Continuous Media With Microstructure

by Albers, Bettina

• ISBN13: 9783642114441
• ISBN10: 364211444X
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-04-03
• Publisher: Springer Verlag

Summary

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, stochastic processes in porous and fractal materials, thermodynamic modeling of composite materials, mathematical analysis of multicomponent systems, phase transformations in solids.

Table of Contents

Scientific Life of Prof Dr. Krzysztof Wilmanski
Curriculum Vitae of Prof Dr. K. Wilmanski	p. 3
Publications of Prof Dr. K. Wilmanski	p. 7
Thermodynamic Modeling
On Pore Fluid Pressure and Effective Solid Stress in the Mixture Theory of Porous Media	p. 19
An Extrapolation of Thermodynamics to Evolutionary Genetics	p. 29
Some Recent Results on Multi-temperature Mixture of Fluids	p. 39
Extensions of Constitutive Laws
Hypocontinua	p. 61
On Constitutive Choices for Smectic Elastomers	p. 71
A Note on the Representation of Cosserat Rotation	p. 83
Material Uniformity and the Concept of the Stress Space	p. 91
Coupled Nonlinear Thermoelastic Equations for an Orthotropic Beam with Thermal and Viscous Dissipation	p. 103
On the Mathematical Modelling of Functionally Graded Composites with a Determistinic Microstructure	p. 117
Micro- and Nanoscale Mechanics
On the Derivation of Biological Tissue Models from Kinetic Models of Multicellular Growing Systems	p. 131
Instabilites in Arch Shaped MEMS	p. 147
Towards Poroelasticity of Fractal Materials	p. 157
The Maxwell Problem (Mathematical Aspects)	p. 165
Continuum-Molecular Modeling of Nanostructured Materials	p. 189
Waves
Linear Wave Propagation in Unsaturated Rocks and Soils	p. 205
Explicit Solution Formulas for the Acoustic Diffraction Problem with a Slit in a Hard and a Soft Screen	p. 221
On the Stability of the Inversion of Measured Seismic Wave Velocities to Estimate Porosity in Fluid-Saturated Porous Media	p. 233
On Two Insufficiently Exploited Conservation Laws in Continuum Mechanics: Canonical Momentum and Action	p. 251
Waves and Dislocations	p. 269
Phase Transitions
Liquid-Solid Phase Transitions in a Deformable Container	p. 285
Composite Beams with Embedded Shape Memory Alloy	p. 301
Microstructures in the Ti50Ni50-xPdx Alloys' Cubic-to-Orthorhombic Phase Transformation: A Proposed Energy Landscape	p. 317
Granular Media
Analysis of Shear Banding with a Hypoplastic Constitutive Model for a Dry and Cohesionless Granular Material	p. 335
Principal Axes and Values of the Dispersion Coefficient in the 2D Axially Symmetric Porous Medium	p. 351
The Importance of Sand in Earth Sciences	p. 357
Author Index	p. 383
Index	p. 385
Table of Contents provided by Ingram. All Rights Reserved.