Beschreibung der Finite Elemente Software-Familie SPC-PM3-AdH-XX für: (S)cientific (P)arallel (C)omputing - (P)rogramm-(M)odul (3)D (ad)aptiv (H)exaederelemente. Für XX stehen die einzelnen Spezialvarianten, die in Teil 2 detailliert geschildert werden. Stand: Ende 2013:1 Allgemeine Vorbemerkungen 2 Grundstruktur 3 Datenstrukturen 4 Gesamtablauf 5 Parallelisierung 6 Die Grundvariante A3D_Original und ihre Bibliotheken

Beschreibung der Finite Elemente Software-Familie SPC-PM3-AdH-XX für: (S)cientific (P)arallel (C)omputing - (P)rogramm-(M)odul (3)D (ad)aptiv (H)exaederelemente. Für XX stehen die einzelnen Spezialvarianten, die in Teil 2 detailliert geschildert werden. Stand: Ende 2013:1 Vorbemerkungen 2 Probleme mit transversal-isotropem Material 3 Gleichungen vom Sattelpunktstyp 4 Probleme der Thermo-Elastizität 5 Nichtlineare Probleme der großen Deformationen

[pt] A análise de fluxo em solos parcialmente saturados exige o conhecimento das propriedades hidráulicas do solo: a curva característica, q(y), e a curva de permeabilidade, k(y). Entre os problemas geotécnicos que envolvem fluxo em meios parcialmente saturados pode-se citar a instabilização de encostas, muitas vezes associada a variações de sucção, e o transporte de contaminantes, pois, freqüentemente, a fonte contaminante está acima do nível d`água. O principal objetivo deste trabalho é a implementação numérica de um programa, baseado num código de elementos finitos, para a realização da retroanálise de parâmetros de fluxo em solos parcialmente saturados a partir de ensaios de campo, e que forneça também informações sobre a qualidade da estimativa obtida. O método de retroanálise utilizado permite a determinação simultânea da curva característica e da curva de permeabilidade a partir de dados de fluxo transiente. O programa desenvolvido foi utilizado para determinar os parâmetros de fluxo de um ensaio realizado no campo experimental II da PUC - Rio. Com base na análise dos resultados obtidos neste ensaio e na análise de sensibilidade foi proposto um ensaio de configuração mais simples que pode fornecer resultados satisfatórios na determinação das propriedades hidráulicas de solos parcialmente saturados. / [en] Flow analysis in partially saturated soils requires the determination of soil hydraulic properties: its characteristic curve, q(y), and its permeability curve k (y). The instabilization of slopes, often associated with suction variations, and the transport of contaminants, where the source of contaminants is often above water leve, are some of the geotechnical problems involving flows in partially saturated media. The main objective of this work is the numerical implementation of a program, based on finite element coding, for the back analysis of flow parameters in partially saturated soils, based on field experiments, capable of providing information on the quality of the estimates obtained. The back analysis method used here allows the simultaneous determination of the characteristic and permeability curves from transient flow data. The program was used to determine flow parameters of a field experiment conducted in Experimental Field II (PUC- Rio). A simpler configuration test is proposed based on the analysis of the results obtained in this field experiment and on a sensitivity analysis. This test may provide satisfactory results in the determination of hydraulic properties of partially saturated soils. / [es] El análisis de flujo en suelos parcialmente saturados exige el conocimiento de las propiedades hidráulicas del suelo: la curva característica, q(y), y la curva de permeabilidade, k(y). Entre los problemas geotécnicos que consideran flujos en medios parcialmente saturados se puede citar la inestabilidad de pendientes, muchas veces asociada a la variaciones de succión; y el transporte de contaminantes, ya que frecuentemente la fuente contaminante está encima del nível de agua. El principal objetivo de este trabajo es la implementación numérica de un programa, basado en un código de elementos finitos, para la realización del retroanálisis de parámetros de flujo en suelos parcialmente saturados a partir de ensayos de campo, y que brinde también informaciones sobre la calidad de la estimatición obtenida. El método de retroanálisis utilizado permite la determinación simultánea de la curva característica y de la curva de permeabilidad a partir de datos de flujo transitorio. El programa desarrollado fue utilizado para determinar los parámetros de flujo de un ensayo realizado en el campo experimental II de la PUC - Rio. Analizando los resultados obtenidos en este ensayo y el análisis de sensibilidad, se propone un ensayo de configuración más simple que puede dar resultados satisfactorios en la determinación de las propiedades hidráulicas de suelos parcialmente saturados.

[pt] Este trabalho estuda problemas geotécnicos e de interação solo-estrutura utilizando o método dos elementos finitos acoplado com a transformada de Fourier. Pela aplicação da transformada de Fourier, as equações diferenciais que governam o problema elástico linear, com as correspondentes condições de contorno, são reescritas no plano de Fourier, permitindo que um problema de natureza tridimensional possa ser numericamente analisado por uma discretização bidimensional. Esta técnica foi empregada neste trabalho para certos problemas de engenharia, como dutovias, túneis e fundações tipo radier, onde a geometria e os parâmetros dos materiais mantêm-se constantes ao longo do eixo longitudinal do corpo, porém admitindo-se variações espaciais no carregamento imposto ao sistema, gerando , assim, um estado tridimensional de tensões. Alguns elementos de interface, com formulação publicada na literatura, foram também considerados na implementação computacional, visto que em problemas de interação solo- estrutura o comportamento do sistema é bastante influenciado pelas propriedades e características mecânicas do solo imediatamente vizinho à estrutura. Os exemplos numéricos apresentados são comparados, sempre que possível, com os resultados obtidos por outra solução analítica ou numérica, procurando discutir as vantagens e limitações do acoplamento da transformada de Fourier com o método dos elementos finitos para a análise de determinada classe de problemas geotécnicos tridimensionais. / [en] In this work some geotechnical and soil-structure interaction problems are studied using the finite element method coupled with a Fourier transform technique. For linear elastic problems, Fourier transforms are applied to the governing field equations, thus enabling that some specific tridimensional problems can be analyzed using a 2D finite element mesh. In conventional finite element applications, a 3D discretization is usually required, but difficulties associated with the preparation of the finite element mesh and the involved computational efforts prevent, in general, the use of a true 3D model. The integral transform method is used in this research for the analysis of some very common problems in geotechnical engineering, such as piping systems, raft foundations and tunnels, where the geometry and the soil profile may be considered constant along a coordinate direction. The applied loading, however, can assume any possible surface distribution, which does not allow to treat the problem under the plane strain assumptions. Some special finite elements presented in the literature, called joint or interface elements, are also incorporated into the finite element computational program written in this research, given that for soil-structure interaction problems the material behavior at the common interface may greatly affect the entire system results. Some numerical examples are presented, and their numerical results are compared, whenever possible, with other solutions obtained using analytical or other numerical technique. Advantages and limitations of the integral transform method to solve tridimensional geomechanics problems are also discussed in this work. / [es] Este trabajo estudia problemas geotécnicos y de interacción suelo-extructura utilizando el método de los elementos finitos acoplado con la transformada de Fourier. Por la aplicación de la transformada de Fourier, las ecuaciones diferenciales que goviernan el problema elástico lineal, con las correspondentes condiciones de contorno, son reescritas en el plano de Fourier, permitiendo que un problema de naturaleza tridimensional pueda ser numericamente analizado por una discretización bidimensional. Esta técnica fue utilizada en este trabajo para ciertos problemas de Ingeniería, como canales, túneles y fundaciones tipo radier, donde la geometría y los parámetros de los materiales se mantienen constantes a lo largo del eje longitudinal del cuerpo, aunque se admiten variaciones espaciales en la carga impuesta al sistema, generando , así, un estado tridimensional de tensiones. En la implementación computacional fueron considerados algunos elementos de la interfaz, con formulación publicada en la literatura, ya que en problemas de interacción suelo-extructura, el comportamiento del sistema está bastante influenciado por las propiedades y características mecánicas del suelo imediatamente vecino a la extructura. Los ejemplos numéricos presentados se compararon, siempre que fue posible, con los resultados obtenidos por otra solución analítica o numérica, discutiendo las ventajas y limitaciones del acoplamiento de la transformada de Fourier con el método de los elementos finitos para el análisis de determinada clase de problemas geotécnicos tridimensionales.

<p>Breast cancer is the most commonly diagnosed cancer type worldwide. Given high survivorship, increased focus has been placed on long-term treatment outcomes and patient quality of life. While breast-conserving surgery (BCS) is the preferred treatment strategy for early-stage breast cancer, anticipated healing and breast deformation (cosmetic) outcomes weigh heavily on surgeon and patient selection between BCS and more aggressive mastectomy procedures. Unfortunately, surgical outcomes following BCS are difficult to predict, owing to the complexity of the tissue repair process and significant patient-to-patient variability. To overcome this challenge, we developed a predictive computational mechanobiological model that simulates breast healing and deformation following BCS. The coupled biochemical-biomechanical model incorporates multi-scale cell and tissue mechanics, including collagen deposition and remodeling, collagen-dependent cell migration and contractility, and tissue plastic deformation. Available human clinical data evaluating cavity contraction and histopathological data from an experimental porcine lumpectomy study were used for model calibration. The computational model was successfully fit to data by optimizing biochemical and mechanobiological parameters through the Gaussian Process. The calibrated model was then applied to define key mechanobiological parameters and relationships influencing healing and breast deformation outcomes. Variability in patient characteristics including cavity-to-breast volume percentage and breast composition were further evaluated to determine effects on cavity contraction and breast cosmetic outcomes, with simulation outcomes aligning well with previously reported human studies. The proposed model has the potential to assist surgeons and their patients in developing and discussing individualized treatment plans that lead to more satisfying post-surgical outcomes and improved quality of life.</p>

A new methodology for the determination of target element sizes for the construction of finite element meshes applicable to the simulation of tidal flow in coastal and oceanic domains is developed and tested. The methodology is consistent with the discrete physics of tidal flow, and includes the effects of bottom stress. The method enables the estimation of the localized truncation error of the nonconservative momentum equations throughout a triangulated data set of water surface elevation and flow velocity. The method's domain-wide applicability is due in part to the formulation of a new localized truncation error estimator in terms of complex derivatives. More conventional criteria that are often used to determine target element sizes are limited to certain bathymetric conditions. The methodology developed herein is applicable over a broad range of bathymetric conditions, and can be implemented efficiently. Since the methodology permits the determination of target element size at points up to and including the coastal boundary, it is amenable to coastal domain applications including estuaries, embayments, and riverine systems. These applications require consideration of spatially varying bottom stress and advective terms, addressed herein. The new method, called LTEA-CD (localized truncation error analysis with complex derivatives), is applied to model solutions over the Western North Atlantic Tidal model domain (the bodies of water lying west of the 60° W meridian). The convergence properties of LTEACD are also analyzed. It is found that LTEA-CD may be used to build a series of meshes that produce converging solutions of the shallow water equations. An enhanced version of the new methodology, LTEA+CD (which accounts for locally variable bottom stress and Coriolis terms) is used to generate a mesh of the WNAT model domain having 25% fewer nodes and elements than an existing mesh upon which it is based; performance of the two meshes, in an average sense, is indistinguishable when considering elevation tidal signals. Finally, LTEA+CD is applied to the development of a mesh for the Loxahatchee River estuary; it is found that application of LTEA+CD provides a target element size distribution that, when implemented, outperforms a high-resolution semi-uniform mesh as well as a manually constructed, existing, documented mesh.

Through enrichment of the elastic potential by the second-order gradient of deformation, gradient elasticity formulations are capable of taking nonlocal effects into account. Moreover, geometry-induced singularities, which may appear when using classical elasticity formulations, disappear due to the higher regularity of the solution. In this contribution, a mixed finite element discretization for finite strain gradient elasticity is investigated, in which instead of the displacements, the first-order gradient of the displacements is the solution variable. Thus, the C1 continuity condition of displacement-based finite elements for gradient elasticity is relaxed to C0. Contrary to existing mixed approaches, the proposed approach incorporates a rot-free constraint, through which the displacements are decoupled from the problem. This has the advantage of a reduction of the number of solution variables. Furthermore, the fulfillment of mathematical stability conditions is shown for the corresponding small strain setting. Numerical examples verify convergence in two and three dimensions and reveal a reduced computing cost compared to competitive formulations. Additionally, the gradient elasticity features of avoiding singularities and modeling size effects are demonstrated.

[pt] Este trabalho tem por objetivo o desenvolvimento de uma ferramenta numérica para avaliação do fluxo saturado-não saturado em encostas de grandes dimensões, com aplicação na análise de estabilidade dessas áreas. Emprega-se o método dos elementos finitos na solução da equação de Richards, considerando a carga de pressão como variável primária e utilizando formulação adequada para minimização dos problemas de conservação de massa, freqüentemente, associados a esse fato. O modelo constitutivo utilizado para a curva característica e função de condutividade hidráulica é o proposto por Van Genuchten (1980). Para solução da não-linearidade, emprega-se um método quasi- Newton (BFGS). Com o objetivo de minimizar os requisitos de memória computacional, utiliza-se esquema de armazenamento de matriz esparsa, associado ao método de gradiente biconjugado, na solução do sistema de equações. Paralelamente, é apresentado algoritmo de geração de malha tridimensional de elementos finitos, a partir de uma malha superficial de triângulos, representativa da topografia. Análises numéricas são executadas com a finalidade de validação do código gerado, comparando-se os resultados obtidos com aqueles gerados por outros programas já consagrados na literatura técnica. É proposta metodologia para geração de mapas de susceptibilidade a escorregamentos translacionais rasos, empregando-se o método do talude infinito, associado à estrutura da malha de elementos finitos e aos resultados do problema de fluxo, incorporando- se, assim, o efeito do estado de não saturação na resistência do material. / [en] The aim of this work is to develop a numerical tool for the analysis of saturated-unsaturated flow in large scale natural slopes, applied to the study of the stability of these areas. The finite element method is applied to solve the Richard`s equation, taking into account the pressure head as the primary variable and using an adequate formulation to minimize the mass conservation issues. The constitutive model used to the characteristic curve and hydraulic constitutive function is the one presented by van Genuchten (1980). A quasi-Newton method (BFGS) is applied for the solution of the non-linearity. A sparse matrix storage scheme, with the objective of reducing the computational memory requirements, is associated to the bi- conjugated gradient method for the solution of the system of equations. An algorithm of finite elements mesh is presented, which generates the 3D mesh from a triangle superficial mesh representing the relief. Numerical analyses are performed in order to validate the code, by comparing the results with those generated by others widely known codes presented in the technical literature. A methodology for the generation of susceptibility maps to shallow translational landslides is delineated, which employs the infinite slope method to the finite elements mesh structure and the flow problem results, considering the effect of the unsaturated state in the material strength.

[pt] Neste trabalho o método dos elementos finitos é empregado para analisar a estabilidade de taludes em solo solapados por voçorocas. Muitos dos deslizamentos de solo que ocorrem em taludes e encostas têm sido causados pelo fenômeno de voçorocas, o resultado de um processo de erosão de solos muito complexo. Uma breve revisão sobre a formação e o crescimento de voçorocas, bem como sobre os seus efeitos na estabilidade de taludes em solo, é feita neste trabalho. Exemplos ilustrativos da aplicação desta técnica para alguns casos de taludes e encostas erodidos por voçorocas são apresentados, incluindo-se duas análises numéricas da estabilidade de encostas situadas na cidade de Goiânia - GO. Dificuldades numéricas devido à baixa taxa de convergência da solução nas proximidades do colapso do talude são também discutidas. / [en] In this work the finite element method is employed to analyze the stability of soil slopes undermined by voçorocas (gulling). Many of the shear slides occurred in both natural slopes and embankments have been caused by the phenomenon of voçorocas, the outcome of a very complex soil erosion mechanism. A brief review about the formation and growing of voçorocas, as well as an overview of their effects on soil slope stability, are made in this work. In the numerical simulation by the finite element method, the potential slip surface is identified through the progressive formation of a region of yielded soil as the erosion process advances. A simple model, consisting of incremental excavations of soil near the foot of the slope, is used in this work to represent the undermining mechanism. Illustrative examples of this technique are presented for some cases of natural soil slopes eroded by voçorocas in the city of Goiania - GO. Numerical difficulties due to the poor convergence of the solution near the soil collapse are also discussed.

The dissertation “Formation of wrinkles on a coated substate“ treats the finite element simulations of controlled wrinkle formation experiments conducted at the Leibniz Institute for Polymer Research. The systems used for the experiments consist of a soft polydimethylsiloxane (PDMS) layer with a thin, stiff layer on top. The wrinkling process is triggered by a stress mismatch between the bulk and the thin layer. To create the stress mismatch, the bulk material is first uni-axially stretched and then the thin layer is created by a low-pressure plasma treatment of the stretched bulk in a vacuum chamber. Under subsequent relaxation, wrinkles form. Their wavelength depends on the choice of the process gas and the duration of the treatment. The use of thin silicon masks placed directly on the PDMS allows to sharply restrict the plasma-exposed area. Sequential exposures of the same sample to multiple treatment processes with and without a mask allow to locally modify the layer thickness and stiffness. With this, we can locally control the wavelength of the resulting wrinkles and trigger the formation of branches and line defects at the boundary between areas of different wavelengths. The dissertation first covers the mathematical model for the coated substrate, a combination of a hyperelastic material model from three-dimensional elasticity for the bulk (an almost incompressible Mooney–Rivlin material model) and a Cosserat shell model for the film on top. A nonlinear and nonconvex minimization problem is deduced and transferred to a suitable finite element space. Existence of minimizers is proven in the continuous and the discrete case before the discrete problem is solved numerically. The numerical simulations show a good agreement with corresponding physical experiments.