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Numerical homogenisation of micromorphic continuua. : Two-scale modelling of micromorphic continua.
The constitutive equations define T and M as functions of the Cosserat strain ε¯ and the curvature κ¯ , cf. de Borst : T = 2μ ε¯ sym + 2μC ε¯ skw + λ (ε : I) I , M = 2μC (lC )2 κ¯ . (5) (6) Therein λ and μ are the Lamé constants known from Hooke’s law describing the symmetric stress tensor for elastic material behavior in the classical theory. The further parameters μC and lC are the already mentioned additional Cosserat parameters representing an additional stiﬀness as well as some kind of internal length.
75 MPa for config. 2. This result indicates that anisotropies are induced by the boundary layers, i. e. constraining the rotations at the top and bottom has a diﬀerent influence on the solution in config. 1 and config. 2. 0 μconfig. 1 μconfig. 0 0 20 40 60 80 h [no. ] Fig. 4 Eﬀective shear modulus for varying sample heights, cf. Table 2. 100 From Lattice Models to Extended Continua 25 Table 2 Eﬀective shear moduli and corresponding relative deviations from μGA . config. 1 no. sample h [no. ] 1 2 3 4 5 6 7 8 1 3 5 9 11 23 47 95 μe f f config.