| 1. |
- Jänicke, Ralf, 1980, et al.
(författare)
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Micromorphic two-scale modelling of periodic grid structures
- 2013
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Ingår i: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 11:2, s. 161-176
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Tidskriftsartikel (refereegranskat)abstract
- The present contribution focuses on the numerical homogenization of periodic grid structures. In order to investigate the micro-to-macroscale transition, a consistent numerical homogenization scheme will be presented, replacing a heterogeneous Cauchy microcontinuum by a homogeneous micromorphic substitute continuum on the macroscale. The extended degrees of freedom, namely, the microdeformation and its gradient, are to be interpreted in terms of geometrical deformation modes and the related loading conditions of the underlying unit cells. Assuming strain energy equivalence of the macro- and the microscale, the effective constitutive properties of a square and a honeycomb grid structure are identified and quantitatively validated in comparison to reference calculations with microscopic resolution.
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| 2. |
- Jänicke, Ralf, 1980, et al.
(författare)
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Numerical homogenisation of micromorphic media
- 2010
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Ingår i: Technische Mechanik. - 0232-3869. ; 30:4, s. 364-373
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Tidskriftsartikel (refereegranskat)abstract
- Due to their underlying microtopology, cellular materialsare known to show a complex mechanical behaviour. For the material modelling, the heterogeneous microcontinuum is commonly replaced by a homogeneous macrocontinuum involving extended kinematics. An appropriate homogenisation methodology will be introduced in order to replace a heterogeneous Cauchy microcontinuum by a homogeneous micromorphic macrocontinuum. For an artificial 2-D periodic microstructure, the present contribution draws a comparison between extended two-scale calculations on the one hand, and a reference solution as well as a first-order FE2 calculation on the other hand.
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| 3. |
- Trinh, Duy Khanh, et al.
(författare)
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Evaluation of generalized continuum substitution models for heterogeneous materials
- 2012
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Ingår i: International Journal for Multiscale Computational Engineering. - 1543-1649. ; 10:6, s. 527-549
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Tidskriftsartikel (refereegranskat)abstract
- Several extensions of standard homogenization methods for composite materials have been proposed in the literature that rely on the use of polynomial boundary conditions enhancing the classical affine conditions on the unit cell. Depending on the choice of the polynomial, overall Cosserat, second gradient, or micromorphic homogeneous substitution media are obtained. They can be used to compute the response of the composite when the characteristic length associated with the variation of the applied loading conditions becomes of the order of the size of the material inhomogeneities. A significant difference between the available methods is the nature of the fluctuation field added to the polynomial expansion of the displacement field in the unit cell, which results in different definitions of the overall stress and strain measures and higher order elastic moduli. The overall higher order elastic moduli obtained from some of these methods are compared in the present contribution in the case of a specific periodic two-phase composite material. The performance of the obtained overall substitution media is evaluated for a chosen boundary value problem at the macroscopic scale for which a reference finite element solution is available. Several unsatisfactory features of the available theories are pointed out, even though some model predictions turn out to be highly relevant. Improvement of the prediction can be obtained by a precise estimation of the fluctuation at the boundary of the unit cell.
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