Titlebook: Constitutive Modelling of Granular Materials; Dimitrios Kolymbas Book 2000 Springer-Verlag Berlin Heidelberg 2000 Constitutive.bifurcation

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Microscopic approach contributions to constitutive modellingwhich is difficult to access in real physical experiments without intruding upon the material response, can lead to reassessment of the underlying concepts and assumptions inbedded in traditional continuum formulations.

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Micromechanically based higher-order continuum models for granular materialso continuum models is that the heterogeneous effects on the particle level can be described more accurately. However, for most granular structures the number of particles is very large, which causes the number of equations that has to be solved for in a discrete system to become large as well.

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Unsupervised and Semi-Supervised Learningterion are studied. A complete shear band localization analysis is given and considered as a special case of non uniqueness of some boundary value problems. Similarly, invertibility and controlability are studied from the same point of view. Finally a general overview of all these results is given.

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https://doi.org/10.1007/978-3-031-61664-8presented. The theories and methods are illustrated by examples such as silo flow, settlement of oriented particles, and trapdoor problems. The director theory presented is a first attempt to model oriented particles within such a framework and will be developed further.