Numerical Simulation Of Waves And Fronts In Inhomogeneous Solids.

Key Features:Includes non-standard topics such as the distinction between true- and quasi-inhomogeneities, the local equilibrium jump relations at discontinuities, and the material description of continuum mechanicsUtilizes numerical experiments to illustrate the strong interaction between the achie...

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Bibliographic Details
Author / Creator:	Maugin, Gerard A.
Other Authors / Creators:	Engelbrecht, Juri. Berezovski, Arkadi.
Format:	eBook Electronic
Language:	English
Imprint:	Singapore : World Scientific Publishing Company, 2008.
Series:	World Scientific Series On Nonlinear Science Series A
Subjects:	Elastic solids. Inhomogeneous materials. Wave-motion, Theory of. Electronic books.
Local Note:	Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2022. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Online Access:	Click to View

Table of Contents:

Intro
Contents
Preface
1. Introduction
1.1 Waves and fronts
1.2 True and quasi-inhomogeneities
1.3 Driving force and the corresponding dissipation
1.4 Example of a straight brittle crack
1.5 Example of a phase-transition front
1.6 Numerical simulations of moving discontinuities
1.7 Outline of the book
2. Material Inhomogeneities in Thermomechanics
2.1 Kinematics
2.2 Integral balance laws
2.3 Localization and jump relations
2.3.1 Local balance laws
2.3.2 Jump relations
2.3.3 Constitutive relations
2.4 True and quasi-material inhomogeneities
2.4.1 Balance of pseudomomentum
2.5 Brittle fracture
2.5.1 Straight brittle crack
2.6 Phase-transition fronts
2.6.1 Jump relations
2.6.2 Driving force
2.7 On the exploitation of Eshelby's stress in isothermal and adiabatic conditions
2.7.1 Driving force at singular surface in adiabatic conditions
2.7.2 Another approach to the driving force
2.8 Concluding remarks
3. Local Phase Equilibrium and Jump Relations at Moving Discontinuities
3.1 Intrinsic stability of simple systems
3.2 Local phase equilibrium
3.2.1 Classical equilibrium conditions
3.2.2 Local equilibrium jump relations
3.3 Non-equilibrium states
3.4 Local equilibrium jump relations at discontinuity
3.5 Excess quantities at a moving discontinuity
3.6 Velocity of moving discontinuity
3.7 Concluding remarks
4. Linear Thermoelasticity
4.1 Local balance laws
4.2 Balance of pseudomomentum
4.3 Jump relations
4.4 Wave-propagation algorithm: an example of finite volume methods
4.4.1 One-dimensional elasticity
4.4.2 Averaged quantities
4.4.3 Numerical fluxes
4.4.4 Second order corrections
4.4.5 Conservative wave propagation algorithm
4.5 Local equilibrium approximation
4.5.1 Excess quantities and numerical fluxes.
4.5.2 Riemann problem
4.5.3 Excess quantities at the boundaries between cells
4.6 Concluding remarks
5. Wave Propagation in Inhomogeneous Solids
5.1 Governing equations
5.2 One-dimensional waves in periodic media
5.3 One-dimensional weakly nonlinear waves in periodic media
5.4 One-dimensional linear waves in laminates
5.5 Nonlinear elastic wave in laminates under impact loading
5.5.1 Problem formulation
5.5.2 Comparison with experimental data
5.5.3 Discussion of results
5.6 Waves in functionally graded materials
5.7 Concluding remarks
6. Macroscopic Dynamics of Phase-Transition Fronts
6.1 Isothermal impact-induced front propagation
6.1.1 Uniaxial motion of a slab
6.1.2 Excess quantities in the bulk
6.1.3 Excess quantities at the phase boundary
6.1.4 Initiation criterion for the stress-induced phase transformation
6.1.5 Velocity of the phase boundary
6.2 Numerical simulations
6.2.1 Algorithm description
6.2.2 Comparison with experimental data
6.3 Interaction of a plane wave with phase boundary
6.3.1 Pseudoelastic behavior
6.4 One-dimensional adiabatic fronts in a bar
6.4.1 Formulation of the problem
6.4.2 Adiabatic approximation
6.4.3 Initiation criterion for the stress-induced phase transformation in adiabatic case
6.4.4 Velocity of the phase boundary
6.4.5 Temperature field
6.5 Numerical simulations
6.5.1 Pulse loading
6.5.2 Temperature distribution
6.5.3 Kinetic behavior
6.6 Concluding remarks
7. Two-Dimensional Elastic Waves in Inhomogeneous Media
7.1 Governing equations
7.1.1 Averaged quantities
7.1.2 Conservation law
7.2 Fluctuation splitting
7.3 First-order Godunov scheme .
7.4 Transverse propagation
7.4.1 Vertical transverse propagation
7.4.2 Horizontal transverse propagation
7.4.3 Boundary conditions.
7.5 Numerical tests
7.6 Concluding remarks
8. Two-Dimensional Waves in Functionally Graded Materials
8.1 Impact loading of a plate
8.2 Material properties
8.3 Numerical simulations
8.4 Centreline stress distribution
8.5 Wave interaction with functionally graded inclusion
8.6 Concluding remarks
9. Phase Transitions Fronts in Two Dimensions
9.1 Material velocity at the phase boundary
9.2 Numerical procedure
9.3 Interaction of a non-plane wave with phase boundary
9.4 Wave interaction with martensitic inclusion
9.5 Concluding remarks
10. Dynamics of a Straight Brittle Crack
10.1 Formulation of the problem
10.2 Stationary crack under impact load
10.3 Jump relations at the crack front
10.4 Velocity of the crack in mode I
10.4.1 Zero excess stress
10.4.2 Non-zero excess stress
10.5 Concluding remarks
11. Summing Up
Appendix A Thermodynamic interaction between two discrete systems in non-equilibrium
A.1 Equilibrium/non-equilibrium contacts
A.1.1 Contact quantities
A.1.2 Partial contact quantities
A.2 Interacting non-equilibrium systems
A.2.1 Replacement quantities
A.2.2 Composite systems
A.2.2.1 The subsystems
A.2.2.2 The composite system
A.3 Compound deficiency
A.3.1 The inequalities
A.3.2 Energy and entropy
A.3.3 Example: An endoreversible system
A.3.4 Excess quantities
A.3.4.1 Excess power exchange, excess mass exchange
A.3.4.2 Excess energy
A.4 Concluding remarks
Bibliography
Index.

Numerical Simulation Of Waves And Fronts In Inhomogeneous Solids.

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