By Bob Svendsen (auth.), Bernd Markert (eds.)
Modern computational ideas, comparable to the Finite aspect technique, have, given that their improvement numerous a long time in the past, effectively exploited continuum theories for varied purposes in technological know-how and know-how. even if commonplace continuum equipment dependent upon the Cauchy-Boltzmann continuum are nonetheless of significant significance and are normal, it more and more looks that fabric houses stemming from microstructural phenomena need to be thought of. this is often quite actual for inhomogeneous load and deformation states, the place lower-scale measurement results start to have an effect on the macroscopic fabric reaction; whatever common continuum theories fail to account for. Following this concept, it really is glaring that ordinary continuum mechanics needs to be augmented to trap lower-scale structural and compositional phenomena, and to make this data obtainable to macroscopic numerical simulations.
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Extra resources for Advances in Extended and Multifield Theories for Continua
Mechanics of generalized continua. Advances in Mechanics and Mathematics, vol. 21. : On the continuum formulation of higher gradient plasticity for single and polycrystals. : Microstructure in linear elasticity. : Second gradient of strain and surface-tension in linear elasticity. : Mesoscopic continuum mechanics. A. ) Geometry, Continua and Microstructure, Collection Travaux en Cours, vol. 60, pp. 49–60. : La mécanique classique, basée sur un axiome d’ objectivité. In: La Méthode Axiomatique dans les Mécaniques Classique et Nouvelles (Colloque International à Paris, 1959), pp.
Aufbau und Identifikation von Stoﬀgleichungen für höhere Kontinua mittels Homogenisierungsmethoden. : Gradient-enhanced computational homogenization for the micro-macro scale transition. : Cellular solids. Cambridge Solid State Science Series. : Micromorphic Media: Interpretation and homogenization. : A numerical homogenisation strategy for micromorphic continuua. : Numerical homogenisation of micromorphic continuua. : Two-scale modelling of micromorphic continua.
Sample h [no. ] 1 2 3 4 5 6 7 8 1 3 5 9 11 23 47 95 μe f f config. 26 μe f f This verification of the micro-models shows their reliability and allows to extract the required reference data sets for the shear stress as well as the nodal displacements and rotations. 3 Reference Data For each sample the shear stress is constant over its height h because of the balance of forces. The results of the micro-structure computations for both configurations can be found in Table 3. As the displacement of the micro-models’ top was applied via a reference node which the top nodes had to follow in the e1 -direction the shear stress could be computed as T 12 = F re f bt (2) with F re f as the reaction force at the reference node, b as the samples’ width and t as their thickness, cf.