Cette thèse présente une approche probabiliste de la modélisation de la mécanique des matériaux et des structures. Le dimensionnement est influencé par l'incertitude des paramètres d'entrée. Le travail est interdisciplinaire et les méthodes décrites sont appliquées à des exemples de biomécanique et de génie civil. La motivation de ce travail était le besoin d'approches basées sur la mécanique dans la modélisation et la simulation des implants utilisés dans la réparation des hernies ventrales. De nombreuses incertitudes apparaissent dans la modélisation du système implant-paroi abdominale. L'approche probabiliste proposée dans cette thèse permet de propager ces incertitudes et d’étudier leurs influences respectives. La méthode du chaos polynomial basée sur la régression est utilisée dans ce travail. L'exactitude de ce type de méthodes non intrusives dépend du nombre et de l'emplacement des points de calcul choisis. Trouver une méthode universelle pour atteindre un bon équilibre entre l'exactitude et le coût de calcul est encore une question ouverte. Différentes approches sont étudiées dans cette thèse afin de choisir une méthode efficace et adaptée au cas d’étude. L'analyse de sensibilité globale est utilisée pour étudier les influences des incertitudes d'entrée sur les variations des sorties de différents modèles. Les incertitudes sont propagées aux modèles implant-paroi abdominale. Elle permet de tirer des conclusions importantes pour les pratiques chirurgicales. À l'aide de l'expertise acquise à partir de ces modèles biomécaniques, la méthodologie développée est utilisée pour la modélisation de joints de bois historiques et la simulation de leur comportement mécanique. Ce type d’étude facilite en effet la planification efficace des réparations et de la rénovation des bâtiments ayant une valeur historique. / This thesis presents a probabilistic approach to modelling the mechanics of materials and structures where the modelled performance is influenced by uncertainty in the input parameters. The work is interdisciplinary and the methods described are applied to medical and civil engineering problems. The motivation for this work was the necessity of mechanics-based approaches in the modelling and simulation of implants used in the repair of ventral hernias. Many uncertainties appear in the modelling of the implant-abdominal wall system. The probabilistic approach proposed in this thesis enables these uncertainties to be propagated to the output of the model and the investigation of their respective influences. The regression-based polynomial chaos expansion method is used here. However, the accuracy of such non-intrusive methods depends on the number and location of sampling points. Finding a universal method to achieve a good balance between accuracy and computational cost is still an open question so different approaches are investigated in this thesis in order to choose an efficient method. Global sensitivity analysis is used to investigate the respective influences of input uncertainties on the variation of the outputs of different models. The uncertainties are propagated to the implant-abdominal wall models in order to draw some conclusions important for further research. Using the expertise acquired from biomechanical models, modelling of historic timber joints and simulations of their mechanical behaviour is undertaken. Such an investigation is important owing to the need for efficient planning of repairs and renovation of buildings of historical value.

Background and objectives: TISSIUM light-activated adhesive was investigated as an alternative to tissue-penetrating products to fix meshes in intraperitoneal laparoscopic ventral hernia repair. The objective of this study was to ensure efficient polymer light activation through commercial meshes and to assess the acute and chronic fixation strength of the light-activated adhesive in a porcine model in comparison to commercial fixation products. Methods: A spectroscopic analysis was conducted on the light-activated adhesive through three different meshes (1, 2, and 3) to quantify the acrylate conversion associated with the level of polymer cross-linking. Two setups were implemented: a static (light source fixed over a drop of polymer) and a dynamic (light source rotated around a pattern of polymer to mimic the surgical procedure). Hernia defects were created in porcine models and repaired either using the light-activated adhesive or a commercial product (A, B, C, and D) to fix a mesh. For each tested condition, the acute and chronic (3 months) fixation strength performances were assessed using burst ball and t-peel mechanical tests. Results: The light activation proved to be effective (more than 90% of the acrylates converted) in static in 7 seconds through the three meshes and in dynamic between 3 min and 5 min 32 sdepending on the considered mesh. In a burst ball test, the light-activated adhesive reached between 42 and 84% of the commercial products’ acute performance with the three meshes (between 75,9 and 95,9 N) and reached 88% of the commercial product A’s chronic performance with mesh 1 (610,1 N). A t-peel test demonstrated similar strength of ingrowth for the repairs using the light-activated adhesive or the commercial product A at the 3-month timepoint with mesh 1 (2,55 and 2,37 N/cm respectively). Conclusions: Data suggest the light-activated adhesive has the potential to be used in intraperitoneal laparoscopic ventral hernia repair. In a reasonable time, the adhesive is efficiently light-activated through commercial meshes. The light-activated adhesive’s performances to fix commercial meshes, both acute and chronic, are similar to commercial products, but with a strong advantage of not being tissue penetrating.