The study of the biomechanical behavior of a system of dental implant, abutment and surrounding bone is essential for a thorough understanding of the load transmission generated by masticatory forces, to develop and optimize the implant design. This article presents an accurate numerical model of implant-abutment-bone system which is subjected to a masticatory loading simulated by axial and horizontal forces acting on the abutment. It is presented a three-dimensional finite element method calculation of stress, displacement, and safety factor, highlighting the influence of bone quality and critical zones of stress concentration by a numerical model as close as possible to reality. The stress distribution pattern is influenced by the loading type and localization, rather than its intensity. Stress values obtained with oblique loading forces are higher than with vertical ones. The loads acting on the structure may cause damage, micro-cracks, and not immediate failure or rupture. The bone quality has an important influence, obtaining lower stress values when the bone is weaker and less resistant to deformation. The novelty of the study consists in developing exclusively by means of computer programs of a geometric model that respects exactly all dimensions and shapes of an actual implant. Once the geometric model of great accuracy is constructed, simulations of various clinical cases can be performed through various loads, various types of materials, boundary conditions, etc. Our study results are consistent with clinical studies observations and similar results from the literature, highlighting critical areas of high stresses at the implant neck and its surrounding bone, potentially responsible for implant failure.

As osseointegration is a time-dependent process, biomechanical assessment is thought to determine whether a fibrous encapsulation or a bone covering will develop around an implant, according to the stress in the implant and surrounding bone. This study proposes a model for stress evaluation by finite element method (FEM) during the osseointegration progress, the main factor implied in implant success or failure. The loadings due to masticatory forces generate stress concentration and consequently, an adequate risk concerning the implant stability should be assessed. An accurate FEM model is used to calculate the stress and displacement in the whole implant–bone system during the osseointegration progress. This process is simulated by taking into account the gradual increase in the damaged biomechanical properties of the cortical bone. The results reveal that as the implant osseointegration occurs gradually, the bone stiffness from the peri-implant area increases gradually, such that in the end (healing) we observed that the cortical bone begins to take over the bending loading. In addition, the displacements decrease as the osseointegration gradually occurs and the cortical bone stress reaches higher values, which are placed in the mandibular ridge. The FEM is suitable to model the osseointegration progress, offering valuable information concerning the stress concentration zones in the implant–bone system and consequently, the risk evaluation, both for pre- and post-osseointegration.

Background: Telocytes (TCs) are unique interstitial or stromal cells of mesodermal origin, defined by long cellular extensions called telopodes (Tps) which form a network, connecting them to surrounding cells. TCs were previously found around stem and progenitor cells, and were thought to be most likely involved in local tissue metabolic equilibrium and regeneration. The roles of telocytes are still under scientific scrutiny, with existing studies suggesting they possess various functions depending on their location. Methods: Human myometrium biopsies were collected from pregnant and non-pregnant women, telocytes were then investigated in myometrial interstitial cell cultures based on morphological criteria and later prepared for time-lapse microscopy. Semi-analytical and numerical solutions were developed to highlight the geometric characteristics and the behavior of telocytes. Results: Results were gathered in a database which would further allow efficient telocyte tracking and indexing in a content-based image retrieval (CBIR) of digital medical images. Mathematical analysis revealed pivotal information regarding the homogeneity, hardness and resistance of telocytes’ structure. Cellular activity models were monitored in vitro, therefore supporting the creation of databases of telocyte images. Conclusions: The obtained images were analyzed, using segmentation techniques and mathematical models in conjunction with computer simulation, in order to depict TCs behavior in relation to surrounding cells. This paper brings an important contribution to the development of bioinformatics systems by creating software-based telocyte models that could be used both for diagnostic and educational purposes.

Numerical modeling is currently widely used in all branches of medicine. In this paper a numerical model of the biomechanical response of bone dental implant system to masticatory loading is presented. The geometrical model is accurately created and used to calculate the stale of stress in bone tissue and dental implant by finite element method. Different types of loadings due to masticatory forces are taken into account and emphasized their influences. The results obtained by the numerical model developed and presented herein are in good agreement with clinical observations and other results from literature.

Modeling living cells behavior is a delicate mission as it involves alike biological, physical, chemical, electrical aspects. This article presents a semi-analytical modeling for telopodes elongation, based on their appearance and behavior captured from in vitro approaches. The semi-analytical solution is determined solving a system of five coupled differential equations and the results are compared both with the numerical solution and with the results of the laboratory tests. A good agreement is obtained.

This paper is devoted to a numerical approach of the biomechanics behavior modeling of a dental implant supported prothesis made up of three elements, and the surrounding bone under the masticatory forces loading. A clinical situation involving both biological (the bone tissue) and non-biological (the three elements of implant prosthesis) materials is simulated. This problem involves fine technical structure details - the threads, tapers, etc with a great impact in masticatory force transmission. Modeling the contact between the implant and the bone tissue is important to a proper bone-implant interface model and implant design. A three-dimensional numerical model is proposed in order to calculate the state of stress and displacement of this complex structure in order to evaluate its stability by determining the risk zones of stress concentration. The results of numerical modeling are in good agreement with other numerical results and clinical cases A comparison between this numerical analysis and clinical cases is performed and a good agreement is obtained.

This paper examines a simplified mathematical model of the aircraft engine, based on the theory of linear and nonlinear systems. The dynamics of the engine was represented by a linear, time variant model, near a nominal operating point within a finite time interval. The linearized equations were expressed in a matrix form, suitable for the incorporation in the MAPLE program solver. The behavior of the engine was included in terms of variation of the rotational speed following a deflection of the throttle. The engine inlet parameters can cover a wide range of altitude and Mach numbers.

This paper is devoted to a numerical approach of the stress and displacement calculation of a system made up of dental implant, ceramic crown and surrounding bone. This is the simulation of a clinical situation involving both biological – the bone tissue, and non-biological – the implant and the crown, materials. On the other hand this problem deals with quite fine technical structure details – the threads, tapers, etc with a great impact in masticatory force transmission. Modeling the contact between the implant and the bone tissue is important to a proper bone-implant interface model and implant design. The authors proposed a three-dimensional numerical model to assess the biomechanical behaviour of this complex structure in order to evaluate its stability by determining the risk zones. A comparison between this numerical analysis and clinical cases is performed and a good agreement is obtained.

Telocytes are a novel interstitial cell type characterized by a small cell body and a number of one to five of extremely long and thin prolongations, named telopodes. This article proposes an analytical and numerical modeling for telopodes elongation, based on their appearance and behavior captured from in vitro approaches. Both the analytical and numerical solutions are developed for a viscoelastic model and they are compared and a good agreement is obtained.

The article is dedicated for identifying a mathematical model which describes the ensemble "pilotaircraft" as an integrated system, being pointed out the pilot's particularities for aircraft command. In the paper are presented two compensatory models, based on the aircraft dynamics. Several approaches of the pilot models (transfer function gain, lead and lag time constants) were considered to choose the methodology that better predicts the airplane dynamic handling quality requirements. Numerical investigations have been performed using Maplesoft environment.

In this paper, a complete biomechanical system made up of bone, implant and ceramic crown under axial loading is investigated by Finite Element Method (FEM). The system response evaluation has a major role in detecting the critical zones where possible damage, failure or rupture may occur jeopardizing the implant stability. Very accurate 3D geometrical model is used to calculate the stress, strain and displacement state in implant and surrounding bone. This analysis is completely concordant with clinical studies.

This paper presents both a numerical and an analytical approach for tunnel excavation and support mounting. The three-dimensional aspect of the tunnel face advance and the lining installation is simulated by a two-dimensional study assuming the hypothesis of gradual decompression of the primary stress on the outline of the tunnel. The numerical approach consists of a tunnel axis in an elasto-viscoplastic rock mass and a concrete elastic lining. This study emphasizes some important factors that influence the tunnel calculation, such as tunnel face, history of excavation phases, timing of the lining mounting, lining stiffness, and depth of the tunnel. The analytical approach is based on the determination and integration of the rock–lining interface differential equation. The author presents the analytical solution for (a) constant and non-constant lining pressure, and (b) taking into account the tunnel face influence. The comparison of the numerical results with the analytical solution is performed, and a good agreement is obtained.

This paper presents the constitutive aspects and a finite element application for an energetic damage criterion within Cristescu’s viscoplastic constitutive law. The numerical model is implemented in finite element code LCPC-CESAR [1] by the author. The numerical solution is used to perform an analysis of the evolution of the damage zones around a circular lined cavity in a viscoplastic material subjected to a far field stress. Two important factors regarding the opening stability, namely the lining mounting time and the tunnel face influence, are analyzed. The initial stress of rock mass varies with the depth at which the tunnel is excavated and this fact determines a bigger displacement of the tunnel bottom than the tunnel ceiling. The time emphasizes this asymmetry. The results obtained are in completely accordance with the practical observations.

This paper is devoted to an analytical approach of the supported tunnel calculation taking into account the tunnel face effect. This is simulated by a two dimensional study assuming the hypothesis of gradual decompression of the primary stress on the outline of the tunnel. The analytical approach is based on the determination and integration of the rock-lining interface differential equation for viscoelastic rock mass. The author extends the solution for taking into account the tunnel face proximity. A comparison between the analysis without the face influence and the analysis with the face influence is presented and a more economical lining design can be predicted in the framework of the last case. The comparison of the analytical solution with numerical results is performed and a good agreement is obtained.

This paper deals with analytical solutions for the bending deformation of rectangular orthotropic elastic composite plates with various boundary conditions. The models are based on the classical laminated plate theory (CLPT). The Ritz method, in conjunction with the weighted residue method for the coefficients calculation is used to analytically determine the bending solutions of orthotropic laminated plates subjected to uniform pressure on the bottom laminate, having clamped edges or possessing two opposite edges simply supported and the remaining two edges clamped, respectively. Numerical examples of laminated plates considering similar boundary value problems as treated analytically are presented. It is presented the experimental device and the experimental test results, as well. Thorough comparison between analytical solutions, numerical results and experimental data is performed and a good agreement is obtained.

© 2012 Roatesi, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Finite Element Analysis for the Problem of Tunnel Excavation Successive Phases and Lining Mounting

This paper presents a finite element application for an energetic damage criterion within Cristescu's elasto-viscoplastic constitutive law. The numerical model is implemented in finite element code LCPC-CESAR by the author. The numerical solution is used to perform an analysis of the evolution of the damage zones around a circular cavity in an elasto-viscoplastic material subjected to a far field stress and an internal pressure on the cavity walls. The numerous figures and the results presented are in completely concordance with the practical observations.

This paper deals with the domain of the physico-chemical exchanges coupling and of the poromechanical behavior of clay. A short presentation of the constitutive model, a semianalytical solution for the borehole problem and the numerical formulation of a chemo-poroelastic model are presented. The variational fomulation imposes certain restrictions on some constituive parameters of the model that is important for the model calibration. The solution of a borehole drilled in a chemically active shale layer using the model is presented as a validation for further FEM implementation of the problem. Borehole mud pressure at rupture via Mohr-Coulomb criterion is also calculated in the framework of the model.

This paper analyses the successive phases of a tunnel excavation in a viscoplastic rock mass with an elastic lining mounting. Tunnel face advancing and the support installing yield to a 3D problem, depending on many parameters as time, influence of the tunnel face, history of excavation phases, etc. The aim of this analysis is to reduce the problem to 2D study, as realistically as possible. The study is performed for a circular tunnel and a hydrostatic primary stress state of the rock mass, that determine an axisymmetrical problem. Some theoretical consideration concerning the 3D redistribution of excavation-induceed stresses exploring the near-field stress paths during the progressive face advancement, with a brief presentation of the hypothesis of gradual decompression of the primary stress on the outline of the tunnel, is also performed. The FEM solution is presented by numerous figures and the results are in completely concordance with the practical observations.