Finite Element Analysis or Finite Element Method is based on the principle of dividing a structure into a finite number of small elements. It is a sophisticated engineering tool, which has been used extensively in design optimization and structural analysis first originated in the aerospace industry to study stress in complex airframe structures. This method is a way of getting a numerical solution to a specific problem, used to analyze stresses and strains in complex mechanical systems. It enables the mathematical conversion and analysis of mechanical properties of a geometric object with wide range of applications in dental and oral health science. It is useful for specifying predominantly the mechanical aspects of biomaterials and human tissues that cannot be measured in vivo. It has various advantages, can be compared with studies on real models, and the tests are repeatable, with accuracy and without ethical concerns.
- finite element analysis
- finite element method
Dentistry is the fastest growing branch of medical field, deals with the study of diagnosis, prevention, and treatment of diseases, disorders, and conditions of the oral cavity. Although primarily associated with teeth, the field of dentistry is not limited to teeth but includes other aspects of the craniofacial complex including the temporomandibular joint (TMJ) and other supporting, muscular, lymphatic, nervous, vascular, and anatomical structures.
Virtually, every phenomenon in nature; whether biological, geological or mechanical, can be described with the aid of law of physics, in terms of algebraic, differential or integral equations relating various quantities of interest. Finite Element Analysis (FEA) or Finite Element Method (FEM) is a computer-based numerical method to analyze the structure based on the principle of dividing a structure into a finite number of small elements that are connected with each other at the corner points called nodes. For each element, its mechanical behaviour can be written as the function of displacement of the nodes. These nodes when subjected to certain loading conditions results in behaviour of the model similar to the structure it represents. When a computer analysis is performed on this, a system of simultaneous equations can be solved to relate all forces and displacement of the nodes. From this, stress and strain can be established in each element and the whole structure can be evaluated .
There were many articles published before on FEA and their uses, this chapter mainly focus on the brief application of FEA in dentistry, apart from the historical perspective, planning of analysis, workflow of FE study, merits, shortcomings, and future of FEA.
2. Historical perspective
The first researcher who developed this technique was Richard Courant, a mathematician with the main goal of minimizing the calculative procedures in gaining absolute solution to bio-mechanical system in early 1940’s. Turner et al
3. Planning of analysis
3.1.1 Specifying the title
It is specifying the name of the problem. This is optional but very useful, especially if a number of design iterations to be completed on the same base model.
3.1.2 Setting the type of analysis
In this, the type of analysis that is going to be used is done. Eg: structural, fluid, thermal or electromagnetic etc.
3.1.3 Creating the model
The model is drawn in 1-D (dimensional), 2-D, or 3-D space in the appropriate units (M, mm, inch etc.).
3.1.4 Defining the element type
This may be 1-D, 2-D, or 3-D.
3.1.5 Applying a mesh
Mesh generation is the process of dividing the analysis continuum into a number of discrete parts or finite elements. The finer the mesh, the better is the result but longer the analysis time.
3.1.6 Assigning properties
Material properties (Young’s modulus, Poisson’s ratio, density and if applicable coefficient of expansion, friction, thermal conductivity, damping effect, specific heat etc.) have to be defined in this step. In addition, element properties may need to be set.
3.1.7 Applying loads
Usually, some type of load is applied to the analysis model. The loading may be in the form of a point load, a pressure or a displacement in a stress (displacement) analysis. The loads may be applied to a point, an edge, a surface or even a complete body.
3.1.8 Applying boundary conditions
When applying a load to the model, in order to stop accelerating infinitely through the computer’s virtual ether, at least one constraint or boundary condition must be applied. A boundary condition may be specified to act in all directions - axes (x, y, z) or in certain directions only. They can be placed on nodes, key points, areas or on lines.
This part is fully automatic and it can be logically divided into three main parts: the pre-solver, the mathematical engine and the post-solver. The pre-solver reads the model created by the pre-processor and formulates the mathematical representation of the model. The results are returned to the solver and the post-solver is used to calculate strains, stresses, etc., for each node within the component or continuum.
Here the results of the analysis are read and interpreted. They can be presented in the form of a contour plot, a table, deformed shape of the component or the mode shapes and natural frequencies if frequency analysis is involved. Most post-processors provide an animation service, which produces an animation and brings the model to life. All post-processors now include the calculation of stress and strains in any of the x, y or z directions or indeed in a direction at an angle to the co-ordinate axes. The principal stresses and strains may also be plotted or if required the yield stresses and strains according to the main theories of failure.
In brief, the FE is a mathematical method for solving differential equations. It has the ability to solve complex problems that can be represented in differential equation form that occur naturally, in virtually all fields of the physical sciences. Accurate modeling is essential to ensure the relevance of the result for the corresponding FEA. The results solely depend on the model that has been created. Workflow of the entire finite element study is shown in Figure 2.
4. Application of FEA in oral radiology
Oral and maxillofacial radiology is the specialty of dentistry concerned with performance and interpretation of diagnostic imaging used in examining the dental, craniofacial, and adjacent structures. Use of FEA in this specialty helps for proper diagnosis and possibility of knowing iatrogenic effects.
Szücs et al
Oenning et al
Kihara et al
5. Application of FEA in restorative dentistry
Restorative dentistry refers to the diagnosis and integrated management of diseases of the teeth and their supporting structures and rehabilitation of the dentition for functional and esthetic requirements of an individual. Restorative dentistry. It is a broader term encompasses the dental specialties of endodontics, prosthodontics, and periodontics.
Many newer materials have been developed owing to the increasing interest in the field of esthetic dental restorations. In order to minimize the stress concentration of the restorative materials and to decrease the incidence of restorative failure; physical properties like modulus of elasticity should be near or equal to that of the natural dental tissue. Due to the lack of proper understanding on the biomechanical principles of the materials involved in restorative procedure, lead too many detrimental effects causing a restorative failure. Therefore, in order to know the behaviour of materials and dental tissue, biomechanical studies are very crucial [6, 7].
Goel et al
Rees in 2002 examined the effect of varying position of an occlusal load on the stress contour in the cervical region of a lower second premolar using a 2-D plane strain FEM. A 500 N load was applied vertically to either of the cusp tips or in various positions along the cuspal inclines. He found that, loads applied to the inner aspects of the buccal or the lingual cuspal inclines produced maximum principal stress values of up to 358 MPa, which is exceeding the known failure stresses for enamel .
Ausiello et al
Ausiello et al
Magne et al., in 2006 described a rapid method of generating FE models of dental structures and restorations. They evaluated five models: natural tooth, mesial-occlusal (MO), and mesial-occlusal-distal (MOD) cavities, MO, and MOD endodontic access preparations and found a progressive loss of cuspal stiffness in MO to MOD to endodontic access, as there is loss of tooth structure with these type of restorations. The natural tooth and the tooth with the MOD ceramic inlay retained 100% cuspal stiffness .
Ichim et al., in 2007 investigated the influence of the elastic modulus (
Asmussen et al., in 2008 analyzed the stresses generated in tooth and restoration by occlusal loading of Class-I and Class-II restorations restored with resin composite; suggested that the occlusal restorations of resin composite should have a high modulus of elasticity in order to reduce the risk of marginal deterioration .
Coelho et al
Magne and Oganesyan in 2009 measured cuspal flexure of intact and restored maxillary premolars with MOD porcelain, and composite-inlay restorations and occlusal contacts (in enamel, at restoration margin, or in restorative material). They found a relatively small cuspal deformation in all the models and an increased cusp-stabilizing effect of ceramic inlays compared with composite ones .
5.1 Dental composites
Composites are the resin restorative materials developed to overcome the disadvantages of amalgam restorations, which are unaesthetic and toxic. Composites are filled resins, exhibit high compressive strength, abrasion resistance, ease of application, and high translucency. FEA has been in use to analyze stresses generated in teeth and restorations. It is a proven useful tool in understanding biomechanics of tooth and the biomimetic approach in restorative dentistry .
Lee et al
Choi et al
Jongsma et al
5.2 Dental ceramics
Dental ceramics are in-organic, non-metallic, and brittle restorative materials producing dental prosthesis that are used to replace missing or damaged dental structures which has high compressive strength and low tensile strength. FEM provides a mathematic analysis to predict strength values without the potential for errors in dental ceramics .
Tensile stresses tend to be more critical than compressive stresses for ceramic materials. The strength of ceramic restorations is significantly affected by the presence of flaws or other microscopic defects. Tensile stress concentration at cementation surface of the ceramic layer suggested as the predominant factor controlling ceramic failure .
Belli et al. in 2005 evaluated the effect of hybrid layer on distribution and amount of stress formed under occlusal loading in a premolar tooth restored with composite or ceramic inlay. They concluded that the hybrid layer has an effect on stress distribution under loading in restored premolar tooth model with composite or ceramic inlay .
Rezaei et al
Thompson et al
Matson et al
6. Application of FEA in endodontics
Endodontology/Endodontics is the branch of dental sciences concerned with the form, function, health, injuries to and the diseases of the dental pulp and periradicular region, and their relationship with systemic health and well-being. Endodontic therapy involves either root canal filling techniques by conventional methods; or endodontic surgery with the use of biocompatible restorative materials, instruments, and techniques performed. The objective of endodontic instrumentation is to produce a tapered continuous preparation that should preserve the anatomy of root canal and maintain a good apical seal and foramen as small as possible, without any deviation from the original canal curvature .
During canal instrumentation, pressure is generated against the dentinal walls that may lead to inappropriate canal preparation or microcracks. These microcracks may lead to vertical fracture - one of the cause for tooth loss. During instrumentation, nickel-titanium (NiTi) are the commonly used for shaping the root canal. So, in order to perform well and avoid instrument breakage inside the canal, the material used and the technique performed should be followed meticulously. FEA helps to analyze and predict the treatment outcome .
Satappan et al
Hong et al
Subramaniam et al
Kim et al
Lee et al
Belli et al
6.1 Application of FEA in post and core
A considerable amount of tooth structure lost due to caries, endodontic therapy, and placement of previous restorations will compromise the tooth structure to resume its full function to serve satisfactorily. The type of the tooth restoring and the amount of remaining coronal tooth structure are the two factors that influence the choice of technique. The second factor is probably the key important indicator in determining the prognosis a tooth that is restored. If a substantial amount of coronal structure is missing, a cast post and core is indicated .
The method of restoring a structurally weakened tooth is post and core system, which is most common and widely used. This system can be categorized into two; custom cast metal posts and cores that are single piece, and a two component design comprising a prefabricated post to which other core materials is subsequently adapted. While fabricating a custom post and core, the difference in the elastic modulus of dentine and post material may be a source for root structure because of stress and debonding of posts due to stress contraction of the cement. Design of the post also effects the stress distribution, which was found as the most common mode of failure. Ferrule preparation creates a positive effect in reducing the stress concentration in an endodontically treated tooth. FEM can be used in various types of materials like carbon, metal, glass fiber, and zirconia ceramic and different configurations of dowel like smooth and serrated on the stress distribution of the teeth [6, 7].
Studies have showed that the increase in elastic modulus of post material cause decrease in the stress in dentin. However, Boschian et al., in 2006 have reported that higher the elastic modulus of post material than dentin can cause a dangerous, non-homogenous stress in root dentin. Also Silva et al., in 2009 reported that the stress distribution is more related to endodontically treated teeth restored with a post than the post’s external configuration. Therefore, whenever the clinician is planning to use a post he has to choose a post material, which has the stiffness similar to dentin. They evaluated the stress distribution in maxillary central incisor, which is endodontically treated and restored with fiberglass and metallic prefabricated posts .
Necchi et al
The use of glass fiber dowels showed less stress than the metal, carbon, and ceramic posts which few researchers found. However, there are some differences in the material properties, boundaries and loading conditions. A study by Eraslan et al., in 2009 showed a reduction in VM stress in an endodontically treated tooth restored with all-ceramic post and core than with zirconium oxide ceramic post and fiber post at the dentin wall and within the post .
In a study by Zhou et al
For fixation of post and core to the remaining tooth structure cements like zinc-phosphate, glass ionomer, resin-modified glass ionomer, and resin cement are used. The difference in elastic modulus of these cements, post materials and dentin results in stress concentration under function. In 2010, Soares et al., found zinc-phosphate and conventional glass ionomer cement producing high stress concentrations at dentin-cement interface. They also demonstrated that resin cement recorded higher fracture resistance values than other cements, which was in accordance with the study done by Suzuki et al., in 2008 .
A systematic review in 2010 by Al-Omiri et al
Al-Omiri et al
7. Application of FEA in prosthodontics and implantology
The branch of dentistry pertaining to the restoration and maintenance of oral function, comfort, appearance, and health of the patient by the restoration of natural teeth and/or the replacement of missing teeth and craniofacial tissues with artificial substitutes. FEA helps in studying the stress patterns and their distribution between the tooth and the material used in restoring the natural or missing tooth/teeth structure and predicting the favorable outcome with least chance of failure.
Zarone et al
FEA has been extensively used in implant dentistry to predict the biomechanical behaviour of various dental implant designs, as well as the effect of clinical factors for predicting the clinical success. Stress patterns in implant components and surrounding bone are well studied. The achievement of any FE study depends on the accuracy of simulating structures used. They are the material properties of implant and bone, surface characteristics and geometry of the implant and its components, loading method and support conditions, and the biomechanical behaviour of implant-bone interface. The prime difficulty in simulating the living tissues and the responses to the applied load can be successfully achieved with the use of advanced imaging techniques .
FEA gives an in-depth idea about the patterns of stress in the implant and more importantly in the peri-implant bone and this helps in the betterment of the implant design and implant insertion techniques. Several studies had been put forward on the effect of material properties of implant, implant number, size (length and diameter), thread profile, and on the quality and quantity of surrounding bone on stress distribution. The stresses of various kinds such as von Mises stress, maximum shear stress, maximum and minimum principal stress are used to assess the mechanical stress on the bone, implant, and bone-implant interface. Amongst, von Mises stress is most frequently and mainly used scalar-valued stress invariant to evaluate the yielding, and or failure behavior of dental materials. While minimum principal stress gives an idea on the compressive stress, maximum principal stress gives on tensile stress. Principal stress is used to study both ductile and brittle properties of a bone .
Siegele and Soltesz in 1989 conducted a study using implants of various shapes to evaluate the patterns of stress generation in the jawbone found that different shapes produced different stress patterns and conical implant showed higher stress than screw shaped and cylindrical implants .
Mailath et al
Geng et al
Chun et al., in 2002 found that the square thread shape filleted with a small radius was more effective in stress distribution than other dental implants used in the analyses also maximum effective stress decreased not only as screw pitch decreased gradually but also as implant length increased .
Himmlova et al
Ding et al., in 2009 conducted a study on immediate loading implants showed that the masticatory force around the implant neck was decreased with increased diameter of an implant. Several studies found higher risk of bone resorption occurring in the implant neck region. By using FEM, authors could able to compare the elastic modulus and deformation with different types of bone, and implant materials which helps clinicians to better understand the process of bone remodeling, and for further improvements in surgical techniques .
Eraslan et al., in 2009 evaluated the effects of different implant thread designs on stress distribution characteristics at supporting structures. Four different thread-form configurations for a solid screw implant was prepared with supporting bone structure. V-thread, buttress, reverse buttress, and square thread designs with a 100-N static axial occlusal load applied to occlusal surface of abutment to calculate the stress distribution. They found that the implant thread forms has no effect on von Mises stress distribution in the supporting bone, but produced dissimilar compressive stress intensities in the bone .
Dos Santos et al
Demenko et al
The increase risk of mechanical failure can occur with the increase in crown to implant ratio, which was substantiated by many FE studies. A study by Verri et al
7.1 Prosthesis for maxillectomy or hemi-mandiblectomy
FEA is important in predicting the success of implant supported prosthetic rehabilitation of maxillectomy patients. In case of maxillary or partial mandibular resection patients, FE models can be used to simulate the resection areas and biomechanics of maxillary obturator or mandibular partial or implant supported prosthesis can be studied. de Sousa and Mattos in 2014 conducted a study to evaluate the stability and functional stress caused by implanted-supported obturator prostheses in simulated maxillary resections of an edentulous maxilla corresponding to Okay Classes Ib, II, and III, with no surgical reconstruction. They found that the implant-supported obturator prostheses tended to rotate toward the surgical resection site, the region where there is no osseous support. As the osseous support and the numbers of implants and clips diminished, the tensile and compressive stresses in the gingival mucosa and in the cortical bone increased. They concluded that the osseous tensile and compressive stresses resulting from the bar-clip retention system for Okay Classes Ib, II, and III maxillectomy may not be favorable to the survival rate of implants .
8. Application of FEA in trauma and fractures
Oral and maxillofacial surgery is one branch of dentistry, which has always been associated with biomechanics. Trauma surgery, orthognathic surgery, reconstructive surgery are the subdivisions where understanding the mechanism of fractures and its biological response to the biomechanical change are worth knowing for optimal treatment method and outcome .
When present technology was not available in the past, cadaveric studies were the only way of information and it is not possible to carry out designing and executing which at present times have ethical issues often challenging to have valid and reliable results. Furthermore, post mortem alterations and the age do not match in a typical facial trauma cadaver. One such example was René Le Fort, a French army surgeon, conducted a series of thorough experiments on the heads of cadavers. His work gave rise to a system of classifying facial fractures, now known as Le Fort types I, II and III [36, 43].
Since the maxillofacial region has vital anatomical structures, intervention in this region needs precise work to be carried out in restoring function and esthetics of the tissues in obtaining predictable and favorable long-term outcomes. In the field of trauma surgery, to identify the craniofacial region that are potential prone to fracture, FEA enables precise mapping of the maxillofacial region to know the biomechanics and stress pattern distribution of trauma that helps in evaluation of patient and optimizing the surgical protocol for treating the fractures .
Today, with the help of FEA mechanical properties of facial hard and soft tissues, osteosynthesis materials, implant components for fixing the fractured parts, and various biological and synthetic bone substitutes can be easily generated and determined due to the advancement in the computing and virtual analysis. It allows the testing of various fixation system to prevent the future failure due to its improper selection or inappropriate positioning. It made us possible to know the impact in biomechanical behaviour of testing materials on the biological responses of the bone tested as well as adjacent anatomical structures more accurate, repeatable, time saving, and cost-effective way regardless of their complexity .
Isolated orbital floor fracture (IOFF), zygomatic bone fracture are the examples of more complex traumas occurring frequently in contact sports and their pathomechanism were also studied with the aid of FEA. In relatively rare facial traumas like in case of blast or gunshot wounds, FEA helps in exploring, analyzing and determining the mechanism of anatomical structures damaged and ways in reconstructing them. The pathomechanism underlying the type and method of fracture is exceptionally important as it may help in designing the helmets, other protecting devices. Rigid fixation is one of the key element in determining the long-term success for osseointegration. Inappropriate selection of an osteosynthesis component for the biological tissues can cause complication in fusion of bone. Therefore, FEA helps in determining and designing various fixation systems and methods [44, 45].
Osteosynthesis of condylar fracture and fixing the element is a challenging aspect for a maxillofacial surgeon due to its specific anatomy and surgical access. Through FEA, it has become possible for the researchers to find the better way and an exceptionally handy, easy mountable and durable element for optimal stabilizing and fixing the fractured fragments. A new type of “A-shape condylar plate” was designed for all levels of neck fractures and it can be used for stabilization of existed coronoid process fracture. FEA has proved to be a useful tool in investing and thorough evaluation of newer materials and solutions, which are more optimized, durable and light weight components before they can be used in the clinical situations .
Bujtár et al
Huempfner-Hierl et al
Murakami et al
Santos et al
9. Application of FEA in orthodontics and dentofacial orthopedics
Orthodontics is a specialty of dentistry, which deals with the diagnosis, prevention and correction of malpositioned teeth and jaws. It also focuses on determining and modifying the facial growth, known as dentofacial orthopedics. Abnormal alignment of the teeth and jaws is common. In the field of Orthodontics and Dentofacial Orthopedics, FEM has proved to be a reliable and valid procedure in evaluating the applied orthodontic forces.
Tanne et al
Many researchers have developed various FE models in order to understand the interaction between tooth mobility and periodontal ligament. Jones et al., in 2001 validated an FE model and found PDL as the main mediator for orthodontic tooth movement and the material properties of PDL are difficult to quantify .
The use of the lingual orthodontic technique has increased over time, as adults dislike the visibility of orthodontic appliances. Sung et al
Cattaneo et al., in 2009 studied on Orthodontic tooth movement (OTM) which occurs when an orthodontic force is applied to the brackets. The modeling and remodeling process of the supporting structures occurs by alteration in the distribution of stress/strain in the periodontium. As per the classical OTM theories, symmetric zones of compression and tension are present in the periodontium. However, they did not consider the complex mechanical properties of the PDL, the morphology of alveolar structures’, and magnitude of the applied force. The authors could not confirm the classical ideal of symmetrical compressive and tensile areas in periodontium as per the OTM scenarios. They found light continuous orthodontics forces will be perceived as intermittent by the periodontium. They expressed that, as the roots and alveolar bone morphology are patient-specific, FEA should not be based on general models .
Lingual orthodontics has developed rapidly in recent years; however, research on torque control variance of the maxillary incisors in both lingual and labial orthodontics is still limited. Liang et al
Field et al
9.1 Orthognathic surgery
Orthognathic surgery also known as corrective jaw surgery or simply jaw surgery is aimed to correct the conditions of jaw and face. They relate to correct the structure, growth modification, disorders of TMJ, sleep apnea, malocclusion problems owing to skeletal disharmonies, or other orthodontic problems that cannot be treated with orthodontic braces. It involves the surgical manipulation of the structures of the facial skeleton in restoring the suitable anatomy and their functional relationship with dentofacial skeletal abnormalities for the patient’s sense of self and well-being. Successful outcome depend on meticulous preoperative planning until finalization of occlusion. Virtual planning promotes a more accurate analysis of dentofacial deformity and preoperative planning with the help of computer-based technique like FEA, an invaluable tool in providing comprehensive patient education. Today’s orthognathic treatment consists of standard orthognathic procedure in correcting jaw deformities like maxillary and mandibular prognathism, open bite, difficulty in chewing and swallowing, TMJ dysfunction pain, excessive wear of the teeth, and receding chins. It includes adjunctive procedures like genioplasty, septorhinoplasty, and lipectomy of the neck to improve hard and soft tissue contours .
Chabanas et al
Erkmen et al
For successful outcome in any orthognathic surgeries, selection of an appropriate bridging element is a key determinant, corrective mandibular surgery like bilateral sagittal split osteotomy (BSSO) is not an exception to stabilize the bony segments with different fixing elements and FEA is an important tool .
Stróżyk et al
Surgically Assisted Palatal Expansion (SARPE) is an orthognathic surgical procedure that is performed frequently in the patients with narrower maxilla. De Assis et al
A more complex surgery involving correction of deformation of both the jaws simulating the maxillary and mandibular jaw osteotomy using FEA was also executed. Fujii et al
Knoops et al
10. Application of FEA in reconstructive surgery
The FEM technique can also be used in oncosurgeries and reconstructive surgery where an extensive resection is needed and reconstruction of jawbones are done. The crucial parameter form the postoperative point of view is the amount of bone segment removed from the surgical site, which includes size, shape, and location. The aim of reconstructing the bone defect should result in restoration of the integrity, its anatomy and the functionality of stomatognathic system. With the aid of digital technology; modeling, simulation and analysis, it is possible to know and compare the stress levels and distribution on and at the bone-graft interface and predictable behaviour of the reconstructed site to identify the most suitable transplant for a given clinical situation and to find the appropriate bone fusion under favorable conditions in the reconstructed area .
Moiduddin et al
Hu et al
11. Application of FEA in periodontics
PDL is a highly specialized soft connective tissue that is present between the tooth root and the alveolar bone. The primary function is to support the tooth and is the most important component of periodontium. Various studies included and investigated on its biomechanics and stress distribution under normal, masticatory, and traumatic loads. PDL is the crucial aspect in designing as it influences the properties of a 3-D model, though it is difficult in modeling and not a concern for the study. Ignoring the PDL may result in inaccurate values of stress and strain distribution .
Tuna et al
12. Merits of finite element method
Results can be easily interpreted in physical terms as well as it has a strong mathematical base.
Non-homogenous structures also can be dealt by merely assigning different properties to different elements.
It is even possible to vary the properties to different elements and within an element according to the polynomial applied.
It minimizes the requirement for laboratory testing, but not replaces entirely.
Applicable to linear and non-linear as well as solid and fluid structural interactions.
Any problems can be split into smaller number of problems.
It is very easy to simulate any biological condition in pre-operative, intra-operative, and post-operative stages for more accurate and reliable results.
Reproducibility of the results does not affect the physical properties of the materials involved.
It can replace stereo lithographic models for pre-surgical planning.
With FEA, static and dynamic analysis is possible.
It is less time consuming even with the complex structures.
No extensive instrumentation is required.
The study can be repeated as many times as the operator wants.
The systematic generality of finite element procedure makes it a powerful and versatile tool for a wide range of problems.
13. Shortcomings of FEM
The major drawback is sensitivity of the solution on the geometry of the element such as type, size, number, shape and orientation of element used.
FEM programs yield a large amount of numerical data as results and it is very difficult to separate out the required results from the pile of numbers.
Inability to simulate the biological dynamics of the tooth and its supporting structure accurately. For example, in non-carious cervical lesions, due to the exposure to oral environment the structure of dentin (tertiary or reparative dentin) undergoes variable amount of changes such as attrition, erosion or abrasion, which has formed as a response to stimulus.
Misguided results due to inaccurate data or information or interpretation.
Due to their complex anatomy and lack of complete knowledge about the mechanical behaviour, modeling of human structures are extremely difficult.
The results depend on the personnel involved in the process due to assumptions.
Until well-defined physical properties of enamel, dentin, PDL, cancellous, and cortical bone are available, the progress and the process in the FEA will be limited.
14. Advances in FEM
The non-linear simulation and dynamic behaviour of PDL and other soft tissue properties has become an increasingly powerful approach that provides precision and reliability in calculating stress and strain with a wide range of tooth movements.
The transient and residual stresses in dental materials are also included in non-linear FEM calculations also include. Residual stresses in ceramic and metal restorations, contraction stresses in composites, and permanent deformation prediction of materials are some to mention for non-linear application to be applied and investigated.
The phenomena of sliding and friction critically affect the stress and strain created on the contact surfaces between teeth that play a major role in the mechanical behaviour. This non-linear property can be solved by contact analysis depend various factors like region of contact, load, material, and environment that are highly unpredictable. The frictional response depends on the pair of surfaces in contact, temperature, and humidity.
Research is also going on polyhedral meshing and mesh-less (or mesh-free) analysis for reducing the meshing time. Advantages of polyhedral meshing being; less meshing time, high accuracy, and too less number of degrees of freedom (DOF).
Hybrid meshing (hex-pyram-tetra) is a very special option but not all software supports its application.
The power of the Finite Element Method is its versatility. It is a well-established numerical analysis used not only in aerospace, automotive industry and civil engineering, but also in health care. It addresses the biomedical problems that are challenging due to structural complexity. The structure analyzed may have arbitrary shape, arbitrary support, and arbitrary loads therefore; it is ideally suited for the analysis of bibliographical structures, which are non-homogeneous. The modeling and simulation of the structures and or materials saves time and money in conducting the experiment. Therefore, this tool has been successfully employed in various areas of dentistry.
A finite element analysis does not produce formula as a solution, nor does it solve a class of problems. This method is a way of getting a numerical solution to a specific problem. Finite element analysis is an accurate tool in assessing stress distribution, only of the given set of values are effective. However, it varies from person to person as the situation and biomechanical properties of living structures interpretation differs. Hence, the obvious shortcomings should be kept in mind before any decision making procedure in experimental as well as clinical dentistry. The experiments done are repeatable with no ethical concern and study designs can be modified as per the requirement. Certain limitations of FEA do exist. Keeping in mind the limitations, FEA research should be accompanied with clinical evaluation.
Conflict of interest
The authors declare no conflict of interest.