By Bob Svendsen (auth.), Bernd Markert (eds.)
Modern computational innovations, comparable to the Finite point approach, have, seeing that their improvement a number of a long time in the past, effectively exploited continuum theories for varied functions in technological know-how and know-how. even though normal continuum equipment dependent upon the Cauchy-Boltzmann continuum are nonetheless of significant value and are widespread, it more and more looks that fabric houses stemming from microstructural phenomena need to be thought of. this can be quite real for inhomogeneous load and deformation states, the place lower-scale dimension results start to have an effect on the macroscopic fabric reaction; anything normal continuum theories fail to account for. Following this concept, it really is obtrusive that normal continuum mechanics needs to be augmented to catch lower-scale structural and compositional phenomena, and to make this knowledge available to macroscopic numerical simulations.
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Additional info for Advances in Extended and Multifield Theories for Continua
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.