Continuous Media with Microstructure / Edition 1

by Bettina Albers

Overview

The contributions to the book concern various aspects of extension of classical continuum models. These extensions are related to the appearance of microstructures both natural as well as these created by processes. To the first class belong various thermodynamic models of multicomponent systems such as porous materials, composites, materials with microscopic heterogeneities. To the second class belong primarily microstructures created by phase transformations. Invited authors cover both fields of thermodynamic modeling and mathematical analysis of such continua with microstructure. In particular the following subjects are covered:

• thermodynamic modeling of saturated and unsaturated porous and granular media,
• linear and nonlinear waves in such materials,
• extensions of constitutive laws by internal variables, higher gradients and nonequilibrium fields,
• shastic processes in porous and fractal materials,
• thermodynamic modeling of composite materials,
• mathematical analysis of multicomponent systems,
• phase transformations in solids.

Product Details

ISBN-13:	9783642114441
Publisher:	Springer Berlin Heidelberg
Publication date:	02/12/2010
Edition description:	2010
Pages:	389
Product dimensions:	6.10(w) x 9.20(h) x 1.10(d)

Table of Contents

Part I Scientific Life of Prof Dr. Krzysztof Wilmanski

Curriculum Vitae of Prof Dr. K. Wilmanski 3

Publications of Prof Dr. K. Wilmanski 7

Part II Thermodynamic Modeling

On Pore Fluid Pressure and Effective Solid Stress in the Mixture Theory of Porous Media I-Shih Liu 19

An Extrapolation of Thermodynamics to Evolutionary Genetics Ingo Müller 29

Some Recent Results on Multi-temperature Mixture of Fluids Tommaso Ruggeri 39

Part III Extensions of Constitutive Laws

Hypocontinua Gianfranco Capriz 61

On Constitutive Choices for Smectic Elastomers Pasquale Giovine 71

A Note on the Representation of Cosserat Rotation J.D. Goddard 83

Material Uniformity and the Concept of the Stress Space Serge Preston Marek Elzanowski 91

Coupled Nonlinear Thermoelastic Equations for an Orthotropic Beam with Thermal and Viscous Dissipation M.B. Rubin 103

On the Mathematical Modelling of Functionally Graded Composites with a Determistinic Microstructure Czeslaw Wozniak Jowita Rychlewska 117

Part IV Micro- and Nanoscale Mechanics

On the Derivation of Biological Tissue Models from Kinetic Models of Multicellular Growing Systems N. Bellomo A. Bellouquid E. De Angelis 131

Instabilites in Arch Shaped MEMS K. Das R. C. Batra 147

Towards Poroelasticity of Fractal Materials M. Ostoja-Starzewski 157

The Maxwell Problem (Mathematical Aspects) Evgeniy V. Radkevich 165

Continuum-Molecular Modeling of Nanostructured Materials Gwidon Szefer Dorota Jasinska 189

Part V Waves

Linear Wave Propagation in Unsaturated Rocks and Soils Bettina Albers 205

Explicit Solution Formulas for the Acoustic Diffraction Problem with a Slit in a Hard and a Soft Screen Matthias Kunik 221

On the Stability of the Inversion of Measured Seismic Wave Velocities to Estimate Porosity in Fluid-Saturated Porous Media Carlo G. Lai Jorge G.F. Crempien de la Carrera 233

On Two Insufficiently Exploited Conservation Laws in Continuum Mechanics: Canonical Momentum and Action G.A. Maugin M. Rousseau 251

Waves and Dislocations Lukasz A. Turski 269

Part VI Phase Transitions

Liquid-Solid Phase Transitions in a Deformable Container Pavel Krejcí Elisabetta Rocca Jürgen Sprekels 285

Composite Beams with Embedded Shape Memory Alloy Mieczyslaw Kuczma 301

Microstructures in the Ti₅₀Ni_50-xPd_x Alloys' Cubic-to-Orthorhombic Phase Transformation: A Proposed Energy Landscape Mario Pitteri 317

Part VII Granular Media

Analysis of Shear Banding with a Hypoplastic Constitutive Model for a Dry and Cohesionless Granular Material Erich Bauer 335

Principal Axes and Values of the Dispersion Coefficient in the 2D Axially Symmetric Porous Medium Leonid G. Fel Jacob Bear 351

The Importance of Sand in Earth Sciences Dimitrios Kolymbas 357

Author Index 383

Index 385