Biomedical Engineering Reference
In-Depth Information
Fig. 7.21 von Mises
effective stress field of the
central incisor obtained with
the NNRPIM
Table 7.2
Maximum principal stress results obtained for the analysis of the central incisor
r
1
(MPa)
Region1
Region2
Region3
Region4
Region5
Region6
Region7
Region8
CTRIA3
-9.80
17.00
57.10
-103.00
97.10
-
-
-
CQUAD8
-18.40
33.80
68.50
-123.00
138.00
-
-
-
NNRPIM
-12.84
27.67
65.74
-106.69
140.23
-86.75
160.37
-112.63
CQUAD8 FEM solutions were obtained with computational meshes with 9,259
nodes and 24,868 nodes respectively, showing that the NNRPIM is capable to
obtain good results with a lower discretization level.
7.2.1.2 Maxillary Bone Tissue Remodelling
The model presented in Fig.
7.20
is used to study the bone tissue remodelling
process of the maxillary bone supporting the central incisive. The same compu-
tational mesh with 4,245 nodes, Fig.
7.20
b, is used to discretize the problem
domain and the considered mechanical properties for the pulp, dentin, enamel and
periodontal ligament are indicated in Table
7.1
. As in previous examples, in the
model upper domain boundary the nodal displacements are constrained in both
directions, Fig.
7.20
b. The four load cases suggested in the literature [
8
], corre-
sponding to the normal solicitation of the incisor due to the daily mastication
activity, are considered in the present analysis.
The four load cases consist in localized loads F
i
¼ F
0
f
cos h
i
;
sin h
i
g
, being
the global force F
0
¼ 100 N and the total angle h
i
¼ 22
:
5
þ
a
i
, Fig.
7.20
b. Load
case 1 is obtained considering i = 5, load case 2 considers i = 4 and load cases 3
and 4 are obtained considering i = 3 and i = 2 respectively. In this work, to
eliminate local stress concentration, all the localized loads F
i
were distributed
along 5 boundary nodes.
For all studied examples, as required by the proposed remodelling algorithm, it
is considered
distribution q
max
app
¼ 2
:
1 g/cm
3
an initial uniform density
and a
