Abstract

We investigate shock propagation in confined, frictionless granular media using discrete element simulations with an elastoplastic contact law. Depending on the level of confinement and loading, elastoplastic systems exhibit a weak or strong shock propagation response similar to an elastic Hertzian system although the details of the shock development differ markedly from the elastic case. Two modes of dynamic stress propagation are observed based on the shock intensity regime: weak shocks carry the stresses via the initial contact path while strong shocks form new contact networks behind the front. However, unlike for elastic shock propagation, there is an upper bound to the front velocity of strong shocks that depends on the maximum intergranular contact stiffness. Since elastoplastic contact is a dissipative process, results show that dissipation is enhanced with confining pressure in the weak shock regime.

References

1.
Nesterenko
,
V. F.
,
1983
, “
Propagation of Nonlinear Compression Pulses in Granular Media
,”
J. Appl. Mech. Tech. Phys.
,
24
(
5
), pp.
733
743
.
2.
Lazaridi
,
A. N.
, and
Nesterenko
,
V. F.
,
1985
, “
Observation of a New Type of Solitary Waves in a One-Dimensional Granular Medium
,”
J. Appl. Mech. Tech. Phys.
,
26
(
3
), pp.
405
408
.
3.
Coste
,
C.
,
Falcon
,
E.
, and
Fauve
,
S.
,
1997
, “
Solitary Waves in a Chain of Beads Under Hertz Contact
,”
Phys. Rev. E
,
56
(
5
), pp.
6104
6117
.
4.
Coste
,
C.
, and
Gilles
,
B.
,
1999
, “
On the Validity of Hertz Contact Law for Granular Material Acoustics
,”
Granular Matter
,
7
(
1
), pp.
155
168
.
5.
Daraio
,
C.
,
Nesterenko
,
V. F.
,
Herbold
,
E. B.
, and
Jin
,
S.
,
2005
, “
Strongly Nonlinear Waves in a Chain of Teflon Beads
,”
Phys. Rev. E
,
72
(
1
), p.
016603
.
6.
Cates
,
M. E.
,
Wittmer
,
J. P.
,
Bouchaud
,
J. P.
, and
Claudin
,
P.
,
1998
, “
Jamming, Force Chains, and Fragile Matter
,”
Phys. Rev. Lett.
,
81
(
9
), pp.
1841
1844
.
7.
Liu
,
C. H.
,
Nagel
,
S. R.
,
Schecter
,
D. A.
,
Coppersmith
,
S. N.
,
Majumdar
,
S.
,
Narayan
,
O.
, and
Witten
,
T. A.
,
1995
, “
Force Fluctuations in Bead Packs
,”
Science
,
269
(
5223
), pp.
513
515
.
8.
Liu
,
A. J.
, and
Nagel
,
S. R.
,
1998
, “
Jamming is Not Just Cool Any More
,”
Nature
,
396
(
6706
), pp.
21
22
.
9.
Majmudar
,
T. S.
, and
Behringer
,
R. P.
,
2005
, “
Contact Force Measurements and Stress-Induced Anisotropy in Granular Materials
,”
Nature
,
435
(
7045
), pp.
1079
1082
.
10.
Liu
,
C. h.
, and
Nagel
,
S. R.
,
1992
, “
Sound in Sand
,”
Phys. Rev. Lett.
,
68
(
15
), pp.
2301
2304
.
11.
Makse
,
H. A.
,
Gland
,
N.
,
Johnson
,
D. L.
, and
Schwartz
,
L.
,
2004
, “
Granular Packings: Nonlinear Elasticity, Sound Propagation, and Collective Relaxation Dynamics
,”
Phys. Rev. E
,
70
(
6
), p.
061302
.
12.
Jia
,
X.
,
Caroli
,
C.
, and
Velicky
,
B.
,
1999
, “
Ultrasound Propagation in Externally Stressed Granular Media
,”
Phys. Rev. Lett.
,
82
(
9
), pp.
1863
1866
.
13.
Somfai
,
E.
,
Roux
,
J.-N.
,
Snoeijer
,
J. H.
,
van Hecke
,
M.
, and
van Saarloos
,
W.
,
2005
, “
Elastic Wave Propagation in Confined Granular Systems
,”
Phys. Rev. E
,
72
(
2
), p.
021301
.
14.
Santibanez
,
F.
,
Zuñiga
,
R.
, and
Melo
,
F.
,
2016
, “
Mechanical Impulse Propagation in a Three-Dimensional Packing of Spheres Confined at Constant Pressure
,”
Phys. Rev. E
,
93
(
1
), p.
012908
.
15.
Goddard
,
J. D.
,
1990
, “
Nonlinear Elasticity and Pressure-Dependent Wave Speeds in Granular Media
,”
Proc. R. Soc. Lond. A: Math. Phys. Sci.
,
430
(
1878
), pp.
105
131
.
16.
Owens
,
E. T.
, and
Daniels
,
K. E.
,
2011
, “
Sound Propagation and Force Chains in Granular Materials
,”
Europhys. Lett.
,
94
(
5
), p.
54005
.
17.
Clark
,
A. H.
,
Petersen
,
A. J.
,
Kondic
,
L.
, and
Behringer
,
R. P.
,
2015
, “
Nonlinear Force Propagation During Granular Impact
,”
Phys. Rev. Lett.
,
114
(
14
), p.
144502
.
18.
Gómez
,
L. R.
,
Turner
,
A. M.
,
van Hecke
,
M.
, and
Vitelli
,
V.
,
2012
, “
Shocks Near Jamming
,”
Phys. Rev. Lett.
,
108
(
5
), p.
058001
.
19.
Gómez
,
L. R.
,
Turner
,
A. M.
, and
Vitelli
,
V.
,
2012
, “
Uniform Shock Waves in Disordered Granular Matter
,”
Phys. Rev. E
,
86
(
4
), p.
041302
.
20.
van den Wildenberg
,
S.
,
van Loo
,
R.
, and
van Hecke
,
M.
,
2013
, “
Shock Waves in Weakly Compressed Granular Media
,”
Phys. Rev. Lett.
,
111
(
21
), p.
218003
.
21.
Wang
,
E.
,
Manjunath
,
M.
,
Awasthi
,
A. P.
,
Pal
,
R. K.
,
Geubelle
,
P. H.
, and
Lambros
,
J.
,
2014
, “
High-Amplitude Elastic Solitary Wave Propagation in 1-D Granular Chains With Preconditioned Beads: Experiments and Theoretical Analysis
,”
J. Mech. Phys. Solids
,
72
(
5
), pp.
161
173
.
22.
Thornton
,
C.
,
1997
, “
Coefficient of Restitution for Collinear Collisions of Clastic-Perfectly Plastic Spheres
,”
J. Appl. Mech.
,
64
(
2
), pp.
383
386
.
23.
Pal
,
R. K.
,
Awasthi
,
A. P.
, and
Geubelle
,
P. H.
,
2013
, “
Wave Propagation in Elasto-Plastic Granular Systems
,”
Granular Matter
,
15
(
6
), pp.
747
758
.
24.
Brake
,
M. R. W.
,
2015
, “
An Analytical Elastic Plastic Contact Model With Strain Hardening and Frictional Effects for Normal and Oblique Impacts
,”
Int. J. Solids Struct.
,
62
, pp.
104
123
.
25.
Pal
,
R. K.
,
Awasthi
,
A. P.
, and
Geubelle
,
P. H.
,
2014
, “
Characterization of Wave Propagation in Elastic and Elastoplastic Granular Chains
,”
Phys. Rev. E
,
89
(
1
), p.
012204
.
26.
Burgoyne
,
H. A.
, and
Daraio
,
C.
,
2015
, “
Elastic–Plastic Wave Propagation in Uniform and Periodic Granular Chains
,”
J. Appl. Mech.
,
82
(
8
), p.
081002
.
27.
Waymel
,
R. F.
,
Wang
,
E.
,
Awasthi
,
A.
,
Geubelle
,
P. H.
, and
Lambros
,
J.
,
2018
, “
Propagation and Dissipation of Elasto-Plastic Stress Waves in Two-Dimensional Ordered Granular Media
,”
J. Mech. Phys. Solids
,
120
(
2
), pp.
117
131
.
28.
Pal
,
R. K.
, and
Geubelle
,
P. H.
,
2014
, “
Impact Response of Elasto-Plastic Granular and Continuum Media: A Comparative Study
,”
Mech. Mater.
,
73
, pp.
38
50
.
29.
Plimpton
,
S.
,
1995
, “
Fast Parallel Algorithms for Short-Range Molecular Dynamics
,”
J. Comput. Phys.
,
117
(
1
), pp.
1
19
.
30.
Zhang
,
J.
,
Majmudar
,
T.
,
Sperl
,
M.
, and
Behringer
,
R.
,
2010
, “
Jamming for a 2d Granular Material
,”
Soft Matter
,
6
(
13
), pp.
2982
2991
.
31.
Vu
,
T.-L.
,
Nezamabadi
,
S.
, and
Mora
,
S.
,
2020
, “
Compaction of Elastic Granular Materials: Inter-Particles Friction Effects and Plastic Events
,”
Soft Matter
,
16
(
3
), pp.
679
687
.
32.
Liao
,
C.-L.
, and
Chan
,
T.-C.
,
1997
, “
A Generalized Constitutive Relation for a Randomly Packed Particle Assembly
,”
Comput. Geotech.
,
20
(
3–4
), pp.
345
363
.
33.
Mouraille
,
O.
, and
Luding
,
S.
,
2008
, “
Sound Wave Propagation in Weakly Polydisperse Granular Materials
,”
Ultrasonics
,
48
(
6–7
), pp.
498
505
.
34.
Marsh
,
S. P.
,
1980
,
LASL Shock Hugoniot Data
, Vol.
5
,
University of California Press
,
Berkeley, CA
.
You do not currently have access to this content.