By Bob Svendsen (auth.), Bernd Markert (eds.)
Modern computational innovations, similar to the Finite point procedure, have, on account that their improvement numerous many years in the past, effectively exploited continuum theories for varied functions in technological know-how and expertise. even if commonplace continuum equipment dependent upon the Cauchy-Boltzmann continuum are nonetheless of significant value and are widespread, it more and more appears to be like that fabric homes stemming from microstructural phenomena must be thought of. this can be really actual for inhomogeneous load and deformation states, the place lower-scale measurement results start to have an effect on the macroscopic fabric reaction; whatever regular continuum theories fail to account for. Following this concept, it's glaring that ordinary continuum mechanics needs to be augmented to trap lower-scale structural and compositional phenomena, and to make this knowledge available to macroscopic numerical simulations.
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Extra resources for Advances in Extended and Multifield Theories for Continua
Open-cell foam structures by beam elements, cf. Gibson and Ashby , Onck et al , and Schraad and Triantaﬀylidis . Also granular materials like concrete can be modeled by lattice structures, cf. Schlangen and van Mier . In foams and granular media size eﬀects can be observed which cannot be described by the classical Boltzmann continuum approach but by extended theories like micropolar or micromorphic theories. The Cosserat theory or micropolar theory in turn incorporates additional rotational degrees of freedom for each material point, cf.
2 Honeycomb micromodel (config. 1) with complete set of boundary conditions for shear test. The size dependent boundary layer eﬀect is caused by clamping boundary conditions ϕ = 0 on top and bottom. u1 = u1 u2 = u2 ϕ = ϕ e2 u1 = 0, u2 = 0, ϕ = 0 e1 h From Lattice Models to Extended Continua 23 u2 = 0, ϕ = 0 Fig. 3 Honeycomb micromodel (config. 2) with complete set of boundary conditions for shear test. The size dependent boundary layer eﬀect is caused by clamping boundary conditions ϕ = 0 on top and bottom.
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. Concerning the subsequent parameter identification this means there is the possibility to reproduce the shear samples’ increasing stiﬀness for decreasing sample height via μC . The constant thickness of the boundary layer in turn can be captured by lC , cf. Diebels and Steeb . 28 S. Diebels and D. Scharding To complete the theory strain measures have to be derived from the kinematic assumptions.