This paper focuses on the application of the damage model for brittle materials proposed in the preceding paper on theory. The evolution rule of damage derived using the Onsager relations is specified according to the experimental observation. The loading-unloading condition is discussed and the tangent modulus is derived. Then, the determination of the modal parameters is presented. For verification, the proposed model is applied to concrete under uniaxial and biaxial loading, and the numerical results are compared with those of other researchers and with the experimental results. The results are generally in good agreement and the proposed model is considered worthy for further research work.

1.
Soh
,
C. K.
,
Liu
,
Y.
,
Yang
,
Y.
, and
Dong
,
Y.
,
2003
, “
A Displacement Equivalence Based Damage Model for Brittle Materials—Part I: Theory
,”
ASME J. Appl. Mech.
,
70
, pp.
1
7
.
2.
Dong
,
L. L.
,
Xie
,
H. P.
, and
Zhao
,
P.
,
1995
, “
Experimental Research on Complete Damage Process of Concrete Under Compression
,”
J. Exp. Mech. (China)
,
10
, pp.
95
102
(in Chinese).
3.
Fonseka
,
G. U.
, and
Krajcinovic
,
D.
,
1981
, “
The Continuous Damage Theory of Brittle Materials- Part 2: Uniaxial and Plane Response Modes
,”
ASME J. Appl. Mech.
,
48
, pp.
816
824
.
4.
Li
,
Q. B.
, and
Ansari
,
F.
,
1999
, “
Mechanics of Damage and Constitutive Relationships for Concrete
,”
J. Eng. Mech. Div.
,
125
, pp.
1
10
.
5.
Dong
,
L. L.
,
Xie
,
H. P.
, and
Li
,
S. P.
,
1996
, “
Continuum Damage Mechanics Constitutive Model of Concrete Under Compression
,”
J. Eng. Mech. (China)
,
13
, pp.
44
53
(in Chinese).
6.
Tasuji
,
M. E.
,
Slate
,
F. O.
, and
Nilson
,
A. H.
,
1978
, “
Stress-Strain Response and Fracture of Concrete in Biaxial Loading
,”
ACI J.
,
7
, (July), pp.
306
312
.
7.
Kupfer
,
H.
, and
Hilsdorf
,
K.
,
1969
, “
Behavior of Concrete Under Biaxial Stresses
,”
ACI J.
,
66
, pp.
656
666
.
8.
Liu
,
T. C. Y.
,
Tony
,
C. Y.
,
Nilson
,
A. H.
, and
Slate
,
F. O.
,
1972
, “
Stress-Strain Response and Fracture of Concrete in Uniaxial and Biaxial Compression
,”
ACI J.
,
69
, pp.
291
295
.
9.
Liu, Y., 2003, “Computational Experiment of Reinforced Concrete Structural Elements Using Damage Mechanics,” Ph.D. thesis, Nanyang Technological University, Singapore.
10.
Rots, J. G., 1998, “Computational Modeling of Concrete Failure,” thesis, Delft Univ. of Tech., Delft, the Netherlands.
11.
Ju
,
J. W.
,
1989
, “
On Energy-Based Coupled Elastoplastic Damage Theories: Constitutive Modeling and Computational Aspects
,”
Int. J. Solids Struct.
,
25
, pp.
803
833
.
You do not currently have access to this content.