The Generalized Finite Element Method (GFEM) is a numerical method based on the Partition of Unity (PU) concept and inspired on both the Partition of Unity Method (PUM) and the hp-Cloud method. According to the GFEM, the PU is provided by first-degree Lagragian interpolation functions, defined over a mesh of elements similar to the Finite Element Method (FEM) meshes. In fact, the GFEM can be considered an extension of the FEM to which enrichment functions can be applied in specific regions of the problem domain to improve the solution. This technique has been successfully employed to solve problems presenting discontinuities and singularities, like those that arise in Fracture Mechanics. However, most publications on the method are related to linear analyses. The present thesis is a contribution to the few studies of nonlinear analyses of Solid Mechanics by means of the GFEM. One of its main topics is the derivation of a segment-to-segment generalized contact element based on the mortar method. Material and kinematic nonlinear phenomena are also considered in the numerical models. An Object-Oriented design was developed for the implementation of a GFEM nonlinear analyses framework written in Python programming language. The results validated the formulation and demonstrate the gains and possible drawbacks observed for the GFEM nonlinear approach. / O Método dos Elementos Finitos Generalizados (MEFG) é um método numérico baseado no conceito de partição da unidade (PU) e inspirado no Método da Partição da Unidade (MPU) e o método das Nuvens-hp. De acordo com o MEFG, a PU é obtida por meio de funções de interpolação Lagragianas de primeiro grau, definidas sobre uma rede de elementos similar àquela do Método dos Elementos Finitos (MEF). De fato, o MEFG pode ser considerado uma extensão do MEF para a qual se pode aplicar enriquecimentos em regiões específicas do domínio, buscando melhorias na solução. Esta técnica já foi aplicada com sucesso em problemas com descontinuidades e singularidades, como os originários da Mecânica da Fratura. Apesar disso, a maioria das publicações sobre o método está relacionada a análises lineares. A presente tese é uma contribuição aos poucos estudos relacionados a análises não-lineares de Mecânica dos Sólidos por meio do MEFG. Um de seus principais tópicos é o desenvolvimento de um elemento de contato generalizado do tipo segmento a segmento baseado no método mortar. Fenômenos não lineares devidos ao material e à cinemática também são considerados nos modelos numéricos. Um projeto de orientação a objetos para a implementação de uma plataforma de análises não-lineares foi desenvolvido, escrito em linguagem de programação Python. Os resultados validam a formulação e demonstram os ganhos e possíveis desvantagens da abordagem a problemas não lineares por meio do MEFG.

Le but du travail présenté est la compréhension puis la simulation numérique des mécanismes d'érosion des augets de turbine Pelton par impacts répétés de gouttes d'eau dans le but de prédire la durée de vie des composants. Tout d'abord, les phénomènes de propagation d'ondes dans les milieux fluide et solide sont étudiés. Cela permet de mettre en lumière l'évolution temporelle et la distribution spatiale des pressions de contact, et l'apparition de microjets par éjection supersonique du fluide au contact. Les études expérimentales de l'érosion par gouttes d'eau traduisent un dommage basé sur la fissuration par fatigue. Des simulations numériques en dynamique rapide couplées fluide-structure sont alors effectuées. Le domaine solide est discrétisé par la Méthode des éléments Finis (MEF), et le domaine fluide par la méthode Smoothed Particle Hydrodynamics (SPH), qui est une méthode particulaire (sans maillage) particulièrement adaptée aux grandes distorsions et au suivi des surfaces libres. L'analyse des états de contraintes vient corroborer la nature cyclique de l'endommagement. La simulation d'érosion est alors réalisée à l'aide de critères de fatigue multiaxiaux. Le choix se porte vers un premier critère général de l'American Society of Mechanical Engineers (ASME), utilisant les valeurs principales des différences de contraintes au cours du temps. Le second choix concerne un critère à plan critique : le critère de Dang Van 2. Il traite séparément la contrainte hydrostatique et le cisaillement alterné maximal local. Ces critères permettent de définir les régions érodées du solide au bout d'un nombre d'impact donné, ce qui fait de cette démarche une méthode prédictive. Une étude paramétrique pour différentes tailles de gouttes et vitesses d'impact est ensuite réalisée, puis on évalue l'influence de la présence d'une couche de coating. / The goal of this work is the comprehension and the numerical simulation of erosion caused by repeated droplet impact on Pelton turbine buckets, to predict the lifetime of these components. First, waves propagation phenomenon inside fluid and solid domains are presented, which allows determining the time evolution and spatial distribution of contact pressure, and the birth of lateral microjets by supersonic ejection of the fluid on the contact. Experimental studies of erosion by droplet impact highlight a fatigue cracking-based erosion mechanism. Then, coupled FSI computation are performed. The solid subdomain is discretized by the Finite Element Method (FEM), and the fluid subdomain by the Smoothed Particle Hydrodynamics (SPH), which is a particle method (meshless) effectively recommended for large distortions and free surface tracking. Stress analysis confirms the cyclic nature of the damage mechanism, and erosion simulation is performed using multiaxial fatigue criteria. The first selected criterion is a general one from the American Society of Mechanical Engineers (ASME) using principal values of stress differences over time. The second one is the Dang van 2 criterion, belonging to the family of critical plane criteria. This criterion considers separately the effects due to hydrostatic stress on one hand, and the ones induced by maximum local shear on the other. These two criteria are used to building the equivalent eroded zones of the solid subdomain for a given number of impacts, which allows to qualify this procedure as a predictive predictive. Finally, a parametric study for different droplet sizes and velocites is computed, and the effects of a coating layer are investigated.

"Mammalian skeletal muscle is a very complicated biological structure to model due to its non-homogeneous and non-linear material properties as well as its complex geometry. Finite element discrete one-dimensional Hill-based elements are largely used to simulate muscles in both passive and active states. There are, however, several shortfalls to utilizing one-dimensional elements, such as the impossibility to represent muscle physical mass and complex lines of action. Additionally, the use of one-dimensional elements restricts muscle insertion sites to a limited number of nodes causing unrealistic loading distributions in the bones. The behavior of various finite element muscle models was investigated and compared to manually calculated muscle behavior. An improved finite element muscle model consisting of shell elements and Hill-based contractile truss elements in series and parallel was ultimately developed. The muscles of the thigh were then modeled and integrated into an existing 50th percentile musculo-skeletal model of the knee-thigh-hip complex. Impact simulations representing full frontal car crashes were then conducted on the model and the pre-loading effects from active thigh muscles on the femur were investigated and compared to cadaver sled test data. It was found that the active muscles produced a pre-load femoral axial force that acted to slightly stabilize the rate of stress intensification on critical stress areas on the femur. Additionally, the active muscles served to direct the distribution of stress to more concentrated areas on the femoral neck. Furthermore, the pre-load femoral axial force suggests that a higher percentage of injuries to the knee-thigh-hip complex may be due to the effects of active muscles on the femur. "

La thèse concerne la prévision du comportement dynamique non linéaire d’équipements optique. Les travaux de recherche menés se concentrent sur la simulation des phénomènes vibratoires en jeu, afin de prévoir la réponse harmonique de l’équipement. Ces travaux ouvrent ainsi la voie à des préconisations d’évolutions dans la conception mécanique du projecteur pour augmenter sa durabilité et le confort de vision. En effet les essais pratiqués montrent que de forts niveaux de vibrations endommagent les composants du projecteur et détériorent la stabilité du faisceau d’éclairage. Afin d’éviter de telles nuisances, la conception du projecteur doit être adaptée grâce à un modèle mécanique qui intègre des comportements non linéaires causés essentiellement par les liaisons pour prévoir le mieux possible les niveaux de vibrations du projecteur embarqué. L’état de l’art est réalisé sur les comportements dynamiques non linéaires, les modèles et méthodes de résolution associés, puis les estimateurs existants de quantification des non linéarités. Les essais d’analyse modale réalisés mettent en évidence la présence de phénomènes non linéaires dus à de multiples causes (jeux-butées, frottements, stick-slip, …) localisées dans les liaisons réflecteur-boitier. Les caractérisations expérimentales menées sur les liaisons, délivrent des boucles efforts-déflexion qui montrent différents types de comportement non linéaire, aident au choix des modèles les plus pertinents et au calage de leurs paramètres. Les limites de validité des modèles de calculs linéaires sont déterminées par des critères formulés empiriquement. Les modèles non linéaires de liaison sélectionnés sont intégrés dans un modèle réduit à un puis à deux degrés de liberté d’un projecteur. La réprésentativité du modèle est évaluée sur la base des analyses modales mesurées du projecteur. Les équations décrivent le comportement dynamique de projecteur et les non linéarités sous l’hypothèse de régime stationnaire. La méthode de balance harmonique associée à une technique de continuation par longueur d’arc résout rapidement les équations et détermine avec précision les réponses dynamiques établies. L’étude est complétée par l’analyse de stabilité selon la théorie de Floquet qui met en évidence la présence des branches de solutions stables ou instables. Enfin des réponses harmoniques sont calculées avec un modèle aux éléments finis du projecteur complet. Les calculs sont basés sur l’identification des modes qui reposent sur la répartition des masses dans la structure, la nature des liaisons. Des études d’influence sont réalisées. Les paramètres étudiés sont les raideurs et précontraintes de contact, le coefficient de frottement, l’amortissement introduit. Leurs impacts sur les niveaux des vibrations sont quantifiés ce qui amène au recalage du modèle éléments finis pour améliorer les résultats modaux du projecteur automobile et sa réponse harmonique forcée. / The thesis deals with the prediction of nonlinear dynamic behavior of automotive headlamps. The attention is focused on building models to estimate the vibration behavior of lighting system to enhance its durability and comfort of vision. Vibration tests show that high levels of vibration damage projector components and degrade the stability of the illuminating beam. To avoid these issus, headlamps design must be adapted to include nonlinear phenomena provided from the joints connecting the reflector and housing subsets. The state of the art is performed on the non-linear dynamic behavior, models and methods and existing estimators quantifying nonlinearities. The modal tests performed demonstrate the presence of non-linear phenomena (clearance, friction, stick-slip, …) located in reflector-housing joints. Experimental investigations carried out on joints show different types of nonlinear behavior and help to identify the most important contact parameters (stiffness and damping). The limits of validity of the linear models are determined by empirically formulated criteria. Selected nonlinear models are integrated in a 1D-model reduced to one then two degrees of freedom of a projector. The representativeness of the model is evaluated basing of modal measurement of headlamp. The Harmonic Balance Method was used to calculate the periodic response. The algorithm calculates also the stability of the periodic solutions found, using Floquet theory, and follows stable or instable branches versus varying system parameters via the arc-length continuation technique. Finally, harmonic responses are predicted with a finite element model of the entire headlamp. The calculations are based on the identification of modes that are based on the weight distribution in the structures and joints proprities. Sensibility studies are carried out on stiffness and preloaded contact, coefficient of friction and damping. Impacts on the vibration levels were quantified that leads to update the finite element model and improve modal and harmonic results of headlamp.

<div>A leading cause of premature failure and excessive wear and tear in mechanical components that rely on compression springs for their operation is the development of unwanted side forces when the spring is compressed.</div><div>These side forces are usually around 10% - 20% of the magnitude of the axial load and point in different directions in the plane perpendicular to the axis of the spring.</div><div>The magnitude and direction of the resultant of side forces varies very non-linearly and unpredictably even though the axial force behavior of the spring is very consistent and predictable.</div><div>Since these side forces have to be resisted by the housing components that hold the spring in place, it is difficult to design these components for optimal operation.</div><div><br></div><div>The hypothesis of this study is that side forces are highly sensitive to small changes in spring geometry and its placement configuration in the housing. <br></div><div><div>Several experiments are conducted to measure the axial and side forces in barrel springs and two different types of finite element models are developed and calibrated to model the spring behavior. </div><div>Spring geometry and placement are parameterized using several control variables and an approach based on design of experiments is used to identify the critical parameters that control the behavior of side-forces. </div><div>The models resulted in deeper insight into the development of side forces as the spring is progressively loaded and how its contact interactions with the housing lead to changes in the side force.</div><div>It was found that side-forces are indeed sensitive to variations in spring geometry and placement.</div><div>These sensitivities are quantified to enable designers to and manufacturers of such springs to gain more control of side force variations between different spring specimens.</div></div>

The Generalized Finite Element Method (GFEM) is a numerical method based on the Partition of Unity (PU) concept and inspired on both the Partition of Unity Method (PUM) and the hp-Cloud method. According to the GFEM, the PU is provided by first-degree Lagragian interpolation functions, defined over a mesh of elements similar to the Finite Element Method (FEM) meshes. In fact, the GFEM can be considered an extension of the FEM to which enrichment functions can be applied in specific regions of the problem domain to improve the solution. This technique has been successfully employed to solve problems presenting discontinuities and singularities, like those that arise in Fracture Mechanics. However, most publications on the method are related to linear analyses. The present thesis is a contribution to the few studies of nonlinear analyses of Solid Mechanics by means of the GFEM. One of its main topics is the derivation of a segment-to-segment generalized contact element based on the mortar method. Material and kinematic nonlinear phenomena are also considered in the numerical models. An Object-Oriented design was developed for the implementation of a GFEM nonlinear analyses framework written in Python programming language. The results validated the formulation and demonstrate the gains and possible drawbacks observed for the GFEM nonlinear approach. / O Método dos Elementos Finitos Generalizados (MEFG) é um método numérico baseado no conceito de partição da unidade (PU) e inspirado no Método da Partição da Unidade (MPU) e o método das Nuvens-hp. De acordo com o MEFG, a PU é obtida por meio de funções de interpolação Lagragianas de primeiro grau, definidas sobre uma rede de elementos similar àquela do Método dos Elementos Finitos (MEF). De fato, o MEFG pode ser considerado uma extensão do MEF para a qual se pode aplicar enriquecimentos em regiões específicas do domínio, buscando melhorias na solução. Esta técnica já foi aplicada com sucesso em problemas com descontinuidades e singularidades, como os originários da Mecânica da Fratura. Apesar disso, a maioria das publicações sobre o método está relacionada a análises lineares. A presente tese é uma contribuição aos poucos estudos relacionados a análises não-lineares de Mecânica dos Sólidos por meio do MEFG. Um de seus principais tópicos é o desenvolvimento de um elemento de contato generalizado do tipo segmento a segmento baseado no método mortar. Fenômenos não lineares devidos ao material e à cinemática também são considerados nos modelos numéricos. Um projeto de orientação a objetos para a implementação de uma plataforma de análises não-lineares foi desenvolvido, escrito em linguagem de programação Python. Os resultados validam a formulação e demonstram os ganhos e possíveis desvantagens da abordagem a problemas não lineares por meio do MEFG.

Sous l’effet des sollicitations mécaniques répétées induites par les passages des trains, on observe l’apparition de fissures de fatigue de contact dans les rails. Une fois amorcées, celles-ci peuvent se propager et mener à la rupture du rail. Dans un contexte d’intensification du trafic et d’augmentation globale des vitesses de circulation, il devient stratégique pour SNCF d’optimiser sa politique de maintenance. Afin de définir des pas de surveillance adaptés et une planification optimisée des opérations de maintenance, une meilleure connaissance des mécanismes d’endommagement par fatigue du rail s’avère nécessaire. Tendre vers cette stratégie de maintenance prédictive passe par la mise en place d’outils de simulation numérique adaptés. Dans ce contexte, une chaîne d’outils a été développée : détermination des sollicitations transmises au rail, des champs de contraintes et de déformations résiduelles, localisation des zones critiques vis-à-vis du risque de fissuration. L’étape suivante consiste à estimer le risque lié à la présence de fissures et à étudier leurs propagations. Elle constitue une partie des objectifs de ces travaux de thèse. La résolution du problème tri-dimensionnel d’une structure fissurée, avec contact et frottement entre les lèvres, est effectuée grâce à un modèle tri-dimensionnel éléments finis étendus multi-échelles. Ce modèle fait appel à une formulation mixte stabilisée où chaque champ est écrit à l’aide d’enrichissement. La fissure est représentée grâce à une stratégie implicite-explicite. Le problème est résolu à l’aide du solveur non-linéaire LATIN. Une étude empirico-numérique a permis de proposer des formules a priori assurant à la méthode de résolution un taux de convergence proche de l’optimal. La simulation de la propagation des fissures de fatigue est réalisée à l’aide de critères spécifiques, adaptés à un chargement multi-axial et non-proportionnel, et d’une loi de propagation dédiée en mode mixte. La confrontation des résultats de simulation avec des essais réalisés sur une configuration cylindre-plan a validé la stratégie X-FEM/LATIN à deux échelles. Tous ces développements ont été implémentés dans le code de calcul éléments finis CAST3M. Des contraintes résiduelles réalistes, provenant d’un logiciel externe, ont été introduites. Cette étape a requis la mise en place d’une procédure de transfert des champs entre les deux maillages (celui utilisé pour le calcul des contraintes résiduelles et celui utilisé pour la résolution du problème de mécanique élastique linéaire de la rupture). L’étude de la flexion du rail a révelé l’influence de ce phénomène uniquement lors du passage du chargement sur la fissure.Enfin, une étude numérique a montré la très forte influence de l’orientation du chargement tangentiel, des contraintes résiduelles et de la présence de plusieurs fissures sur la direction et les vitesses de propagation des fissures de fatigue. / To optimize the rail grinding strategy, the prediction of crack growth rates has a vital role. Contact, with friction between the crack faces, notably occurs in rolling contact fatigue (RCF) problems. These time-dependent, multi-axial, non proportional loadings may lead to a crack initiation and propagation, and sometimes to the development of very complex 3D crack network. Numerical simulations of frictional fatigue crack are efficiently performed using the eXtended Finite Element Method (X-FEM). Within this method, the mesh does not need to conform to the crack geometry. Most difficulties associated to complex mesh generation around the crack and the re-meshing steps during the propagation are hence avoided. A 3D two-scale frictional contact fa-tigue crack model developed within the X-FEM framework is presented. It allows the use of a refined discretization of the crack interface independent from the underlying finite element mesh and adapted to the frictional contact crack scale. The model is used here to analyze the crack propagation, rate and direction, under rolling contact fatigue. The wheel-rail contact loading is modeled as a traveling hertzian load. The stress intensity factors are computed at the crack tips during the wheel passage. Criteria for determining crack growth direction under multiaxial non proportional conditions and mixed mode Paris’ law are used. Actual residual stresses are accounted for in the simulation. They are determined thanks to a dedicated model used at SNCF in which the asymptotic mechanical state of the rail is computed when submitted to cyclic loads. A non-uniform elastic-plastic stabilized state is calculated and introduced, by projection of the mechanical fields onto the finite element mesh, in the crack propagation simulation. All this strategy has been implemented in CAST3M and is now used to model 3D frictional crack growth under RCF.

The research presented in this work addresses open questions regarding (i) the fundamental understanding of powder compaction, and (ii) the complex mechanical response of particle-binder composites under large deformations. This work thus benefits a broad range of industries, from the pharmaceutical industry and its recent efforts on continuous manufacturing of solid tablets, to the defense and energy industries and the recurrent need to predict the performance of energetic materials. Powder compacts and particle-binder composites are essentially confined particulate systems with significant heterogeneity at the meso (particle) scale. While particle mechanics strategies for modeling evolution of mesoscale microstructure during powder compaction depend on the employed contact formulation to accurately predict macroscopic quantities like punch and die wall pressures, modeling of highly nonlinear, strain-path dependent macroscopic response without a distinctive yield surface, typical of particle-binder composites, requires proper constitutive modeling of these complex deformation mechanisms. Moreover, continued loading of particle-binder composites over their operational life may introduce significant undesirable changes to their microstructure and mechanical properties. These challenges are addressed with a combined effort on theoretical, modeling and experimental fronts, namely, (a) novel contact formulations for elasto-plastic particles under high levels of confinement, (b) a multi-scale experimental procedure for assessing changes in microstructure and mechanical behavior of particle-binder composites due to cyclic loading and time-recovery, and (c) a finite strain nonlinear elastic, endochronic plastic constitutive formulation for particle-binder composites.

<div>As physical testing does not always yield insight into the mechanistic cause of failures, computational modeling is often used to develop an understanding of the goodness of a design and to shorten the product development time. One common, and widely used analysis technique is the Finite Element Method. A significant difficulty with the finite element method is the effort required to generate an analysis-suitable mesh due to the difference in the mathematical representation of geometry CAD and CAE systems. CAD systems commonly use Non-Uniform Rational B-Splines (NURBS) while the CAE tools rely on the finite element mesh. Efforts to unify CAD and CAE by carrying out analysis directly using NURBS models termed Isogeometric Analysis reduces the gap between CAD and CAE phases of product development. However, several challenges still remain in the field of isogeometric analysis. A critical challenge relates to the output of commercial CAD systems. B-rep CAD models generated by commercial CAD systems contain uncoupled NURBS patches and are therefore not suitable for analysis directly. Existing literature is largely missing methods to smoothly couple NURBS patches. This is the first topic of research in this thesis. Fracture-caused failures are a critical concern for the reliability of engineered structures in general and semiconductor chips in particular. The back-end of the line structures in modern semiconductor chips contain multi-material junctions that are sites of singular stress, and locations where cracks originate during fabrication or testing. Techniques to accurately model the singular stress fields at interfacial corners are relatively limited. This is the second topic addressed in this thesis. Thus, the overall objective of this dissertation is to develop an isogeometric framework for parametric domain decomposition and analysis of singular stresses using enriched isogeometric analysis.</div><div><br></div><div>Geometrically speaking, multi-material junctions, sub-domain interfaces and crack surfaces are lower-dimensional features relative to the two- or three-dimensional domain. The enriched isogeometric analysis described in this research builds enriching approximations directly on the lower-dimensional geometric features that then couple sub-domains or describe cracks. Since the interface or crack geometry is explicitly represented, it is easy to apply boundary conditions in a strong sense and to directly calculate geometric quantities such as normals or curvatures at any point on the geometry. These advantages contrast against those of implicit geometry methods including level set or phase-field methods. In the enriched isogeometric analysis, the base approximations in the domain/subdomains are enriched by the interfacial fields constructed as a function of distance from the interfaces. To circumvent the challenges of measuring distance and point of influence from the interface using iterative operations, algebraic level sets and algebraic point projection are utilized. The developed techniques are implemented as a program in the MATLAB environment named as <i>Hierarchical Design and Analysis Code</i>. The code is carefully designed to ensure simplicity and maintainability, to facilitate geometry creation, pre-processing, analysis and post-processing with optimal efficiency. </div><div><br></div><div>To couple NURBS patches, a parametric stitching strategy that assures arbitrary smoothness across subdomains with non-matching discretization is developed. The key concept used to accomplish the coupling is the insertion of a “parametric stitching” or p-stitching interface between the incompatible patches. In the present work, NURBS is chosen for discretizing the parametric subdomains. The developed procedure though is valid for other representations of subdomains whose basis functions obey partition of unity. The proposed method is validated through patch tests from which near-optimal rate of convergence is demonstrated. Several two- and three-dimensional elastostatic as well as heat conduction numerical examples are presented.</div><div><br></div><div>An enriched field approximation is then developed for characterizing stress singularities at junctions of general multi-material corners including crack tips. Using enriched isogeometric analysis, the developed method explicitly tracks the singular points and interfaces embedded in a non-conforming mesh. Solution convergence to those of linear elastic fracture mechanics is verified through several examples. More importantly, the proposed method enables direct extraction of generalized stress intensity factors upon solution of the problems without the need to use <i>a posteriori</i> path-independent integral such as the J-integral. Next, the analysis of crack initiation and propagation is carried out using the alternative concept of configurational force. The configurational force is first shown to result from a configurational optimization problem, which yields a configurational derivative as a necessary condition. For specific velocities imposed on the heterogeneities corresponding to translation, rotation or scaling, the configurational derivative is shown to yield the configurational force. The use of configurational force to analyze crack propagation is demonstrated through examples.</div><div><br></div><div>The developed methods are lastly applied to investigate the risk of ratcheting-induced fracture in the back end of line structure during thermal cycle test of a epoxy molded microelectronic package. The first principal stress and the opening mode stress intensity factor are proposed as the failure descriptors. A finite element analysis sub-modeling and load decomposition procedure is proposed to study the accumulation of plastic deformation in the metal line and to identify the critical loading mode. Enriched isogeometric analysis with singular stress enrichment is carried out to identify the interfacial corners most vulnerable to stress concentration and crack initiation. Correlation is made between the failure descriptors and the design parameters of the structure. Crack path from the identified critical corner is predicted using both linear elastic fracture mechanics criterion and configurational force criterion. </div>

Hållfasthetslära är ett viktigt och centralt område inom ingenjörsutbildningar. Men att ha grundläggande kunskap om vad som gör konstruktioner hållfasta är dock något som inte enbart bör vara förbehållet ingenjörer, utan det är även ett område som tillhör allmänbildningen. Det är av den anledningen området hållfasthet tas upp redan i grundskolans lägre åldrar i skolämnet Teknik och fördjupas successivt upp till gymnasiets tekniska program. I denna studie har fem läroböcker för ämnet Teknik för grundskolans årskurs 7-9 samt två läroböcker för kursen Teknik 1 i gymnasieskolans årskurs 1, studerats för att utreda hur området hållfasthetslära beskrivs. Metoden som används i analysen är textanalys i form av en kvantitativ innehållsanalys av förekomsten av hållfasthetsrelaterade begrepp samt en kvalitativ analys av hur begreppen beskrivs. Därtill görs en analys av hur läromedlen uppfyller styrdokumentens krav och riktlinjer. Studien visar att böckerna har stor variation i hur området hållfasthetslära framställs, dock med generaliseringar att högstadieboken beskriver området med text och gymnasieboken med formler. De studerade läroböckerna tar visserligen upp många ämnesspecifika begrepp men det är en markant skillnad mellan böckerna hur dessa begrepp beskrivs. Den fördjupade analysen som studerar om läroböckerna uppfyller styrdokumentens kursplaner i Teknik för grundskolan och Teknik 1 för gymnasieskolan påvisar även den en stor spridning mellan läroböckerna. Av studiens valda bedömningskriterier kan utläsas att området behandlas utförligt endast av två av böckerna: grundskolans Teknik Direkt (2018) från förlaget Sanoma Utbildning samt gymnasiets Teknik (2011) från förlaget Liber. Gemensamt för de valda gymnasieböckerna är att området hållfasthet behandlas mycket mer matematiskt än i högstadieböckerna och stort fokus ligger på olika former av spänningsberäkningar. Dock är det ett markant språng i abstraktionsnivå från de enklare textbaserade högstadieböckerna till gymnasieböckerna med matematiska beräkningar. Slutsatsen av detta är att varken högstadieböckerna eller gymnasieböckerna ger en heltäckande bild av viktiga grundläggande begrepp inom området hållfasthet. Studien visar att de bästa av böckerna kan i viss mån komplettera varandra, men med ogrundade val av läromedel riskerar det att bli osammanhängande. Det är därmed viktigt att läraren noggrant utvärderar lämpliga läromedel så de uppfyller det tänkta syftet i undervisningen. / Strength of materials and solid mechanics theory is an important and central area in engineering education. But having a basic knowledge of what makes structures durable, however, is not only reserved for engineers, but is also an area that belongs to general education. For this reason, the area of strength is already taken up in the elementary school's lower age in the subject of technology and is gradually expanded up to the high school's technical program. In this study, five textbooks for the subject of Technology for comprehensive school upper stage, grade 7-9, and two textbooks for the course Technology 1 in high school year 1 were studied to investigate how the field of strength theory is described. The method used in the analysis is text analysis in the form of a quantitative content analysis of the presence of strength-related concepts as well as a qualitative analysis of how the concepts are described. In addition, an analysis is made of how the teaching materials meet the requirements and guidelines of the steering documents. The study shows that the books have a great variety in how the field of strength theory is presented, however with generalizations that the upper stage textbook describes the area with text and the high school describes with formulas. Although the textbooks studied have many subject-specific concepts, it is markedly different between the books how these concepts are described. The in-depth analysis that studies whether the textbooks meet the syllabus of the steering documents in Teknik for the elementary school and Teknik 1 for the upper secondary school also shows a large distribution between the textbooks. From the chosen assessment criteria in the study, it can be seen that the area is in depth covered by only two of the books: Teknik Direkt (2018) from publisher Sanoma Utbildning (for the elementary school) and Teknik (2011) from publisher Liber (from upper secondary school). Common to all the selected high school books is that the area of strength is treated much more mathematically than for the upper stage books and great focus is placed on various forms of stress calculations. However, there is a significant leap in abstraction level from the simpler text-based upper stage books to the high school books with mathematical calculations. The conclusion of this is that neither the upper stage school books nor the high school books provide a comprehensive picture of important basic concepts in the area of strength. The study shows that the best of the books can to some extent complement each other, but with unfounded choice of study material it risks becoming incoherent. It is therefore important that the teacher carefully evaluates appropriate teaching material so that they fulfill the intended purpose of the teaching.