82 Other examples involve the bending of archimat beams, 77,82 the propagation of cracks within archimats 93 and studies on the complex deformation behaviour of tetra-chiral archimats. 85 For the sake of completeness, substructuring techniques shall be mentioned. These techniques have been used to study buckling in periodic frame-like structures with low memory usage 98,99 and can also be adopted for example to treat topology optimization problems in archimats.…”

Local micromorphic non-affine anisotropy for materials incorporating elastically bonded fibers

“…[20]). The internal length scale parameters can be used to define size of the representative volume element (RVE) in homogenisation approaches controlling the non-local material behaviour [1,50,29,45,7]. In granular mechanics, the micromorphic continuum formulation has been shown to be able to address scale-dependent material behaviour as linked to an independent micro-kinematics of interacting particles [17,24,58].…”