Numerical Simulation of Waves and Fronts in Inhomogeneous Solids

The following sections are included:

• Preface

• Contents

The following sections are included:

• Waves and fronts

• True and quasi-inhomogeneities

• Driving force and the corresponding dissipation

• Example of a straight brittle crack

• Example of a phase-transition front

• Numerical simulations of moving discontinuities

• Outline of the book

The following sections are included:

• Kinematics

• Integral balance laws

• Localization and jump relations
  • Local balance laws
  • Jump relations
  • Constitutive relations

• True and quasi-material inhomogeneities
  • Balance of pseudomomentum

• Brittle fracture
  • Straight brittle crack

• Phase-transition fronts
  • Jump relations
  • Driving force

• On the exploitation of Eshelby's stress in isothermal and adiabatic conditions
  • Driving force at singular surface in adiabatic conditions
  • Another approach to the driving force

• Concluding remarks

The following sections are included:

• Intrinsic stability of simple systems

• Local phase equilibrium
  • Classical equilibrium conditions
  • Local equilibrium jump relations

• Non-equilibrium states

• Local equilibrium jump relations at discontinuity

• Excess quantities at a moving discontinuity

• Velocity of moving discontinuity

• Concluding remarks

The following sections are included:

• Local balance laws

• Balance of pseudomomentum

• Jump relations

• Wave-propagation algorithm: an example of finite volume methods
  • One-dimensional elasticity
  • Averaged quantities
  • Numerical fluxes
  • Second order corrections
  • Conservative wave propagation algorithm

• Local equilibrium approximation
  • Excess quantities and numerical fluxes
  • Riemann problem
  • Excess quantities at the boundaries between cells

• Concluding remarks

The following sections are included:

• Governing equations

• One-dimensional waves in periodic media

• One-dimensional weakly nonlinear waves in periodic media

• One-dimensional linear waves in laminates

• Nonlinear elastic wave in laminates under impact loading
  • Problem formulation
  • Comparison with experimental data
  • Discussion of results

• Waves in functionally graded materials

• Concluding remarks

The following sections are included:

• Isothermal impact-induced front propagation
  • Uniaxial motion of a slab
  • Excess quantities in the bulk
  • Excess quantities at the phase boundary
  • Initiation criterion for the stress-induced phase transformation
  • Velocity of the phase boundary

• Numerical simulations
  • Algorithm description
  • Comparison with experimental data

• Interaction of a plane wave with phase boundary
  • Pseudoelastic behavior

• One-dimensional adiabatic fronts in a bar
  • Formulation of the problem
  • Adiabatic approximation
  • Initiation criterion for the stress-induced phase transformation in adiabatic case
  • Velocity of the phase boundary
  • Temperature field

• Numerical simulations
  • Pulse loading
  • Temperature distribution
  • Kinetic behavior

• Concluding remarks

The following sections are included:

• Governing equations
  • Averaged quantities
  • Conservation law

• Fluctuation splitting

• First-order Godunov scheme

• Transverse propagation
  • Vertical transverse propagation
  • Horizontal transverse propagation
  • Boundary conditions

• Numerical tests

• Concluding remarks

The following sections are included:

• Impact loading of a plate

• Material properties

• Numerical simulations

• Centreline stress distribution

• Wave interaction with functionally graded inclusion

• Concluding remarks

The following sections are included:

• Material velocity at the phase boundary

• Numerical procedure

• Interaction of a non-plane wave with phase boundary

• Wave interaction with martensitic inclusion

• Concluding remarks

The following sections are included:

• Formulation of the problem

• Stationary crack under impact load

• Jump relations at the crack front

• Velocity of the crack in mode I
  • Zero excess stress
  • Non-zero excess stress

• Concluding remarks

Most dynamic processes at the macroscoppic level are governed by hyperbolic conservation laws. The theoretical description and numerical methods for the corresponding simulation of wave propagation in homogeneous materials are well developed and broadly applied. However, inhomogeneous materials are much more difficult to deal with although they can be formally modelled…

The following sections are included:

• Appendices
  • Thermodynamic interaction between two discrete systems in non-equilibrium
    • Equilibrium/non-equilibrium contacts
      • Contact quantities
      • Partial contact quantities
    • Interacting non-equilibrium systems
      • Replacement quantities
      • Composite systems
        • The subsystems
        • The composite system
    • Compound deficiency
      • The inequalities
      • Energy and entropy
      • Example: An endoreversible system
      • Excess quantities
        • Excess power exchange, excess mass exchange
        • Excess energy
        • Excess entropy

• Concluding remarks

• Bibliography

• Index