In this dissertation, we developed cell stiffness as a biomarker in ovarian cancer for the purpose of grading metastatic potential. By measuring single cell stiffness with atomic force microscopy and quantifying in vitro invasiveness of healthy and cancerous ovarian cells, we demonstrated that cancerous ovarian cells have reduced stiffness compared to the healthy ones and invasive ovarian cancer cells are more deformable than noninvasive ovarian cancer cells. The difference in cell stiffness between two genetically similar cell lines was attributed to actin-mediated cytoskeletal remodeling as revealed by comparative gene expression profile analysis, and was further confirmed by fluorescent visualization of actin cytoskeletal structures. The actin cytoskeletons were innovatively quantified and correlates with cell stiffness distributions, further implicating actin-mediated cytoskeletal remodeling in stiffness alteration from the perspective of structure-property relationship. The correlation between stiffness and metastatic potential was also demonstrated in pancreatic cancer cell line AsPC-1, which shows reduced invasivess and increased stiffness upon treatment with N-acetyl-L-cysteine (NAC), a well known antioxidant, reactive oxygen species (ROS), scavenger and glutathione precursor. The correlation between cell stiffness and metastatic potential as demonstrated in ovarian and pancreatic cancer cells indicated that mechanical stiffness may be a useful biomarker to evaluate the relative metastatic potential of ovarian and perhaps other types of cancer cells, and might be useful clinically with the development of rapid biomechanical assaying techniques. We have also investigated the stiffness evolution through progression of the cell cycle for the healthy ovarian phenotype and the invasive cancer ovarian phenotype, and found that the healthy phenotype at G1 phase are significantly stiffer than other single cells except the invasive phenotype at late mitosis; other groups are not significantly different from each other. We have also investigated intracellular heterogeneity and mechanical nonlinearity in single cells. To this end, we developed a methodology to analyze the deformation-dependent mechanical nonlinearity using a pointwise Hertzian method, and tested the method on ultrathin polydimethylsiloxane (PDMS) films which underwent extremely large strains (greater than 50%). Mechanical stiffening due to large strain and geometrical confinement were observed. The onset of nonlinearity or mechanical stiffening occurs at 45% of the film thickness, the geometry induced stiffening causes an increase in stiffness which shows a strong power law dependence on film thickness. By applying the pointwise Hertzian method on stiffness measurements with AFM that were collected on living cells, we also investigated the nonlinear and heterogeneous mechanics of single cells, since attachment of cells to stiff substrate during indentation may impact their mechanical responses. Even under natural biological conditions, cells confined in narrow spaces may experience heightened mechanical stiffness. Through indentation-dependent force mapping, analysis of the local cell stiffness demonstrated spatial variation. The results indicated that the mechanical properties of single cells are highly nonlinear and are dependent upon the subcellular features under the applied force as well as the dimensions of the cellular material. We identified single cell stiffness as a potential biomarker of the metastatic potential in ovarian cancer, and quantified the effect of geometrical confinement on cell mechanics. The results presented in this dissertation not only made contributions to the development of accurate, non-invasive clinical methods to estimate metastatic potential of ovarian and perhaps other types of cancer, but also shed light on the intracellular mechanical information by developing new techniques to quantify the effect of geometry on cell mechanics.

The aim of this study is to evaluate a methodology for modeling the influence of crystallographic grain orientation on key parameters in normal and sliding contacts. The simulations of interfering cylindrical asperities, using finite element analysis, were conducted using two different plasticity models for copper: a conventional isotropic, homogeneous J2 plasticity model and a continuum crystal plasticity model. A normal contact study was conducted in which crystallographic orientation effects on different parameters were investigated. The model was then adapted for sliding contacts, which allowed other parameters such as energy dissipation to be investigated. Using crystal plasticity, the dependence of crystallographic orientation on plastic deformation and energy dissipation can be determined. The relative trends predicted using crystal plasticity are consistent with experiments that show friction depends on crystallographic orientation when plastic deformation is one of the primary energy dissipation mechanisms.

La simulation des systèmes multicorps avec une dynamique non régulière trouve ses applications dans différents domaines comme l'aéronautique, l'automobile, le ferroviaire, la robotique, la réalité virtuelle et même l'industrie horlogère. Ces industries ont de plus en plus d'exigences sur la rapidité ainsi que la précision des méthodes utilisées pour calculer la dynamique. Par conséquent, la recherche dans le domaine de la mécanique non régulière est très active et a pour objectif constant de proposer des algorithmes plus robustes et plus rapides pour calculer la dynamique ainsi que de développer de meilleurs modèles pour le contact avec ou sans frottement. Les méthodes proposées doivent en plus bien gérer les sauts dans la vitesse et l'accélération des systèmes, ces sauts résultent de phénomènes tels que l'impact et le frottement. Dans ce manuscrit, quelques méthodes d'intégration d'équations différentielles algébriques d'index 3, 2 et 1 sont testées sur plusieurs mécanismes industriels avec contraintes unilatérales et bilatérales. Ces méthodes sont ensuite comparées sur la base de la satisfaction des contraintes bilatérales, de l'efficacité numérique et de leur capacité à gérer une dynamique raide. Cette étude a aussi permis d'apporter une réponse claire sur le choix de la méthode d'intégration pour un système mécanique connaissant ses caractéristiques (nombre de contacts, présence de contraintes bilatérales, dynamique raide...). La deuxième partie de ce travail traite certains problèmes qui sont fréquemment rencontrés dans la simulation des systèmes multicorps, notamment: le phénomène d'accumulation des impacts, la résolution du frottement, ainsi que la gestion des sauts qui peuvent être provoqués par la présence de singularités géométriques. Calculer la dynamique dans ces cas est particulièrement difficile dans le cadre des schémas event-driven. La solution proposée est un schéma d'intégration mixte "event-driven/time-stepping" dont le but est d'utiliser les avantages de chacune des familles d'intégration (event-driven et time-stepping). Notre algorithme est ensuite testé sur de nombreux exemples. / The applications of the nonsmooth multibody systems field cover several fields including aeronautics, automotive, robotics, railway, virtual reality and watch industry to cite a few. These industrial applications have ever more stringent requirements on both accuracy and speed of the numerical methods used for the computation of the dynamics. As a consequence, the research in the nonsmooth mechanics domain is very active, to provide better integration methods for the resolution of the equations of motions and to develop better models for the contact problems with and without friction. Since the nonsmooth mechanics framework allows for jumps in the velocity and in the acceleration of the mechanical systems, the resulting algorithms have to handle such non-smoothness. In this PhD, several numerical schemes for the resolution of index-3, index-2 and index-1 DAEs are compared on industrial benchmarks with bilateral and unilateral constraints. The aim is to improve the efficiency of the Ansys Rigid Body solver which is based on an event-driven integration strategy. Points of comparison include the enforcement of the bilateral constraints, time efficiency and handling the stiff dynamics. This study also aimed at having a clear idea on the choice of the most suitable integration method for a given mechanical system knowing its characteristics (number of contacts, presence of bilateral constraints, stiff dynamics...). The second part discusses several issues that frequently occur in the simulation of multibody systems, namely, the problem of accumulation of impacts, the resolution of friction and handling the jumps resulting from the presence of some geometrical singularities. Dealing with such issues is very difficult, especially in the framework of event-driven schemes. In order to handle these problems, a mixed event-driven/time-stepping scheme is developed which takes advantage of both integration families (event-driven and time-stepping). Several examples are used to validate our methodology.

abstract: Current trends in the Computer Aided Engineering (CAE) involve the integration of legacy mesh-based finite element software with newer solid-modeling kernels or full CAD systems in order to simplify laborious or highly specialized tasks in engineering analysis. In particular, mesh generation is becoming increasingly automated. In addition, emphasis is increasingly placed on full assembly (multi-part) models, which in turn necessitates an automated approach to contact analysis. This task is challenging due to increases in algebraic system size, as well as increases in the number of distorted elements - both of which necessitate manual intervention to maintain accuracy and conserve computer resources. In this investigation, it is demonstrated that the use of a mesh-free B-Spline finite element basis for structural contact problems results in significantly smaller algebraic systems than mesh-based approaches for similar grid spacings. The relative error in calculated contact pressure is evaluated for simple two dimensional smooth domains at discrete points within the contact zone and compared to the analytical Hertz solution, as well as traditional mesh-based finite element solutions for similar grid spacings. For smooth curved domains, the relative error in contact pressure is shown to be less than for bi-quadratic Serendipity elements. The finite element formulation draws on some recent innovations, in which the domain to be analyzed is integrated with the use of transformed Gauss points within the domain, and boundary conditions are applied via distance functions (R-functions). However, the basis is stabilized through a novel selective normalization procedure. In addition, a novel contact algorithm is presented in which the B-Spline support grid is re-used for contact detection. The algorithm is demonstrated for two simple 2-dimensional assemblies. Finally, a modified Penalty Method is demonstrated for connecting elements with incompatible bases. / Dissertation/Thesis / Ph.D. Mechanical Engineering 2010

Dans cette thèse, nous développons une méthode locale de type "mortar" pour traiter le problème de contact avec maillages incompatibles de manière optimale dans un code de calcul par éléments finis de niveau industriel. Dans la première partie de la thèse, nous introduisons le cadre mathématique de la méthode intitulée "Local Average Contact" (LAC). Cette approche consiste à imposer la condition de non-interpénétration en moyenne sur chaque élément d'un macro-maillage défini de manière idoine. Nous commençons par développer une nouvelle technique de preuve pour démontrer l'optimalité des approches de type inéquation variationnelle discrétisée par éléments finis standards pour le problème de Signorini, sans hypothèse autre que la régularité Sobolev de la solution du problème continu. Puis nous définissons la méthode LAC et démontrons, à l'aide des nouveaux outils techniques, l'optimalité de cette approche locale modélisant le contact unilatéral dans le cas général des maillages incompatibles. Pour finir, nous introduisons la formulation mixte équivalente et démontrons son optimalité et sa stabilité. Dans la seconde partie de la thèse, nous nous intéressons à l'étude numérique de la méthode LAC. Nous confirmons sa capacité à gérer numériquement le contact unilatéral avec maillages incompatibles de manière optimale à l'instar des méthodes "mortar" classiques, tout en restant facilement implémentable dans un code de calcul industriel. On montre ainsi, entre autres, que la méthode passe avec succès le patch test de Taylor. Finalement, nous montrons son apport en terme de robustesse et au niveau de la qualité des pressions de contact sur une étude de type industrielle. / In this thesis, we develop a local "mortar" kind method to deal with the problem of contact with non-matching meshes in an optimal way into a finite element code of industrial level. In the first part of the thesis, we introduce the mathematical framework of the Local Average Contact method (LAC). This approach consists in satisfying the non-interpenetration condition in average on each element of a macro-mesh defined in a suitable way. We start by developing a new technique for proving the optimality of variational inequality approaches discretized by finite elements modeling Signorini problem without other hypothesis than the Sobolev regularity of the solution of the continuous problem. Then we define the LAC method and prove, using the new technical tools, the optimality of this local approach modeling the unilateral contact in the general case of non-matching meshes. Finally, we introduce the equivalent mixed formulation and prove its optimality and stability. In the second part of the thesis, we are interested in the numerical study of the LAC method. We confirm its ability to optimally treat the contact problem when considering non-matching meshes like standard "mortar" methods, while remaining easily implementable in an industrial finite element code. We show, for example, that the method successfully passes the Taylor patch test. Finally, we show its contribution in terms of robustness and at the quality of the contact pressures on an industrial study.

Orientador: Auteliano Antunes dos Santos Júnior / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-24T19:33:54Z (GMT). No. of bitstreams: 1 Fumes_FabianoGonzaga_M.pdf: 12049048 bytes, checksum: df4dc1dd45d74bbdc31c6a5893edd4fe (MD5) Previous issue date: 2014 / Resumo: Este trabalho apresenta a comparação entre os diversos critérios de fadiga multiaxial de alto ciclo aplicados ao problema de contato roda-trilho. Para isto, é utilizado um modelo elastoplástico tridimensional de elementos finitos capaz de permitir o cálculo tanto das tensões geradas pelo rolamento de uma roda livre de tensões residuais de fabricação como de uma roda que contenha as tensões residuais provenientes do processo de tratamento térmico, obtidas através de uma simulação térmico-estrutural. Estes dois cenários são avaliados segundo critérios de fadiga multiaxial baseados tanto em planos críticos, como Dang Van, Matake e McDiarmid, quanto nos baseados em invariantes do tensor de tensões, como Sines, Crossland e Kakuno Kawada. Pela natureza da fadiga de contato, que não possui condição de vida infinita, é estimado para cada critério um número de ciclos para o aparecimento das trincas. Como resultado, observa-se que para alguns critérios como Dang Van, Sines e Kakuno-Kawada, a vida em fadiga é beneficiada pelo processo de tratamento térmico, enquanto para os demais, as tensões residuais de fabricação provocam uma redução no número de ciclos para o aparecimento das trincas / Abstract: This work presents a comparison of different high cycle multiaxial fatigue criteria, applied to wheel- rail contact. For this, it is used a three-dimensional elastoplastic finite element model able to calculate stresses generated by the rolling of a wheel free of residual stresses from manufacturing process and also by a wheel containing the residual stresses from heat treatment process, generated by a thermal-structural simulation. These two scenarios are evaluated according to multiaxial fatigue criteria based on critical planes, as Dang Van, Matake and McDiarmid, and also based on the invariants of the stress tensor, as Sines, Crossland and Kakuno Kawada. Due to the nature of rolling contact fatigue, which has no condition of infinite life, a number of cycles for crack appearance are estimated for each criterion. It can be notice that for some criteria, such as Dang Van, Sines and Kakuno-Kawada, fatigue life is benefited by the heat treatment process, while for others the residual stresses from manufacturing promote a reduction in the number of cycles / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Les roulements à billes sont l’un des composants les plus importants et les plus critiques dans les turbomachines ou dans les éoliennes. Les butées à billes rencontrées dans les pieds de pales d’éoliennes doivent supporter des chargements très élevés, avec des bagues très fines par rapport aux dimensions du palier. Le roulement à quatre points de contact à haute vitesse est un autre exemple de bagues minces, où la cinématique interne est fortement liée à la géométrie des pistes qui elle, dépend de la rigidité des bagues et des logements. Pour cette application, les pistes intérieures et extérieures sont archées et bien souvent constituées de deux demi-bagues. La souplesse de ces dernières ainsi que celle du logement modifie la géométrie interne et l’interaction entre les composants. Il est proposé dans cette thèse un modèle permettant de dimensionner des roulements à billes à quatre points de contact, principalement dans le domaine d'application des turbines aéronautiques. Ce modèle est capable de rendre compte des déformations globales des bagues et de leur logement et environnement proche. Un ensemble de travaux existants et différentes possibilités envisagées pour la mise en place d’un modèle de roulement à bagues déformables est présenté pour définir une stratégie de couplage efficace entre un modèle analytique et un modèle éléments finis. La prise en compte de la souplesse des bagues s’appuie sur la résolution préalable d’un problème semi analytique de modélisation avec bagues rigides. Ensuite un couplage entre les résultats de ce modèle et un modèle éléments finis est réalisée pour prendre en compte la souplesse des bagues. Des choix sont nécessaires pour ce couplage, notamment sur la modélisation des contacts billes/bagues par l’utilisation de forces nodales pour simuler fidèlement ces contacts. Plusieurs méthodes sont ainsi évaluées pour calculer au mieux la nouvelle géométrie de la bague, en observant son comportement lorsqu'elle est soumise au contact d'une bille. Finalement, cette souplesse est intégrée au modèle semi analytique pour comparer le comportement d'un roulement à bagues rigides à celui d'un roulement à bagues souples. Des premiers résultats numériques sur une géométrie académique montrent des variations des grandeurs internes du roulement (angles de contact, ellipse de contact) ainsi qu’une meilleure répartition du chargement. Des essais ont été réalisés pour valider expérimentalement le modèle développé dans cette thèse. Les comparaisons par mesures du déplacement axial des bagues et des ondulations en surface des bagues montrent que la souplesse du support n’est pas négligeable, même dans le cas de bagues larges. Egalement, ces essais ont démontré la pertinence du couplage entre un modèle analytique et un modèle éléments finis pour rendre compte des déformations de bagues de roulements à billes à quatre points de contact. / Ball bearings are one of the most important and most critical part in turbomachine and wind turbine. They require a careful design in order to create reliability and economic relevance, which leads to compact bearings with high dynamic and static load capacity. Then ball bearing encountered in wind turbine must carry high loads, with thin rings regarding mean diameter of the bearing. High speed four point contact ball bearing is another example of thin rings, where internal kinematics is highly linked to raceway geometry, and raceway geometry depends on rings and housing stiffness. For this application, internal and external ring are arched and frequently made of two parts. There stiffness change the internal geometry and interaction with bearings components. It implies a change in load distribution and internal speed. As a consequence bearing and housing stiffness is an important parameter in order to estimate the admissible loads for the bearing. This thesis propose a model for the four point contact ball bearing, mainly for aeronautical turbine engine. This model can account for structural ring deformation as well as of housing deformation. Some existing work and different possibility for such a model are presented in order to define a coupling strategy between an analytical model and a finite element model. The accounting for ring stiffness rely on the resolution of a rigid ring semi analytical model. Then a coupling between this results and finite element results is done in order to account for ring stiffness. Some choices are made for the coupling, especially on ball/ring interaction by using nodal forces to model contact with fidelity. Some methods are evaluated to compute new ring geometry due to contacts with balls. Finally this stiffness is integrated in the semi analytical model in order to compare the behavior of rigid ring bearing with deformable ring bearing. First numerical results on an academic bearing shows change in internal parameter (contact angle, contact ellipse) and a better load distribution. Some experimental tests are made in order to validate the model presented in this thesis. Comparison on axial displacement and ring surface undulation shows that housing stiffness is not negligible even with large ring bearing. This tests show the relevance of a coupling between an analytical model and a finite element model in order to account for ring deformation in four point contact ball bearing.

Orientador: Katia Lucchesi Cavalca Dedini / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-22T07:50:24Z (GMT). No. of bitstreams: 1 Reis_VitorLuiz_M.pdf: 22501479 bytes, checksum: 7dcc42bed756f7cd1dc28e2f763f91ed (MD5) Previous issue date: 2013 / Resumo: Este trabalho apresenta o desenvolvimento de um modelo dinâmico para o mecanismo biela-manivela com folga na junta de revolução pino-pistão. As equações do movimento para este sistema são obtidas através do método de Lagrange e os efeitos relacionados ao contato, atrito e lubrificação que atuam nos elementos com folga são alvo de estudo. O modelo da força de contato utilizado baseia-se na formulação de Hertz, considerando a inclusão do efeito dissipativo associado ao impacto entre o pino e o pistão. A força de atrito adotada baseia-se no atrito de Coulomb, porém adaptada à abordagem da dinâmica multicorpos. Tais modelos são validados com os resultados encontrados na literatura recente. A pesquisa apresenta contribuição na avaliação do efeito introduzido pela lubrificação hidrodinâmica na junta com folga. Dois modelos de lubrificação hidrodinâmica são avaliados: o primeiro apresenta uma solução direta e de baixo custo computacional; o segundo modelo obtém uma solução numérica que leva em consideração o efeito da aceleração imposta ao fluido lubrificante pelo movimento do mecanismo. A resposta dinâmica é obtida sob a variação paramétrica do tamanho da folga e a velocidade de rotação da manivela. Ao final, agrega-se ao sistema um modelo simplificado de geração da curva de pressão para um motor de combustão interna típico. Observou-se que a inclusão do modelo de lubrificação proposto não garante a sustentação do pino-pistão em regime de lubrificação hidrodinâmica durante as simulações efetuadas. Desta maneira, faz-se necessário o desenvolvimento de um modelo de lubrificação hidrodinâmica e elastohidrodinâmica capaz de determinar o comportamento no contato pino-pistão de maneira mais realista / Abstract: This work presents the development of a dynamic model for the slider-crank mechanism with clearance on the piston-pin revolute joint. The equations of motion for this system are obtained by Lagrange's method and the effects related to contact, friction and lubrication at the elements that operate in the clearance are the targets of study. The contact force model used in this work is based on Hertz formulation, considering the inclusion of the dissipative effect associated with the impact between the pin and the piston. The frictional force adopted is based on the Coulomb friction but adapted to the multibody dynamics approach. Such models are validated with the results found in recent literature. The research presents contribution in evaluating the effect introduced by hydrodynamic lubrication in the revolute joint clearance. Two models of hydrodynamic lubrication are investigated: the first model presents a direct solution of low computational cost, the second model results in a numerical solution that consider the effect of the acceleration of the lubricant fluid imposed on the movement of the mechanism. The dynamic response is studied for different sets of parameters of clearance and rotational speed of the crank. Moreover, a simplified model of the generation of the pressure curve for a typical internal combustion engine was included in the system. It was observed that the present lubrication model does not guarantee the support of the pin-piston system for hydrodynamic lubrication in the present simulations. Therefore, it is necessary to develop a more realistic model of hydrodynamic lubrication and elastohydrodynamic lubrication that is capable of reproducing the behavior of the piston-pin contact / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Orientadores: Paulo Sollero, Eder Lima de Albuquerque / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-28T12:08:28Z (GMT). No. of bitstreams: 1 Shaterzadeh-Yazdi_MohammadHossein_M.pdf: 5411191 bytes, checksum: 83da697ff892a31af99059f3e88bd338 (MD5) Previous issue date: 2015 / Resumo: Em problemas de contato mecânico entre dois corpos elásticos, o cálculo de tensões e deformações dos componentes é de grande importância. Em casos particulares os corpos estão sujeitos a cargas normal e tangencial na presença de atrito, o qual aumenta a complexidade do problema. O estudo do fenômeno e a modelagem do problema, empregando o método dos elementos de contorno (MEC), é apresentado neste trabalho. Devido à presença de atrito e restrições de contato, esse problema torna-se um caso não linear. A não linearidade do problema foi contornada com a aplicação incremental de carga e o uso de um método de resolução de sistemas não lineares. A zona de contato é uma das variáveis do problema e pode conter estados de adesão e escorregamento, simultaneamente. Esses estados dependem dos esforços normais e tangenciais no componente e podem variar durante o processo de aplicação de carga. Dessa forma, cada incremento de carga pode perturbar em relação ao estado anterior. Portanto, o cálculo de variáveis e a atualização do sistema de equações em cada iteração é indispensável. Por este motivo, um algoritmo robusto para definição dos estados de contato é proposto. Como o sistema de equações obtido é não linear, o uso de um método numérico adequado é exigido. Para a solução deste sistema, o método de Newton foi aplicado, o qual permite a verificação do estado de contato em cada incremento. A análise é feita com o uso de elementos quadráticos contínuos, apresentando resultados contínuos e sem oscilação. A comparação dos resultados com as soluções analíticas de Hertz e Mindlin-Cattaneo mostram boa concordância / Abstract: The computation of stresses and strains on the components is of great importance, when the contact mechanics problems between two elastic bodies are analyzed. In particular cases, bodies are subjected to normal and shear loading in the presence of friction, which increases the complexity of the problem. The study of the phenomenon and modeling of the problem, using the boundary element method (BEM), are presented in this work. Due to the presence of friction and natural restrictions, this problem becomes non-linear. The non-linearity of the problem was solved with an incremental applied load and with the use of solvers to non linear systems. The contact zone can contain stick and slip states, simultaneously. These states are dependent on the normal and shear forces on the component and can vary during the application load process. Thus, each load increment can violate the previous state and therefore, the evaluation of variables and the updating of the system of equations after each iteration is indispensable For this reason, a robust algorithm for contact state definition is suggested. Since a non linear system of equations is obtained, an appropriate numerical method is required. To solve this system, Newton¿s method is applied, which allows the verification of the state of contact at each increment. The analysis is done with the use of quadratic continuous elements and provides continuous and non-oscillatory results. Comparisons of the results with the analytical solutions of Hertz and Mindlin-Cattaneo show good agreement / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

Nowadays, high demands are made on filling materials in modern dentistry: Durability, Reliability &Aesthetic Requirements Thus, a group of physicists and an independent practicing dentist investigated 11 different teeth fillings (composite materials) as used in modern dental practices according to their stability and ability to withstand contact loadings.