186
S. D. Arutyunov et al.
implantation [6], shape, and position corrections [7] are needed for computer-aided
simulations. Many high-level dental clinics are equipped by high performance system
for measuring different parameters such as compressive force, occlusion, and so on.
The recent progress in 3D techniques allows to reconstruct the geometry of dentation and profiles of the oral cavity by non-contact methods. Also, the progress in
3D techniques such as 3D scanning and 3D printing forced the dental specialists to
develop the personalized solution in implantation, prosthetics, and teeth repairing.
The personalized model has a quite complex shape close to the patient’s native structure, but the result of a such calculation are strongly depended on chosen models
of human soft tissues and corresponding boundary conditions. It is well known that
physical and mechanical properties of the bones and tissues are quite different for
different patients and cannot be correctly determined by non-destructive methods.
Moreover, these properties can change in time, age, sex, and other individual parameters. Therefore, a general model of denture is requested for the determination of the
main reaction of the prosthesis to the different geometry modifications. This model
should have a simple shape and clear physically based boundary conditions. Such
simple models are proposed for upper [8] and lower laminar prosthesis basis [9] with
the physically based boundary conditions.
The chapter is organized as follows. Section 14.2 provides a mathematical
modeling of laminar dentures of the upper and lower jaws. The boundary conditions and chewing loads are given in Sect. 14.3. Section 14.4 presents the results and
discussions, while Sect. 14.5 concludes the chapter.
14.2 Mathematical Modeling of Laminar Dentures
of the Upper and Lower Jaws
The simple models of upper and lower laminar prosthesis basis are presented in
Fig. 14.1. The model consists of two parts: denture blade (in pink color) and dentition.
The dentition is separated into four logical blocks: incisors, fang, premolars, and
molars. The prosthesis blade is assumed to be made of homogeneous and isotropic
material (Acryl plastic R) providing in Table 14.1. The thickness of the prosthesis
base is contestant at all locations and equal to 1 mm. The teeth models have visible and
hidden parts. The geometries for the dentition are taken from the work of Arutyunov
[10]. The visible part is shown in Fig. 14.1 while the hidden part is integrated into
the basis. The connection is realized by chemical bond that allows us to simulate this
contact as a full grip. The material for the teeth model is also assumed homogeneous
and isotropic with the following mechanical properties, Table 14.1.
The model of the upper prosthesis basis (Fig. 14.1a) has a shell-formed connection
of parts covering the alveolar ridges. Both models have special technological notches
that are used for cords pathing. The lower prosthesis basis has four such notches.
The poly methyl methacrylate acryl (PMMA) is the most common material used
to fabricate the complete and partial dentures [11–13]. According to literature data
S. D. Arutyunov et al.
implantation [6], shape, and position corrections [7] are needed for computer-aided
simulations. Many high-level dental clinics are equipped by high performance system
for measuring different parameters such as compressive force, occlusion, and so on.
The recent progress in 3D techniques allows to reconstruct the geometry of dentation and profiles of the oral cavity by non-contact methods. Also, the progress in
3D techniques such as 3D scanning and 3D printing forced the dental specialists to
develop the personalized solution in implantation, prosthetics, and teeth repairing.
The personalized model has a quite complex shape close to the patient’s native structure, but the result of a such calculation are strongly depended on chosen models
of human soft tissues and corresponding boundary conditions. It is well known that
physical and mechanical properties of the bones and tissues are quite different for
different patients and cannot be correctly determined by non-destructive methods.
Moreover, these properties can change in time, age, sex, and other individual parameters. Therefore, a general model of denture is requested for the determination of the
main reaction of the prosthesis to the different geometry modifications. This model
should have a simple shape and clear physically based boundary conditions. Such
simple models are proposed for upper [8] and lower laminar prosthesis basis [9] with
the physically based boundary conditions.
The chapter is organized as follows. Section 14.2 provides a mathematical
modeling of laminar dentures of the upper and lower jaws. The boundary conditions and chewing loads are given in Sect. 14.3. Section 14.4 presents the results and
discussions, while Sect. 14.5 concludes the chapter.
14.2 Mathematical Modeling of Laminar Dentures
of the Upper and Lower Jaws
The simple models of upper and lower laminar prosthesis basis are presented in
Fig. 14.1. The model consists of two parts: denture blade (in pink color) and dentition.
The dentition is separated into four logical blocks: incisors, fang, premolars, and
molars. The prosthesis blade is assumed to be made of homogeneous and isotropic
material (Acryl plastic R) providing in Table 14.1. The thickness of the prosthesis
base is contestant at all locations and equal to 1 mm. The teeth models have visible and
hidden parts. The geometries for the dentition are taken from the work of Arutyunov
[10]. The visible part is shown in Fig. 14.1 while the hidden part is integrated into
the basis. The connection is realized by chemical bond that allows us to simulate this
contact as a full grip. The material for the teeth model is also assumed homogeneous
and isotropic with the following mechanical properties, Table 14.1.
The model of the upper prosthesis basis (Fig. 14.1a) has a shell-formed connection
of parts covering the alveolar ridges. Both models have special technological notches
that are used for cords pathing. The lower prosthesis basis has four such notches.
The poly methyl methacrylate acryl (PMMA) is the most common material used
to fabricate the complete and partial dentures [11–13]. According to literature data