This book puts the theory for a mixture of hypoplastic constituents on a rigorous basis using Müller and Liu's thermodynamic analysis. It addresses a continuum mechanical formulation of structured solid-fluid mixtures for elasto-viscous-frictional materials.

Mixture concepts are nowadays used in a great number of subjects of the - ological, chemical, engineering, natural and physical sciences (to name these alphabetically) and the theory of mixtures has attained in all these dis- plines a high level of expertise and specialisation. The digression in their development has on occasion led to di?erences in the denotation of special formulations as 'multi-phase systems' or 'non-classical mixtures', 'structured mixtures', etc. , and their representatives or defenders often emphasise the di?erences of these rather than their common properties. Thismonographisanattempttoviewtheoreticalformulationsofprocesses which take place as interactions among various substances that are spatially intermixedandcanbeviewedtocontinuously?llthespacewhichtheyoccupy as mixtures. Moreover, we shall assume that the processes can be regarded to becharacterisedbyvariableswhichobeyacertaindegreeofcontinuityintheir evolution, so that the relevant processes can be described mathematically by balance laws, in global or local form, eventually leading to di?erential and/or integralequations,towhichtheusualtechniquesoftheoreticalandnumerical analysis can be applied. Mixtures are generally called non-classical, if, apart from the physical laws (e. g. balances of mass, momenta, energy and entropy), also further laws are postulated,whicharelessfundamental,butmaydescribesomefeaturesofthe micro-structure on the macroscopic level. In a mixture of ?uids and solids thesearesometimescalledparticleladensystemsthefractionofthevolume that is occupied by each constituent is a signi?cant characterisation of the micro-structure that exerts some in?uence on the macro-level at which the equations governing the processes are formulated. Forsolid-?uid mixtures at high solids fraction where particle contact is essential, friction between the particles gives rise to internal stresses, which turn out to be best described by an internal symmetric tensor valued variable.

Addresses a continuum mechanical formulation of structured solid-fluid mixtures for elasto-viscous-frictional materials Suitable for particle laden and dense solid-fluid flows under small to catastrophic motions Includes supplementary material: sn.pub/extras

Auteur
Lukas Schneider studierte an der Universtität Mannheim Betriebswirtschaft, mit den Schwerpunkten Finanzierung und Industriebetriebslehre. Schon während seines Studiums hat er sein Interesse für Turnaround- und Krisensituationen von mittelständischen und großen Unternehmen entwickelt. Hierbei ging er vor allem der Frage nach dem Erfolg von klassischen Restrukturierungen zu einer Restrukturierung durch Private Equity/Distressed Debt Investoren nach. Als Diplom-Kaufmann stieg er 2006 bei der Unternehmensberatung Roland Berger Strategy Consultants als Berater ein. Seither hat er im Rahmen seiner Tätigkeit im Competence Center Corporate Finance & Restructuring eine Vielzahl von Restrukturierungsfällen bearbeiten können. Heute arbeitet er als Vorstand einer eigenen Internet Start-up Gründung und als Freelance Berater in Turnaroundsituationen auf ausgewählten Projekten.

Contenu
Mathematical Preliminaries and Notations.- to Mixture Theory.- Constitutive Assumptions.- Entropy Principle and Transformation of the Entropy Inequality.- Thermodynamic Analysis I Liu Identities, One-Forms and Integrability Conditions.- Thermodynamic Analysis II Residual Inequality, Thermodynamic Equilibrium, Isotropic Expansion.- Reduced Model.- Discussions and Conclusions.