Numerical simulation of waves and fronts in inhomogeneous solids / Arkadi Berezovski, Jüri Engelbrecht, Gérard A. Maugin.

Includes bibliographical references and index.

This book shows the advanced methods of numerical simulation of waves and fronts propagation in inhomogeneous solids and introduces related important ideas associated with the application of numerical methods for these problems. Great care has been taken throughout the book to seek a balance between the thermomechanical analysis and numerical techniques. It is suitable for advanced undergraduate and graduate courses in continuum mechanics and engineering. Necessary prerequisites for this text are basic continuum mechanics and thermodynamics. Some elementary knowledge of numerical methods for p.

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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. 2.4. True and quasi-material inhomogeneities. 2.5. Brittle fracture. 2.6. Phase-transition fronts. 2.7. On the exploitation of Eshelby's stress in isothermal and adiabatic conditions. 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. 3.3. 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. 4.5. Local equilibrium approximation. 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. 5.6. Waves in functionally graded materials. 5.7. Concluding remarks -- 6. Macroscopic dynamics of phase-transition fronts. 6.1. Isothermal impact-induced front propagation. 6.2. Numerical simulations. 6.3. Interaction of a plane wave with phase boundary. 6.4. One-dimensional adiabatic fronts in a bar. 6.5. Numerical simulations. 6.6. Concluding remarks -- 7. Two-dimensional elastic waves in inhomogeneous media. 7.1. Governing equations. Fluctuation splitting. 7.3. First-order Godunov scheme. 7.4. Transverse propagation. 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. 10.5. Concluding remarks -- 11. Summing up.

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