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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Author / Creator: | |
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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
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Subjects: | |
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.