Continuum models of microstructure

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Continuum models of microstructure

Preface

Advanced lecture course for PhD students of the Magdeburg University, January 2012.

Full title: On the application of continuum models of the microstructure for description of non-mechanical processes on the macro-level.

Lecturer: Elena A. Ivanova.

Contents

Lecture 1

Mathematics necessary for description of continua with microstructure. Models of particles with complex structure as the base of modeling continua with microstructure.

Lecture 2

Modelling of continua with microstructure: equations of motion, strain measures and constitutive equations. Continua with inner rotational degrees of freedom.

Lecture 3

Application of continuum models with microstructure to description of processes of non-mechanical nature at the macro-level: historical remarks and state-of-the-art.

Lecture 4

Application of the continuum model with microstructure (continua with inner rotational degrees of freedom) to description on the macro-level of heat conductivity and heat radiation processes.

Lecture 5

Application of the continuum model with microstructure (continua with inner rotational degrees of freedom) to description on the macro-level of electro-magnetic processes: simplest theory leading to Maxwell’s equations.

Lecture 6

Application of the continuum model with microstructure (continua with inner rotational degrees of freedom) to description on the macro-level of electro-magnetic processes: theory connecting electro-magnetic and heat processes.

Lecture 7

Application of the continuum model with microstructure (continua with inner translation and rotational degrees of freedom) to description of piezoelectric effect. Specifics of the description of the piezoelectric effect in polar and non-polar piezoelectric continua.

Lecture 8

Application of the continuum model with microstructure (continua with inner rotational degrees of freedom) to description of quantum effects: possibilities to describe ferromagnetism, deduction of Schrödinger’s and Klein-Gordon equations.