E. Ávalos and S. Sen, How solitary waves collide in discrete granular alignements, Phys. Rev. E, vol.79, issue.046607, 2009.

N. Brilliantov, F. Spahn, J. M. Hertzsch, and T. Pöschel, Model for collisions in granular gases, Physical Review E, vol.34, issue.5, pp.5382-5392, 1996.
DOI : 10.1016/0021-9991(80)90104-7

URL : http://arxiv.org/pdf/cond-mat/0203598v1.pdf

B. Brogliato, Nonsmooth Mechanics, 1999.
DOI : 10.1007/978-1-4471-0557-2

URL : https://hal.archives-ouvertes.fr/hal-01236953

R. Carretero-gonzález, D. Khatri, M. A. Porter, P. G. Kevrekidis, and C. Daraio, Dissipative Solitary Waves in Granular Crystals, Physical Review Letters, vol.102, issue.2, p.24102, 2009.
DOI : 10.1209/epl/i2002-00118-y

V. Ceanga and Y. Hurmuzlu, A New Look at an Old Problem: Newton???s Cradle, Journal of Applied Mechanics, vol.68, issue.4, pp.575-583, 2001.
DOI : 10.1115/1.1344902

C. Coste and B. Gilles, On the validity of Hertz contact law for granular material acoustics, The European Physical Journal B, vol.7, issue.1, pp.155-168, 1999.
DOI : 10.1007/s100510050598

P. Cundall and O. Strack, A discrete numerical model for granular assemblies, G??otechnique, vol.29, issue.1, pp.47-69, 1979.
DOI : 10.1680/geot.1979.29.1.47

C. Daraio and V. Nesterenko, Strongly nonlinear wave dynamics in a chain of polymer coated beads, Physical Review E, vol.92, issue.2, 2006.
DOI : 10.1088/0022-3727/27/6/030

C. Daraio, V. Nesterenko, E. Herbold, and S. Jin, Strongly nonlinear waves in a chain of Teflon beads, Physical Review E, vol.92, issue.1, 2005.
DOI : 10.1063/1.1427920

C. Daraio, V. F. Nesterenko, and E. B. Herbold, Energy Trapping and Shock Disintegration in a Composite Granular Medium, Physical Review Letters, vol.36, issue.5, p.96, 2006.
DOI : 10.1103/PhysRevE.72.016603

URL : http://arxiv.org/pdf/cond-mat/0509622

G. Darboux, Etude geometrique sur les percussions et le choc des corps, Nelineinaya Dinamika, vol.4, issue.1, pp.126-160, 1880.
DOI : 10.20537/nd1002013

R. L. Doney and S. Sen, Impulse absorption by tapered horizontal alignments of elastic spheres, Physical Review E, vol.39, issue.4, 2005.
DOI : 10.1007/s10035-002-0119-1

S. Dorbolo, D. Volfson, L. Tsimring, and A. Kudrolli, Dynamics of a Bouncing Dimer, Physical Review Letters, vol.65, issue.4, p.95, 2005.
DOI : 10.1103/PhysRevE.71.062301

URL : http://cds.cern.ch/record/840287/files/0506060.pdf

E. Falcon, C. Laroche, S. Fauve, and S. Coste, Collision of a 1-D column of beads with a wall, The European Physical Journal B, vol.5, issue.1, pp.111-131, 1998.
DOI : 10.1007/s100510050424

M. Gharib, A. Celik, and Y. Hurmuzlu, Shock Absorption Using Linear Particle Chains With Multiple Impacts, Journal of Applied Mechanics, vol.78, issue.3, p.78, 2011.
DOI : 10.1115/1.4003349

C. Glocker, Concepts for modeling impacts without friction, Acta Mechanica, vol.168, issue.1-2, pp.1-19, 2004.
DOI : 10.1007/s00707-004-0076-3

URL : http://www.zfm.ethz.ch/~glocker/publicationpdf/journal publications/bw_2004_actamechanica.pdf

U. Harbola, A. Rosas, M. Esposito, and K. Lindenberg, Pulse propagation in tapered granular chains: An analytic study, Physical Review E, vol.92, issue.3, 2009.
DOI : 10.1103/PhysRevE.63.021505

URL : http://arxiv.org/pdf/0905.4512

U. Harbola, A. Rosas, A. H. Romero, M. Esposito, and K. Lindenberg, Pulse propagation in decorated granular chains: An analytical approach, Physical Review E, vol.92, issue.5, p.80051302, 2009.
DOI : 10.1103/PhysRevE.80.025602

U. Harbola, A. Rosas, A. H. Romero, and K. Lindenberg, Pulse propagation in randomly decorated chains, Physical Review E, vol.92, issue.1, 2010.
DOI : 10.1201/9781420036268

E. Hascoë and H. J. Herrmann, Shocks in non-loaded bead chains with impurities, The European Physical Journal B, vol.14, issue.1, pp.183-190, 2000.
DOI : 10.1007/s100510050119

K. Hunt and F. Crossley, Coefficient of Restitution Interpreted as Damping in Vibroimpact, Journal of Applied Mechanics, vol.42, issue.2, pp.440-445, 1975.
DOI : 10.1115/1.3423596

URL : https://hal.archives-ouvertes.fr/hal-01333795

S. Job, F. Melo, A. Sokolow, and S. Sen, How Hertzian Solitary Waves Interact with Boundaries in a 1D Granular Medium, Physical Review Letters, vol.26, issue.17, p.94, 2005.
DOI : 10.1103/PhysRevE.53.5382

URL : https://hal.archives-ouvertes.fr/hal-00624695

S. Job, F. Melo, A. Sokolow, and S. Sen, Solitary wave trains in granular chains: experiments, theory and simulations, Granular Matter, vol.59, issue.1, pp.13-20, 2007.
DOI : 10.1007/978-1-4757-3524-6

URL : https://hal.archives-ouvertes.fr/hal-00624713

S. Job, F. Santibanez, F. Tapia, and F. Melo, Wave localization in strongly nonlinear Hertzian chains with mass defect, Physical Review E, vol.8, issue.2, p.25602, 2009.
DOI : 10.1016/j.ultras.2008.03.006

URL : https://hal.archives-ouvertes.fr/hal-00624740

K. Johnson, Contact Mechanics, 1985.

J. B. Keller, Impact With Friction, Journal of Applied Mechanics, vol.53, issue.1, pp.1-4, 1986.
DOI : 10.1115/1.3171712

G. Kuwabara and K. Kono, Restitution Coefficient in a Collision between Two Spheres, Japanese Journal of Applied Physics, vol.26, issue.Part 1, No. 8, pp.1230-1233, 1987.
DOI : 10.1143/JJAP.26.1230

A. N. Lazaridi and V. F. Nesterenko, Observation of a new type of solitary waves in a one-dimensional granular medium, Journal of Applied Mechanics and Technical Physics, vol.26, issue.3, pp.405-408, 1985.
DOI : 10.1007/BF00910379

C. Liu, Z. Zhao, and B. Brogliato, Energy dissipation and dispersion effects in a granular media, Phys. Rev. E, vol.78, 2008.

C. Liu, Z. Zhao, and B. Brogliato, Frictionless multiple impacts in multibody systems. I. Theoretical framework, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.142, issue.2100, pp.3193-3211, 2008.
DOI : 10.1016/0022-460X(90)90665-M

URL : https://hal.archives-ouvertes.fr/inria-00204018

C. Liu, Z. Zhao, and B. Brogliato, Frictionless multiple impacts in multibody systems. II. Numerical algorithm and simulation results, Proc. R. Soc. A 465, pp.1-23, 2009.
DOI : 10.1007/s004190050240

URL : https://hal.archives-ouvertes.fr/inria-00204018

S. Luding, Introduction to discrete element methods, Discrete Modelling of Geomaterials, pp.785-826, 2008.
DOI : 10.1115/1.2897191

M. Manciu, S. Sen, and A. J. Hurd, Impulse propagation in dissipative and disordered chains with power-law repulsive potentials, Physica D: Nonlinear Phenomena, vol.157, issue.3, pp.226-240, 2001.
DOI : 10.1016/S0167-2789(01)00302-5

F. Melo, S. Job, F. Santibanez, and F. Tapia, Experimental evidence of shock mitigation in a Hertzian tapered chain, Physical Review E, vol.34, issue.4, 2006.
DOI : 10.1016/S0375-9601(97)00241-7

URL : https://hal.archives-ouvertes.fr/hal-00624706

B. Mishra and C. Murty, On the determination of contact parameters for realistic DEM simulations of ball mills, Powder Technology, vol.115, issue.3, pp.290-297, 2001.
DOI : 10.1016/S0032-5910(00)00347-8

M. Nakagawa, J. H. Agui, D. T. Wu, and D. V. Extramiana, Impulse dispersion in a tapered granular chain, Granular Matter, vol.4, issue.4, pp.167-174, 2003.
DOI : 10.1007/s10035-002-0119-1

V. F. Nesterenko, Propagation of nonlinear compression pulses in granular media, Journal of Applied Mechanics and Technical Physics, vol.24, issue.5, pp.733-743, 1984.
DOI : 10.1007/BF00905892

V. F. Nesterenko, Solitary waves in discrete media with anomalous compressibility and similar to "sonic vacuum", Journal de Physique IV, Colloque C8, pp.8-729, 1994.
DOI : 10.1051/jp4:19948112

URL : https://hal.archives-ouvertes.fr/jpa-00253354

V. F. Nesterenko, Dynamics of Heterogeneous Materials, 2001.
DOI : 10.1007/978-1-4757-3524-6

V. F. Nesterenko, C. Daraio, E. B. Herbold, and S. Jin, Anomalous Wave Reflection at the Interface of Two Strongly Nonlinear Granular Media, Physical Review Letters, vol.36, issue.15, pp.95-158702, 2005.
DOI : 10.1016/j.physleta.2004.04.042

N. S. Nguyen and B. Brogliato, Shock dynamics in granular chains: numerical simulations and comparison with experimental tests, Granular Matter, vol.465, issue.2107, 2011.
DOI : 10.1098/rspa.2008.0520

URL : https://hal.archives-ouvertes.fr/inria-00597468

L. Paoli, CONTINUOUS DEPENDENCE ON DATA FOR VIBRO-IMPACT PROBLEMS, Mathematical Models and Methods in Applied Sciences, vol.359, issue.01, pp.1-41, 2005.
DOI : 10.1098/rsta.2001.0859

M. D. Payr, An experimental and theoretical study of perfect multiple contact collisions in linear chains of bodies, 2008.

J. Pfannnes, S. Sen, S. Chakravarti, and F. I. Surve, Energy absorption and recovery in tapered granular chains: small chains and low tapering, Mater. Res. Soc. Symp. Proc, vol.759, pp.147-154, 2003.

L. Ponson, N. Boechler, Y. M. Lai, M. A. Porter, P. G. Kevrekidis et al., Nonlinear waves in disordered diatomic granular chains, Physical Review E, vol.82, issue.2, 2010.
DOI : 10.1103/PhysRevB.27.715

URL : http://arxiv.org/pdf/0904.0426

M. A. Porter, C. Daraio, I. Szelengowicz, E. B. Herbold, and P. G. Kevrekidis, Highly nonlinear solitary waves in heterogeneous periodic granular media, Physica D: Nonlinear Phenomena, vol.238, issue.6, 2009.
DOI : 10.1016/j.physd.2008.12.010

URL : http://arxiv.org/pdf/0712.3552

T. Pöschel and N. V. Brilliantov, Extremal collision sequences of particles on a line: Optimal transmission of kinetic energy, Physical Review E, vol.82, issue.2, 2001.
DOI : 10.1103/PhysRevLett.78.1596

A. Rosas, A. H. Romero, V. F. Nesterenko, and K. Lindenberg, Observation of Two-Wave Structure in Strongly Nonlinear Dissipative Granular Chains, Physical Review Letters, vol.24, issue.16, p.98, 2007.
DOI : 10.1103/PhysRevE.68.021303

M. Sadd, Q. Tai, and A. Shukla, Contact law effects on wave propagation in particulate materials using distinct element modeling, International Journal of Non-Linear Mechanics, vol.28, issue.2, pp.251-265, 1993.
DOI : 10.1016/0020-7462(93)90061-O

F. Santibanez, R. Munoz, A. Caussarieu, S. Job, and F. Melo, Experimental evidence of solitary wave interaction in Hertzian chains, Physical Review E, vol.45, issue.2, 2011.
DOI : 10.1103/PhysRevE.82.031305

URL : https://hal.archives-ouvertes.fr/hal-00624750

S. Sen, J. Hong, J. Bang, E. Avalos, and R. L. Doney, Solitary waves in the granular chain, Physics Reports, vol.462, issue.2, pp.21-66, 2008.
DOI : 10.1016/j.physrep.2007.10.007

S. Sen, F. Manciu, and M. Manciu, Thermalizing an impulse, Physica A: Statistical Mechanics and its Applications, vol.299, issue.3-4, pp.551-558, 2001.
DOI : 10.1016/S0378-4371(01)00340-5

A. Sokolow, E. G. Bittle, and S. Sen, Solitary wave train formation in Hertzian chains, Europhysics Letters (EPL), vol.77, issue.2, p.77, 2007.
DOI : 10.1209/0295-5075/77/24002

A. Sokolow, J. M. Pfannes, R. L. Doney, M. Nakagawa, J. H. Agui et al., Absorption of short duration pulses by small, scalable, tapered granular chains, Applied Physics Letters, vol.92, issue.25, 2005.
DOI : 10.1063/1.338151

W. J. Stronge, Impact Mechanics, 2000.
DOI : 10.1017/CBO9780511626432

L. Vergara, Model for Dissipative Highly Nonlinear Waves in Dry Granular Systems, Physical Review Letters, vol.92, issue.11, 2010.
DOI : 10.1007/BF02055765

O. Walton and R. Braun, Viscosity, granular???temperature, and stress calculations for shearing assemblies of inelastic, frictional disks, Journal of Rheology, vol.30, issue.5, pp.949-980, 1986.
DOI : 10.1122/1.549893

D. T. Wu, Conservation principles in solitary impulse propagation through granular chains, Physica A: Statistical Mechanics and its Applications, vol.315, issue.1-2, pp.194-202, 2002.
DOI : 10.1016/S0378-4371(02)01240-2

A. Yigit, A. Ulsoy, and R. Scott, Spring-dashpot models for the dynamics of a radially rotating beam with impact, Journal of Sound and Vibration, vol.142, issue.3, pp.515-525, 1990.
DOI : 10.1016/0022-460X(90)90665-M

C. Zener, The Intrinsic Inelasticity of Large Plates, Physical Review, vol.6, issue.8, pp.669-673, 1941.
DOI : 10.1103/PhysRev.15.277

D. Zhang and W. Whiten, The calculation of contact forces between particles using spring and damping models, Powder Technology, vol.88, issue.1, pp.59-64, 1996.
DOI : 10.1016/0032-5910(96)03104-X

H. Zhang and B. Brogliato, The planar rocking block: analysis of kinematic restitution laws, and a new rigid-body impact model with friction At http, 2011.

Z. Zhao, C. Liu, and B. Brogliato, Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations, Proc. R. Soc. A 465, pp.2267-2292, 2009.
DOI : 10.1115/1.2910825

URL : https://hal.archives-ouvertes.fr/hal-00755926