Elastoplastic deformation occurs widely in engineering impact. Although many empirical solutions of elastoplastic impact between two spheres have been obtained, the analytical solution, verified by means of other methods, to the impact model has not been put forward. This paper proposes a dynamic pattern of elastoplastic impact for two spheres with low relative velocity, in which three stages are introduced and elastic and plastic regions are both considered. Finite element analyses with various parameters are carried out to validate the above model. The numerical results prove to agree with the theoretical predictions very well. Based on this model, the dissipation nature of elastoplastic impact are then analyzed, and the conclusion can be drawn that materials with lower yield strength, higher elastic modulus, and higher mass density have better attenuation and dissipation effects. The study provides a basis to predict the particle impact damping containing plastic deformation and to model the impact damped vibration system enrolling microparticles as a damping agent.

1.
Wang
,
S.
, 2003, “
New Fine Particle Impact Damping and Its Structure
,”
Tenth International Congress on Sound and Vibration
, Stockholm, pp.
1635
1642
.
2.
Vu-Quoc
,
L.
,
Zhang
,
X.
, and
Walton
,
O. R.
, 2000, “
A 3-D Discrete Element for Dry Granular Flows of Ellipsoidal Particles
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
187
(
3–4
), pp.
483
528
.
3.
Wu
,
C. -Y.
,
Dihoru
,
L.
, and
Cocks
,
A. C. F.
, 2003, “
The Flow of Powder Into Simple and Stepped Dies
,”
Powder Technol.
0032-5910,
134
(
1-2
), pp.
24
39
.
4.
Weir
,
G.
, and
McGavin
,
P.
, 2008, “
The Coefficient of Restitution for the Idealized Impact of a Spherical, Nano-Scale Particle on a Rigid Plane
,”
Proc. R. Soc. London, Ser. A
0950-1207,
464
, pp.
1295
1307
.
5.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
,
Cambridge
, Secs. 6.1–6.4, 11.5, pp.
153
184
,
361
366
.
6.
Stronge
,
W. J.
, 1995, “
Theoretical Coefficient of Restitution for Planar Impact of Rough Elastoplastic Bodies
,” Impact, Waves and Fracture, ASME, Vol.
AMD-205
, pp.
351
362
.
7.
Thornton
,
C.
, 1997, “
Coefficient of Restitution for Collinear Collisions of Elastic Perfectly Plastic Spheres
,”
ASME J. Appl. Mech.
0021-8936,
64
, pp.
383
386
.
8.
Wu
,
C. -Y.
,
Li
,
L. -Y.
, and
Thornton
,
C.
, 2005, “
Energy Dissipation During Normal Impact of Elastic-Plastic Spheres
,”
Int. J. Impact Eng.
0734-743X,
32
(
1–4
), pp.
593
604
.
9.
Zhang
,
X.
, and
Vu-Quoc
,
L.
, 2002, “
Modeling the Dependence of the Coefficient of Restitution on the Impact Velocity in Elasto-Plastic Collisions
,”
Int. J. Impact Eng.
0734-743X,
27
, pp.
317
341
.
10.
Vu-Quoc
,
L.
, and
Zhang
,
X.
, 1999, “
An Elastoplastic Contact Force-Displacement Model in the Normal Direction: Displacement-Driven Version
,”
Proc. R. Soc. London, Ser. A
0950-1207,
455
, pp.
4013
4044
.
11.
Vu-Quoc
,
L.
,
Zhang
,
X.
, and
Lesburg
,
L.
, 2000, “
A Normal Force-Displacement Model for Contacting Spheres, Accounting for Plastic Deformation: Force-Driven Formulation
,”
ASME J. Appl. Mech.
0021-8936,
67
(
2
), pp.
363
371
.
12.
Plantard
,
G.
, and
Papini
,
M.
, 2005, “
Mechanical and Electrical Behaviors of Polymer Particles. Experimental Study of the Contact Area Between Two Particles. Experimental Validation of a Numerical Model
,”
Granular Matter
1434-5021,
7
(
1
), pp.
1
12
.
13.
Vu-Quoc
,
L.
,
Lesburg
,
L.
, and
Zhang
,
X.
, 2004, “
An Accurate Tangential Force-Displacement Model for Granular-Flow Simulations: Contacting Spheres With Plastic Deformation, Force-Driven Formulation
,”
J. Comput. Phys.
0021-9991,
196
(
1
), pp.
298
326
.
14.
Zhang
,
X.
, and
Vu-Quoc
,
L.
, 2007, “
An Accurate Elastoplastic Frictional Tangential Force-Displacement Model for Granular Flow Simulations: Displacement-Driven Formulation
,”
J. Comput. Phys.
0021-9991,
225
(
1
), pp.
730
752
.
15.
Mesarovic
,
S. Dj.
, and
Fleck
,
N. A.
, 1999, “
Spherical Indentation of Elastic-Plastic Solids
,”
Proc. R. Soc. London, Ser. A
0950-1207,
455
, pp.
2707
2728
.
16.
Mesarovic
,
S. Dj.
, and
Johnson
,
K. L.
, 2000, “
Adhesive Contact of Elastic-Plastic Spheres
,”
J. Mech. Phys. Solids
0022-5096,
48
(
10
), pp.
2009
2033
.
17.
Kogut
,
L.
, and
Etsion
,
I.
, 2002, “
Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat
,”
ASME J. Appl. Mech.
0021-8936,
69
, pp.
657
662
.
18.
Etsion
,
I.
,
Kligerman
,
Y.
, and
Kadin
,
Y.
, 2005, “
Unloading of an Elastic-Plastic Loaded Spherical Contact
,”
Int. J. Solids Struct.
0020-7683,
42
, pp.
3716
3729
.
19.
Weir
,
G.
, and
Tallon
,
S.
, 2005, “
The Coefficient of Restitution for Normal Incident, Low Velocity Particle Impacts
,”
Chem. Eng. Sci.
0009-2509,
60
(
13
), pp.
3637
3647
.
20.
Du
,
Y.
,
Wang
,
S.
,
Zhu
,
Y.
,
Li
,
L.
, and
Han
,
G.
, 2008, “
Performance of a New Fine Particle Impact Damper
,”
Adv. Acoust. Vib.
,
2008
, p.
140894
.
21.
Gladwell
,
G. M. L.
, 1980,
Control Problems in the Classical Theory of Elasticity
,
Sijthoff & Noordhoff
,
Germantown
.
22.
Yu
,
T.
, 1989,
Plasticity Mechanics
,
Higher Education
,
Beijing
.
23.
Rao
,
S. S.
, 1990,
Mechanical Vibrations
,
2nd ed.
,
Addison-Wesley
,
Reading, MA
.
24.
Panossian
,
H. V.
, 1992, “
Structural Damping Enhancement Via Non-Obstructive Particle Damping Technique
,”
J. Vib. Acoust.
0739-3717,
114
, pp.
101
105
.
This content is only available via PDF.
You do not currently have access to this content.