Manufacturing Simulation Using Finite Element - Finite Element Analysis for Satellite Structures - page 307

Fig. 7.33 Damage progress
of ductile material (ABAQUS
6.11 manual [ 19 ])

with a scalar damage equation. During simulation, the stress tensor for the current
material property is calculated according to the following equation,

r ¼ 1 D ð Þ r ð 7 : 7 Þ

r ¼ effective stress tensor
r ¼ damaged stress tensor
D ¼ Scalar damage variable

Figure 7.33 shows the material behavior under progressive damage. The onset
of damage is at point [r yo , e p o ]. e pl f is the equivalent plastic strain at failure. The
equivalent plastic strain e pl is mesh dependant, which makes estimating the
damage scalar parameter D not practical. In an effort to resolve this issue,
ABAQUS uses the equivalent plastic displacement u pl

instead, which is defined as,

e pl ð 7 : 8 Þ
Then damage evolution (D) as a function of the equivalent plastic displacement u pl
can be defined in linear or exponential form,

_ _

u ¼ð Element characteristic length)

1 exp ð a u pl
u pl
f

Þ

D ¼ _

u pl
u pl
f

or D ¼ ð 7 : 9 Þ

1 exp ð a Þ

where a is a material constant that can be adjusted to match experimental results.
A second parameter that can be used to match experimental results is the maxi-
mum degradation parameter D max at which ABAQUS deletes the elements from
the mesh. The default value of this parameter is (0.99).
Then, the reader can ask a question, why do we need parameters to adjust finite
element simulation results to match experimental ones? As in doing so it may
reduces the value of finite element analysis!. The answer is no, and the finite
element solution is as good as the material model used. The material models