This thesis further developments strain smoothing techniques in finite element methods for structural analysis. Two methods are investigated and analyzed both theoretically and numerically. The first is a smoothed finite element method (SFEM) where an assumed strain field is derived from a smoothed operator of the compatible strain field via smoothing cells in the element. The second is a nodally smoothed finite element method (N-SFEM),where an assumed strain field is evaluated using the strain smoothing in neighbouring domains connected with nodes. For the SFEM, 2D, 3D, plate and shell problems are studied in details. Two issues based on a selective integration and a stabilization approach for volumetric locking are considered. It is also shown that the SFEM in 2D with a single smoothing cell is equivalent to a quasi-equilibrium model. For the N-SFEM, a priori error estimation is established and the convergence is confirmed numerically by benchmark problems. In addition, a quasi-equilibrium model is obtained and as a result a dual analysis is very promising to estimate an upper bound of the global error in finite elements. It is also expected that two present approaches are being incorporated with the extended finite element methods to improve the discontinuous solution of fracture mechanics.

No description available.

Thesis (Ph.D.)--University of Iowa, 2009. / Thesis supervisor: Jia Lu. Includes bibliographical references (leaves 123-131).

Rheumatic heart disease (RHD) is identified as a serious health concern in developing countries, specifically amongst young individuals, accounting for between 250 000 and 1.4 million deaths annually. As such, the attention of this research is initially placed on the importance of the development of a cardiac analysis toolbox with functionality for pathophysiological analysis of the disease. Subsequently, in order to further the understanding of the mechanisms of the disease as linked to cardiomyocyte growth and remodelling of the microstructure, a continuum bi-phasic model applicable to cardiac tissue is formulated based on the theory of porous media (TPM). This makes it possible to account for interactions and contributions of multiple phases of constituent materials, which in computational cardiac modelling are the solid phase - the cardiac tissue - and the liquid phase - blood and interstitial uid. Subsequent attention is paid to the cardiac model development in order to implement a sound base on which to add strain-driven phase transition via a mass supply function proposed within this study. To this end, based on thermodynamical restrictions, constitutive relations are proposed for stress, permeability, seepage velocity, mass supply and interaction forces such as friction. The approach is implemented in the in-house computational cardiac mechanics toolbox SESKA which supports finite element as well as Element- free Galerkin-based approximations. This investigation considers the passive and active non-linear elastic material behaviour of the myocardium of the left ventricle coupled with porous media theory, along with an an additional coupling to the haemodynamics of the circulatory system, facilitating modelling of the full cardiac cycle. As such, an initial cardiac growth and remodelling computer model is developed as an initial step to computational modelling of the adverse effects of RHD and other similar in ammatory heart diseases, with the potential to limit the invasiveness and risk of in-vivo patient studies. A patient specific case study is conducted, making use of cardiovascular magnetic resonance scans taken over a period of two years from a patient affected by RHD to generate realistic 3D computer models, from which information is drawn with regards to the pathophysiological behaviour of the disease.

This thesis presents a combined numerical and experimental study on the response of kidney cells to shock waves. The motivation was to develop a mechanistic model of cell deformation in order to improve the clinical use of shock waves, by either enhancing their therapeutic action against target cells or minimising their impact on healthy cells. An ultra-high speed camera was used to visualise individual cells, embedded in tissue-mimicking gel, in order to measure their deformation when subject to a shock wave from a clinical shock wave source. Advanced image processing was employed to extract the contour of the cell from the images. The evolution of the observed cell contour revealed a relatively small deformation during the compressional phase and a much larger deformation during the tensile phases of a shock wave. The experimental observations were captured by a numerical model which describes the volumetric cell response with a bilinear Equation of State and the deviatoric cell response with a viscoelastic framework. Experiments using human kidney cancer cells (CAKI-2) and noncancerous kidney cells (HRE and HK-2) were compared to the model in order to determine their mechanical properties. The differences between cancerous and noncancerous cells were exploited to demonstrate a design process by which shock waves may be able to improve the specificity on targeted cancer cells while having minimal effect on normal cells. The cell response to shock waves was studied in a more biophysically realistic environment to include influence of cell size, shape and orientation, and the presence of neighbouring cells. The most significant difference was predicted when cells were in a cluster in which case the presence of neighbouring cells resulted in a four-fold increase on the von Mises stress and the membrane strain. Finally the numerical model was extended to capture the effect of cell damage using one of two paradigms. In the first paradigm the model captured microdamage during one shock wave but then assumed that the cell recovered by the time the next shock wave arrived. The second model allowed microdamage to accumulate with increasing number of shock waves. These models may be able to explain the strong effect that shock wave loading rate has on tissue damage. In conclusion a validated numerical model has been developed which provides a mechanistic understanding of how cells respond to shock waves. The model has application in suggesting improved strategies for current uses of shock waves, e.g., lithotripsy, as well as opening up new indications such as cancer treatment.

Elastography is an emerging functional imaging technique of current clinical research interest due to a direct relation between mechanical material parameters, especially the tissue stiffness, and tissue pathologies such as cancer. Digital Image Elasto-Tomography (DIET) is a new method that aims to develop elastographic techniques and create a simplified, improved breast cancer screening process. The elastic material information of breast tissue is reconstructed in the DIET concept from mechanically excited steady-state harmonic motion observed on the surface of the breast. While this inversion process has been traditionally approached using finite element methods, this surface-orientated problem is naturally suited to the use of Boundary Element Methods (BEMs) requiring the discretization only on the surface of the domain and on the interface of a potential inclusion. As only approximate information is available about breast tissue material parameters, this thesis presents the development of BEM based inverse problem algorithms suitable for the reconstruction of all material parameters in a proportionally damped isotropic linear elastic solid, where only the material density is known. The highly nonlinear identification process of a potential inclusion is treated through the combination of a systematic Grid-Search with gradient descent techniques. This algorithm is extended to a three-step algorithm that performs a background material parameter estimation before the subsequent identification of an inclusion and thus provides a confident indication for the differentiation between cancerous and healthy breast tissue. The development of these algorithms is illustrated by several simulation studies highlighting important reconstruction behaviors relevant to the elastographic inverse problem. A first experimental test on a silicon based breast phantom is presented.

In recent history, the area of physics-based engineering simulation has seen rapid increases in both computer workstation performance as well as common model complexity, both driven largely in part by advances in memory density and availability of clusters and multi-core processors. While the increase in computation time due to model complexity has been largely offset by the increased performance of modern workstations, the increase in model setup time due to model complexity has continued to rise. As such, the major time requirement for solving an engineering model has transitioned from computation time to problem setup time. This is due to the fact that developing the required mesh for complex geometry can be an extremely complicated and time consuming task. Consequently, new solution techniques which are capable of reducing the required amount of human interaction are desirable. The subject of this thesis is the development of a novel meshless method that promises to eliminate the need for structured meshes, and thus, the need for complicated meshing procedures. Although the savings gain due to eliminating the meshing process would be more than sufficient to warrant further study, the proposed method is also capable of reducing the computation time and memory footprint compared to similar models solved using more traditional finite element, finite difference, finite volume, or boundary element methods. In particular, this thesis will outline the development of an interactive, meshless, physically accurate modeling environment that provides an extensible framework which can be applied to a multitude of governing equations encountered in computational mechanics and thermofluids. Additionally, through the development of tailored preprocessing routines, efficiency and accuracy of the proposed meshless algorithms can be tested in a more realistic and flexible environment. Examples are provided in the areas of elasticity, heat transfer and computational fluid dynamics.

Les matériaux composites stratifiés sont de plus en plus utilisés dans l'aéronautique, mais ils peuvent être sujets à large délaminage si soumis à impact. La nécessité d'effectuer des simulations numériques pour prédire l’endommagement devient essentielle pour l’ingénieur. Dans ce contexte, l'utilisation d'une modélisation fine semble préférable. En revanche, le coût de calcul associé serait prohibitif pour larges structures. Le but de ce travail consiste à réduire ce coût de calcul, en couplant le modèle fin, restreint à la zone active de délaminage, avec un modèle grossier appliqué au reste de la structure. En raison du comportement transitoire des problèmes d'impact, l'adaptabilité dynamique des modèles pour suivre les phénomènes évolutifs représente un point crucial de la stratégie de couplage. Des méthodes avancées sont utilisées pour coupler différents modèles. Par exemple, la méthode de Décomposition de Domaines, appliquée à l'adaptabilité dynamique, doit être combinée avec une stratégie de remaillage, considérée comme intrusive pour la mise en œuvre d'un logiciel pour Analyse à Eléments Finis. Dans ce travail, les bases d'une approche faiblement intrusive, la méthode de Substitution, sont présentés dans le domaine de la dynamique explicite. Il s’agît d’une formulation globale-locale, conçue pour appliquer un modèle grossier sur tout le domaine pour obtenir une réponse globale: ce pré-calcul est ensuite corrigé itérativement par l'application du modèle raffiné appliqué seulement où nécessaire. La vérification de la méthode de Substitution en comparaison avec la méthode de Décomposition de Domaines est présentée. / Composite laminates are increasingly employed in aeronautics, but can be prone to extensive delamination when submitted to impact loads. The need of performing virtual testing to predict delamination becomes essential for engineering workflows, in which the use of a fine modeling scheme appears nowadays to be the preferred one. The associated computational cost would be prohibitively high for large structures. The goal of this work consists in reducing such computational cost coupling the fine model, restricted to the surroundings of the delamination process zone, with a coarse one applied to the rest of the structure. Due to the transient behavior of impact problems, the dynamic adaptivity of the models to follow evolutive phenomena represents a crucial feature for the coupling. Many methodologies are currently used to couple multiple models, such as non-overlapping Domain Decomposition method, that, applied to dynamic adaptivity, has to be combined with a re-meshing strategy, considered as intrusive implementation within a Finite Element Analysis software. In this work, the bases of a weakly-intrusive approach, called Substitution method, are presented in the field of explicit dynamics. The method is based on a global-local formulation and is designed so that it is possible to make use of the pre-fixed coarse model the meshes the whole structure to obtain a global response: this pre-computation is then iteratively corrected considering the application of the refined model only where required, in the picture of an adaptive strategy. The verification of the Substitution method in comparison with the Domain Decomposition method is presented.

No description available.

Understanding the mechanical behavior of composite materials requires extensive knowledge of fracture behavior as a crack approaches an interface between the bulk material and the reinforcement structure. Overall material toughness can be greatly influenced by the propensity of an impinging crack to propagate directly through the substrate or deflect along an interface boundary. As the basis for this thesis; the assertion that an impinging crack may encounter a reinforcement structure at various incident angles is explored. This requires the ability to predict crack penetration/ deflection behavior not only normal to the reinforcement, but at various incident angles. Previous work in the area of interface fracture mechanics has used a stress or energy based approach, with recent advances in the field of a combined cohesive-zone method. Work presented here investigates the interaction between strength and toughness when using the cohesive-zone method on the problem of an impinging crack not normally incident to the interface of a composite material. Computational mechanics methods using Abaqus and user-define cohesive elements will be applied to this angled incident crack problem. A circular model based on the displacement field equations for mode-I fracture loading is introduced and verified against well-established LEFM solutions. This circular model is used to study the effects of incident crack angle on the penetration vs. deflection behavior of an impinging crack at various angles of incidence. Additionally, the effects of angle on the load applied to the model at fracture are explored. Finally, a case study investigating how the interaction between strength and toughness found using the cohesive-zone method helps to explain some of the inconsistencies seen in the interface indentation fracture test procedure. / Graduation date: 2013