Facemask performance during maxillary protraction: a finite element analysis (FEA) evaluation of load and stress distribution on Delaire facemask
Gazzani et al. Progress in Orthodontics
Facemask performance during maxillary protraction: a finite element analysis (FEA) evaluation of load and stress distribution on Delaire facemask
Francesca Gazzani 0 2
Chiara Pavoni 0 1 2
Aldo Giancotti 0 2
Paola Cozza 0 1 2
Roberta Lione 0 1 2
0 Department of Clinical Sciences and Translational Medicine, University of Rome 'Tor Vergata' , Via Collazia 29, 00183 Rome , Italy
1 Department of Dentistry, UNSBC , Tirana , Italy
2 Department of Clinical Sciences and Translational Medicine, University of Rome 'Tor Vergata' , Via Collazia 29, 00183 Rome , Italy
Background: To evaluate load and stress distribution on Delaire facemask (FM) during maxillary protraction in class III growing patients by means of finite element analysis (FEA). A three-dimensional geometry of a Delaire FM was reconstructed from the original CAD 3D prototype, using software package (ANSYS 5.7). FM presented forehead and chin supports and stainless steel framework characterized by two lateral vertical bars connected to a crossbar with two pawls for elastic attachment. Two traction intensities (7.8 and 9.8 N) were applied on the FM pawls along three different downward inclined directions with respect to the occlusal plane (0°, 30°, or 50°, respectively). Resulting stresses and deformations were then tested through the von Mises yield criterion in order to underline the FM wear performance. Results: The analysis showed that higher stresses and deformations are mostly related to axial forces of 9.8 N rather than 7.8 N. Stresses also progressively increased with increasing downward force inclinations (0°, 30°, and 50° with respect to the occlusal plane). The overall tensions were inferior to the limit of the elastic behavior (yield point) characterizing the material they are applied on. Thus, the FM structure absorbed the load applied with an elastic deformation of the lateral and horizontal bars. Conclusions: Resulting stresses and deformations were directly proportional to protraction load amounts and to increasing downward inclination of forces. In all tested conditions, protraction forces were not able to determine plastic deformation on FM structure compromising its performance and efficiency.
Delaire face mask; Maxillary protraction; Class III malocclusion; FEM analysis
Maxillary protraction with facemask (FM) is an
orthopedic approach widely used in the treatment of class
III growing patients [
]. The FM was firstly
described more than 100 years ago, but its use was
lately diffused by Jean Delaire [
protraction therapy aims to transmit extra-oral tension
forces on the circum-maxillary sutures in order to
obtain a forward displacement of the maxilla stimulating
bone apposition in the suture areas and resulting in
an improvement of skeletal sagittal relationship [
]. Although several anchorage devices have been
] to maximize the efficiency of the
anchorage system, the Delaire FM design has never
been changed over the years. Delaire FM consists of
two extraoral anchorage regions, forehead and chin
cups, connected to rigid and square-shaped metal
]. Metal component is composed of
two lateral vertical bars and a crossbar with two
pawls for elastic attachment [
4, 9, 10
]. The horizontal
bar is connected to lateral vertical bars by means of
two cylindrical stainless steel latches. Both the FM
plastic and metallic components can be adjusted
individually to adapt the FM to the size of patient’s
face. Maxillary protraction usually requires 3.9 to
4.9 N of force per side with a downward inclination
of 30° with respect to the occlusal plane [
Previously, Tanne et al. [
] using finite element analysis
(FEA) concluded that the elastics have to be applied
with a variable downward direction of about 30° to
the occlusal plane in order to control the possibility
of an upward displacement of the maxillary complex
6, 7, 15, 17, 19
]. Although many studies [
have analyzed the stress and load distribution on the
facial complex during maxillary protraction by means
of FEA, no data are available in literature on the
mechanical properties of the FM. During maxillary
protraction treatment, the management of the FM
components plays an important role to control the
load application . Differences in magnitude,
direction, and duration of loads may produce several
patterns of displacement and distribution of forces on
maxillary complex [
]. Hence, the aim of the
present investigation was to evaluate the dislocation
and stress distribution on the FM structure by means
of three-dimensional (3D) FEA in order to use the
device under ideal conditions.
In order to perform the FEA, the following parameters
– Geometrical features of the FM;
– Material properties for each element of the FM;
– Mesh (number, shape, and size of the elements used
to discretize the FM)
– Constrains and loads applied on the system.
The ANSYS 5.7 software (Ansys Inc., Canonsburg,
PA, USA) was used for the FEA. According to the input
data, the software was able to solve the steady-state
condition of a rigid body in the space. In particular, the
system of algebraic equations was solved iteratively
until the convergence of the solution is reached. As for
the output data, the software evaluated the stress and
strain state of the rigid body. The 3D model of a
Delaire FM as originally described by Delaire
(M0774-01, Leone S.p.A., Florence, Italy) was
constructed and then the meshes were generated (Fig. 1).
The FM structure is composed by chin and forehead
supports in ABS plastic
(acrylonitrile-butadiene-styrene) and stainless steel framework. ABS and stainless
steel belong to different material chemistries with
difference in properties. ABS is a carbon chain copolymer
belonging to styrene ter-polymer chemical family. The
advantage of ABS is that it combines the strength and
rigidity of the acrylonitrile and styrene polymers with
the toughness of the polybutadiene rubber [
general, the most important mechanical properties of
ABS are high tensile strength, stiffness, high impact
resistance, and toughness [
]. Stainless steel is a
metal commonly used in orthodontics for its greater
strength, higher modulus of elasticity, and good
resistance to corrosion . Its hardness and strength are
greater when compared with ABS as shown by the
increment of tensile strength and Young’s modulus
(Table 2). The mechanical properties of each
component were incorporated in the 3D FM structure
(Table 2). The SOLID45 geometry (an element defined
by eight nodes) was used for the 3D modeling of solid
structures. The realized numerical model consisted of
40,178 elements (Fig. 2). Furthermore, the FEA was
then conducted to evaluate different constraint and
loading conditions. A FEA static simulation was
performed. Thus, the behavior of the FM was studied with
the application of a static load. The mesh phase and the
loads were applied thanks to the interactive interface of
the software. Two different traction intensities of 7.8
and 9.8 N were analyzed. The traction loads were
Fig. 2 3D model meshes. Twenty-eight thousand six hundred
ninetysix nodes and 40,178 elements characterized the numerical model
applied with three different downward inclinations with
respect to the occlusal plane (0°, 30°, or 50°) to
highlight the relationship between loads, characteristics of
the FM materials, constraints, and deformations. In
order to underline the displacement and stress
distribution on the FM structure, all the different conditions of
loads and constrains were evaluated according to von
Mises yield criterion. The amount of elastic energy
absorption was calculated for both intensity loads (7.8
and 9.8 N) inclined of 0° to the occlusal plane in order
to quantify the deformation state induced on the FM.
The results of the von Mises yield criterion are shown
in Figs. 3, 4, and 5. The resulting tensions are reported
in Newton per square millimeter (N/mm2). Tensile
strength distribution analysis showed that greater
stresses were assessed on the lateral bars of the
structure (Table 1, Fig. 3). When comparing protraction
intensities, the analysis showed that higher stresses and
deformations are mostly related to axial forces of 9.8 N
rather than 7.8 N. However, the overall tensions
observed in the simulated conditions were inferior to
the limit of the elastic behavior (Yield point)
characterizing the material they are applied on (stainless steel
limit 800 N/mm2; ABS limit 46 N/mm2) (Table 2).
Stresses progressively increased with increasing
downward force inclinations (respectively, 0°, 30°, and 50° to
the occlusal plane). The FM structure showed an elastic
behavior during its application without any implication
on the own functionality.
Early orthopedic treatment of maxillary protraction with
FM is recommended for class III growing patients [
]. Stresses and load distribution developed on
skeletal structures during maxillary protraction were
widely analyzed by means of FEA [
11, 13, 27
no studies exist in literature with regard to mechanical
properties of FM components and their behavior under
different tensile forces. Therefore, the objective of the
present study was to analyze the stresses generated
during maxillary protraction and their effects on FM
structure. The overall results did not highlight any risks of
permanent plastic deformations of the FM structures
related to the variables analyzed. Regarding load
conditions, the FEA confirmed that the maximum forces
analyzed (9.8 N) were inferior to the tensile strength of
structures’ materials (Table 2). The tensile strength is
defined as the maximum tensile stress a material can
endure without tearing [
]. Both plastic and metallic
structures presented values of tensile strength greater
than the stresses they were undergone. The maximum
tensions reported on the stainless steel structure are
200 N/mm2 while its tensile strength is equal to 800 N/
mm2. Similarly, the maximum tensions reported on the
chin cup and on the forehead support were 10 N/mm2
while the tensile strength of the ABS plastic is equal to
46 N/mm . The maximum stresses were observed on
the connection between the horizontal and lateral
vertical bars in correspondence of two cylindrical stainless
steel latches. Although high stresses transmitted on the
structure, the high value of the yield strength typical of
stainless steel granted the absence of plastic
deformation. The yield strength is defined as the amount of
stress (yield point) that a material can undergo before
moving from elastic deformation into plastic and
permanent deformation [
]. The yield point represents the
upper limit to forces that can be applied without
permanent deformation. In the present investigations, the
yield point of the mechanical components was always
under the limit. Highest forces (9.8 N) determined
greater stresses and more elastic deformations on the
FM structure when compared with lower 7.8 N.
However, no non-reversible plastic deformations and
consequently any effects on the device efficiency were
observed. A greater amount of stresses and tension loads
was observed when the downward force direction was
progressively inclined with respect to the occlusal plane
of 0°, 30°, and 50°. The 50° inclined plane was mostly
related to a plastic deformation of the structure with a
more dispersion of the force applied and a fewer
transmission of the forces on the maxillary complex. Thus,
the clinical application of 3.9 or 4.9 N of forces per side
with downward direction of about 30° to occlusal plane
] did not determine any damaging stresses on the FM
structure. Both the intensity of forces and the inclination
were correlated to an increment of the stresses
generated on FM structure during maxillary protraction
treatment without any possibility of plastic deformation. The
results obtained confirmed that the control of
magnitude, direction, and duration of force is able to grant
high FM performance and treatment predictability, since
plastic deformation significantly influences mechanical
efficiency and material performance. Thus, the clinical
control of the orthopedic force and the mechanical
properties of FM components preserve the structure
from any risks of damage allowing to use the FM under
A careful facemask management during orthopedic
treatment plays an important role in granting its best
performance and condition of use. Both the ABS chin
and frontal supports need to be individually adjusted
to fit the patient’s face maximizing the contact
surface with the skin for a homogeneous distribution of
the loads applied. In terms of magnitude, most
studies reported that heavy forces ranging from 7.8 to
9.8 N are important to induce a more efficient
maxillary growth and anterior displacement [
According to the existing literature [
results showed that the most favorable force vector
direction is represented by an inclination of 30° to
the occlusal plane. It allows a counterclockwise
rotation of the maxillary complex reducing stresses and
tensile forces on the facemask device. This parameter
is strictly related and conditioned to the position of
horizontal bar. Therefore, it is necessary to modify
the vertical position of the horizontal bar to calibrate
the force vector direction setting the inclination of
the elastics to 30° in downward direction. Finally, the
Delaire FM did not show permanent shape changes
and plastic deformations of the ABS and metallic
components when undergone heavy forces preventing
any risk of loads dispersion.
N Newton; mJ milliJoule, 1 mJ is equivalent to 0.001 J (Joule); ABS Acrilonitrile butadiene stirene
Tensile strength (N/mm2)
ABS Acrilonitrile butadiene stirene; MPa MegaPascal. 1MP a is equivalent
to 1 N/mm2
Amount of stresses and deformations are related to load
intensity and inclination of force direction. The clinical
application of 3.9 or 4.9 N of forces per side with
downward direction of about 30° to the occlusal plane did not
determine any plastic deformation on FM structure.
ABS: Acrylonitrile-butadiene-styrene; FEA: Finite Element Analysis; FM: Face
Mask; N: Newton
The authors wish to thank to Dr. Gabriele Scommegna for his advice in
performing the experimental analysis and Engineers Marouue J. and Gervasi
G.L. for their competence and scientific support.
Availability of data and materials
The materials and results obtained in this study by Finite Element Analysis
belong to the authors and are therefore available only upon request, after
approval by the author.
All authors contributed equally. All authors read and approved the final
Ethics approval and consent to participate
The authors declare that they have no competing interests.
Springer Nature remains neutral with regard to jurisdictional claims in published
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