By Bob Svendsen (auth.), Bernd Markert (eds.)
Modern computational suggestions, corresponding to the Finite point approach, have, because their improvement numerous many years in the past, effectively exploited continuum theories for varied functions in technology and know-how. even if regular continuum equipment established upon the Cauchy-Boltzmann continuum are nonetheless of significant significance and are widespread, it more and more appears to be like that fabric houses stemming from microstructural phenomena need to be thought of. this is often fairly actual for inhomogeneous load and deformation states, the place lower-scale dimension results start to have an effect on the macroscopic fabric reaction; anything regular continuum theories fail to account for. Following this concept, it really is obvious that normal continuum mechanics should be augmented to seize lower-scale structural and compositional phenomena, and to make this knowledge obtainable to macroscopic numerical simulations.
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Extra resources for Advances in Extended and Multifield Theories for Continua
This corresponds to clamping boundary conditions at the micromodel’s top and bottom. For the finite element computations this means locking of the nodal rotations at the model’s top and bottom. To prevent softening eﬀects due to free beams at the model’s lateral bounds periodic boundary conditions corresponding to an infinitely long shear layer are applied there, cf. Figs. 2 and 3. The clamping boundary conditions at the model’s top and bottom will cause a boundary layer eﬀect under shear leading to size dependent macroscopic eﬀective properties, cf.
Thus, in this contribution full-resolution micro-models will only serve to provide virtual experimental reference data for stress and strain quantities to be followed by a parameter identification algorithm in order to solve the inverse problem of determining the unknown set of material parameters incorporated in the extended constitutive equations of the linear Cosserat theory. A common way to recreate full-resolution micro-models for cellular materials or foams, respectively, is to reproduce the struts of e.
A closer look to Figs. 2 and 3 shows that there are several possible orientations of the honeycomb structure with respect to the shear direction, cf. Teko˘glu and Onck . What can be expected is a dependency of the mechanical properties from the hexagons’ orientation. For that reason another configuration in which the hexagons are rotated by 90◦ is examined too, cf. Fig. 3. Note that Gibson and Ashby  u1 = u2 = 0, ϕ = 0 Fig. 2 Honeycomb micromodel (config. 1) with complete set of boundary conditions for shear test.
Advances in Extended and Multifield Theories for Continua by Bob Svendsen (auth.), Bernd Markert (eds.)