Structural analysis methods, Finite element calculation method

The bone segments, which together constitute the supporting structure of our body, are naturally structured following an evolutionary optimization process in order to support the static and dynamic loads deriving from all human activities.
Both the use of correction elements external to the bone and the insertion of elements in the bone environment substantially modify the behavior of the original structure. In the case of insertion of synthetic or prosthetic elements the alteration of the initial system is particularly complex as materials with extremely different mechanical characteristics and structural components with different stiffness are coupled. The occurrence due to a wrong design of a coupling between contiguous structural elements (bone synthesis element or prosthesis or implant) causes stress concentrations to be created in the bone structure and in the prosthetic or implant element that most of the time compromise the success of the operation causing micro-fractures, necrosis and bone resorption followed by detachments or ruptures of the implant.
For these reasons it is advisable to resort, upstream of any dental or orthopedic operation, to structural analyzes which, by quantifying the redistribution of the forces constituting the structure’s loading system and the variation of the stress state in the bone following a modification of external forces or the insertion of a foreign element which, due to the rigidity and mechanical characteristics of the material that constitutes it, alters its continuity, allows the design of orthotic, synthetic, prosthetic or implant systems which, in the first case, lead to the desired correction and other cases disturb the natural structural optimization of the bone structure to a minimum.
The mechanical bioengineer studies the bio-mechanical systems, constituted by the coupling of biological structures to artificial structures, adopting both experimental and theoretical methods of structural analysis. Depending on whether the analysis methods are experimental or theoretical, the models used can be physical or mathematical, ie described by a series of equations.
Experimental analyzes can be conducted in vivo or in vitro.
The mathematical formulation of the problem, regardless of the level of approximation achieved with the model, can be solved analytically, for example with beam theory, or numerically, for example with the finite element method.
The finite element method, known as Finite Element Method and with the FEM or FEA (Finite Element Analysis) acronyms, is currently the most valid instrument for conducting structural analyzes in the biomechanical field and in particular with applications in the odontostomatology and orthopedic field, ie when the biological structure involved is constituted by the bone tissue, since, together with a representation of the geometry of the bone elements that can be very satisfactory, it allows to approximate the continuous variation of the mechanical characteristics of the bone taking into account its inhomogeneity and anisotropy.
The term “finite elements” first appeared in the technical literature in 1960. This method originally introduced as a solution for solving structural mechanical problems was soon recognized as a general numerical approximation procedure applicable to all those physical problems that can be described . from a system of equations; it was also recognized that its roots, based on approximation processes, date back to the beginning of the century and that, in a more general definition, the finite element method unifies all alternative approximation processes, such as finite differences and solution methods to side dish.
A finite element model describes the four fundamental aspects of a structure (geometry, properties of constituent materials, load conditions, boundary and interface conditions).
The procedure consists in subdividing a complex structure into a set of simple geometric elements and well-defined characteristics, connected to each other. The schematization thus obtained simulates the real structure and allows the numerical resolution of the problem under examination, once the constraint and load conditions have been defined. The result of this initial procedure is called mesh (fig. 5).

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immediate loading implantology, screw implants, atraumatic implantology, painless implantology

Figure 5. Example of a finite element model of a human mandible

With the finite element method, therefore, the structural behavior of a continuous system (single body) is simulated, replacing it with a discrete system (body divided into several parts), consisting of a certain number of elements, from which the mechanical properties must then be defined. .
Thanks to this methodology it is possible to evaluate the physical behavior of single structures or complex structures formed by several components that interact with each other and then study voltage or temperature distributions or any other physical quantity in simple or complex bodies, homogeneous or heterogeneous, isotropic or anisotropic. In most of the finite element analyzes in the biomechanical field a linear elastic behavior of biological tissues is hypothesized.
The real skill of the analyst is to build a model that simulates reality well without exceeding in finesse of discretization in the points of scarce structural interest and in identifying the constraints and the loads that reflect the physics of the problem. The application of this method therefore requires a good basic theoretical knowledge that allows a targeted choice of the elements to be used, in relation to the analysis to be carried out, and a critical interpretation of the results obtained in light of the limitations and approximations of the method . It is also necessary to pay constant attention to the experimental analyzes that allow us to validate the hypothesized approximations.

Phases of the realization of a finite element model

The structural analysis of finite elements develops in the phases listed here:
• Preparation of the geometric model
• Discretization of the entire volume in finite elements (tetrahedrons or parallelepipeds) (fig. 6)
• Assignment of mechanical properties of materials
• Identification of loads and constraint points
• Choice of the type of solution (static or dynamic analysis, linear or non-linear, etc.)
• Analysis of the results

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immediate loading implantology, screw implants, atraumatic implantology, painless implantology

Figure 6. Example of finite elements used in the construction of three-dimensional models