Chapter 20 -Multiscale Methods for Wave Problems in Heterogeneous Media, Handbook of Numerical Methods for Hyperbolic Problems, vol.18, pp.545-576, 2017. ,
Loss of specular reflection due to nonlinear crack-face interaction, Journal of Nondestructive Evaluation, vol.3, issue.4, pp.229-239, 1982. ,
Homogenization of a 1D nonlinear dynamical problem for periodic composites, ZAMM -Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, vol.91, issue.6, pp.523-534, 2011. ,
Reflection of ultrasonic waves by an array of microcracks, Review of Progress in Quantitative Nondestructive Evaluation, pp.83-89, 1985. ,
High-frequency homogenisation in periodic media with imperfect interfaces ,
URL : https://hal.archives-ouvertes.fr/hal-02615237
Ultrasonic scattering from imperfect interfaces: A quasi-static model, J. Nondestruct. Eval, vol.4, issue.3-4, pp.177-196, 1984. ,
Fundamentals of rock joint deformation, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.20, issue.6, pp.249-268, 1983. ,
Asymptotic analysis for periodic structures, 2011. ,
Modelling of nonlinear crack-wave interactions for damage detection based on ultrasound-a review, Journal of Sound and Vibration, vol.333, issue.4, pp.1097-1118, 2014. ,
Second-order homogenization of boundary and transmission conditions for one-dimensional waves in periodic media, International Journal of Solids and Structures, pp.88-102, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02297483
Transient waves in 1D periodic media : second-order homogenization of transmission conditions and source points ,
Hyperbolic Conservation Laws in Continuum Physics, 2005. ,
Numerical Approximation of Hyperbolic Systems of Conservation Laws, 1996. ,
Hysteresis in response of nonlinear bistable interface to continuously varying acoustic loading, Ultrasonics, vol.41, issue.8, pp.643-654, 2003. ,
Thermoelastic properties of fiber composites with imperfect interface, Mechanics of Materials, vol.8, pp.333-348, 1990. ,
Thin interphase/imperfect interface in elasticity with application to coated fiber composites, J. Mech. Phys. Solids, vol.50, issue.12, pp.2509-2537, 2002. ,
, Contact Mechanics, 1985.
Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave, SIAM Journal on Applied Mathematics, vol.70, issue.3, pp.735-761, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00339279
Dilatation of a one-dimensional nonlinear crack impacted by a periodic elastic wave, SIAM Journal on Applied Mathematics, vol.70, issue.3, pp.735-761, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00339279
Interaction between periodic elastic waves and two contact nonlinearities, Mathematical Models and Methods in Applied Sciences, vol.22, issue.04, p.1150022, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00549051
Multiple-scale homogenization for weakly nonlinear conservation laws with rapid spatial fluctuations, Studies in Applied Mathematics, vol.101, issue.2, pp.127-183, 1998. ,
Dispersive effective models for waves in heterogeneous media, Mathematical Models and Methods in Applied Sciences, vol.21, issue.09, pp.1871-1899, 2011. ,
Hyperbolic systems of conservation laws ii, Comm. Pure Appl. Math, vol.10, issue.4, pp.537-566, 1957. ,
Development of singularities of solutions of nonlinear hyperbolic partial differential equations, J. Math. Phys, vol.5, issue.5, pp.611-613, 1964. ,
Asymptotic behavior of a hard thin linear elastic interphase: An energy approach, International Journal of Solids and Structures, vol.48, issue.3, pp.441-449, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00589975
Higher order interfacial effects for elastic waves in one dimensional phononic crystals via the Lagrange-Hamilton's principle, European Journal of Mechanics -A/Solids, vol.67, pp.58-70, 2018. ,
Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, 2002. ,
Dynamics of elastic bodies connected by a thin adhesive layer, Ultrasonic Wave Propagation in Non Homogeneous Media, vol.128, pp.99-110, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00574684
Modélisation numérique de la propagation et de la diffraction d'ondes mécaniques, 2010. ,
How to incorporate the spring-mass conditions in finite-difference schemes, SIAM J. Sci. Comput, vol.24, issue.4, pp.1379-1407, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00004812
Modeling 1-D elastic P-waves in a fractured rock with hyperbolic jump conditions, J. Comput. App. Math, vol.204, pp.292-305, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00095896
Effective properties of non-linear elastic laminated composites with perfect and imperfect contact conditions, Adv. Mater. Struc, vol.15, issue.5, pp.375-385, 2008. ,
Stop-pass behavior of acoustic waves in a 1D fractured system, J. Acoust. Soc. Am, pp.40-50, 2000. ,
Willis elastodynamic homogenization theory revisited for periodic media, Journal of the Mechanics and Physics of Solids, vol.77, pp.158-178, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01112307
Nonlinear interaction of plane ultrasonic waves with an interface between rough surfaces in contact, The Journal of the Acoustical Society of America, vol.113, issue.6, pp.3065-3072, 2003. ,
Anisotropy in seismic velocities and amplitudes from multiple parallel fractures, J. Geophys. Res, pp.345-358, 1990. ,
Harmonic generation at an unbonded interface-i. planar interface between semi-infinite elastic media, International Journal of Engineering Science, vol.17, issue.1, pp.73-85, 1979. ,
Analysis of boundary conditions for elastic wave interaction with an interface between two solids, J. Acoust. Soc. Am, vol.89, issue.2, pp.503-515, 1991. ,
, Non-Homogeneous Media and Vibration Theory, 1978.
A dispersive effective medium for wave propagation in periodic composites, SIAM Journal on Applied Mathematics, vol.51, issue.4, pp.984-1005, 1991. ,
Elastic wave behavior across linear slip interfaces, J. Acoust. Soc. Am, vol.68, issue.5, pp.1516-1521, 1980. ,
Connections between different models describing imperfect interfaces in periodic fiber-reinforced composites, International Journal of Solids and Structures, vol.49, issue.13, pp.1518-1525, 2012. ,
Ultrasonics of non-linear contacts: propagation, reflection and NDE-applications, Ultrasonics, vol.36, issue.1, pp.383-390, 1998. ,
Effective constitutive relations for waves in composites and metamaterials, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.467, pp.1865-1879, 2011. ,
Variational principles for dynamic problems for inhomogeneous elastic media, Wave Motion, vol.3, issue.1, pp.1-11, 1981. ,