O objetivo central deste trabalho é implementar modelos constitutivos hiperelásticos não lineares em um código computacional que faz análise não linear geométrica de cascas. São necessários, para este propósito, conceitos sobre álgebras linear e tensorial, cinemática, deformação, tensão, balanços, princípios variacionais, métodos numéricos e hiperelasticidade. Tal programa usa a formulação Lagrangiana posicional, o método dos elementos finitos, o princípio dos trabalhos virtuais e o método iterativo de Newton-Raphson para solução das equações não lineares. O elemento finito de casca possui dez nós, sete parâmetros por nó e variação linear da deformação ao longo da espessura. Para dedução dos novos modelos usou-se a decomposição multiplicativa do gradiente da função mudança de configuração, o tensor deformação de Green-Lagrange e o tensor da tensão de Piola-Kirchhoff de segunda espécie. O código desenvolvido foi usado em simulações de diversos exemplos e apresentou boa precisão na análise mecânica de polímeros naturais altamente deformáveis. A ocorrência do fenômeno travamento não se manifestou nas análises realizadas. A presente pesquisa confirmou outros trabalhos, reforçou a necessidade de se usar modelos hiperelásticos não lineares para simular o comportamento mecânico de polímeros naturais e apresentou resultados condizentes com dados experimentais existentes na literatura científica e às respectivas soluções analíticas. / The main objective of this work is to implement nonlinear hyperelastic constitutive models in a computational code of geometrically nonlinear analysis of shells. For this purpose, concepts of linear and tensor algebras, kinematics, strain, stress, balances, variational principles, numerical methods and hyperelasticity are necessary. Such program uses the positional Lagrangian formulation, the finite element method, the principle of virtual work and the iterative method of Newton-Raphson for the solution of the nonlinear equations. The shell finite element has ten nodes, seven parameters per node and presents linear variation of the strain along the thickness. To achieve the new constitutive models the multiplicative decomposition of the deformation gradient, the Green-Lagrange strain tensor and the second Piola-Kirchhoff stress tensor are used. The developed code is tested for simulations of various examples and presents good accuracy in the mechanical analysis of highly deformable natural rubber. The locking phenomena didn\'t appear in the proposed analysis. The present research confirms other works, corroborates the need of using nonlinear hyperelastic models to simulate the mechanical behavior of natural rubber and presents suitable results when compared to existent experimental data of the scientific literature and to the respective analytical solutions.

Neste estudo se propõe o desenvolvimento de um modelo numérico para a ligação deslizante entre elementos sólidos bidimensionais, aplicável à simulação de sistemas deslizantes de isolação de base para estruturas. A formulação implementada é baseada no Método dos Elementos Finitos Posicional (MEFP) para análise dinâmica não linear geométrica de estruturas escrita na forma Lagrangeana total. Elementos triangulares planos e isoparamétricos de aproximação cúbica com matriz de massa completa são utilizados principalmente na elaboração da parte sólida dos dispositivos de ligação entre estruturas reticuladas e a base móvel. Esses elementos também poderm ser utilizados na modelagem da estrutura em si, porém, para esse fim, elementos finitos isoparamétricos de barra geral com massa distribuída por unidade de comprimento foram implementados. As equações de movimento são integradas no tempo aplicando o método de Newmark e o problema de deslizamento é resolvido com o algoritmo baseado na técnica dos multiplicadores de Lagrange, onde a restrição das posições de um nó escravo é feita em relação a uma sequência de superfícies mestres. Elementos de barra geral foram usados para simular as superfícies mestres de contato, o que aumenta as possibilidades de aplicações, incluindo mecanismos compostos apenas por barras gerais. Analisam-se exemplos disponíveis na literatura para a validação da formulação proposta e propõem-se aplicações diversas na engenharia das estruturas. / This study proposes the development of a numerical model for the sliding joint between two-dimensional solid elements, applicable to the simulation of sliding base isolation systems. The implemented formulation is based on the Positional Finite Element Method (PFEM) for geometrical nonlinear dynamic analysis of structures written in the total Lagrangian form. Plane and isoparametric triangular cubic approximation elements with full mass matrix are mainly used in the elaboration of the solid part of the devices of joints between reticulated structures and mobile base. These elements can also be used in the modeling of the structure itself, however, for that purpose, isoparametric elements of general bar with mass distributed per unit of length were implemented. The motion equations are integrated in time by applying the Newmark method and the sliding problem is solved with the algorithm based on the technique of Lagrange multipliers, where the constraint of the positions of a slave node is made in relation to a sequence of master surfaces. General bar elements were used to simulate the master contact surface, which increases the possibilities of applications, including mechanisms composed only of general bars. Analyze examples available in the literature for the validation of the proposed formulation and proposed diverse applications in the engineering of the structures.

Neste trabalho foi implementada uma técnica para considerar ligações semirrígidas elastoplásticas para a análise não linear geométrica de pórticos planos. As ligações semirrígidas foram consideradas com o comportamento elastoplástico multilinear e modeladas via o Método dos Elementos Finitos (MEF). Esta técnica foi acoplada ao programa AcadFrame, baseado no Método dos Elementos Finitos Posicional (MEFP) para a análise não linear geométrica de pórticos planos e treliças planas. O acoplamento numérico foi realizado através de uma formulação algébrica em que a matriz de rigidez das ligações semirrígidas elastoplásticas e as forças internas das ligações são somadas à matriz e ao vetor de forças internas da estrutura a cada iteração no processo de Newton-Raphson. Conceitos de álgebra linear e tensorial, dinâmica não linear, deformação, tensão, princípios variacionais e métodos numéricos são necessários para este propósito. Simular-se-ão diversos exemplos de ligações semirrígidas de estruturas metálicas e de concreto pré-moldado para a verificação das implementações realizadas. O trabalho permite a análise não linear geométrica de pórticos planos considerando as ligações semirrígidas elastoplásticas. / This work presents a technique to consider elastoplastic semi-rigid connections for geometric nonlinear analysis of plane frames. The connections were considered semi-rigid with elastoplastic behavior and modeled by The Finite Element Method (FEM). This technique was coupled to AcadFrame program, based on the Finite Element Method for geometric nonlinear analysis of plane frames and trusses flat. The numerical coupling is made by an algebraic formulation where, at each iteration of the Newton-Raphson process, the connections stiffness matrix and elastoplastic internal forces of are added to the Hessian matrix and the internal force vector of the structure. Concepts of linear and tensor algebra, non-linear strain, stress, variational principles and numerical methods are needed for this purpose. Several examples with semi-rigid connections are solved to verify the proosed formulation and performed implementations. This study allows geometric nonlinear analysis of plane frames considering elastoplastic semi-rigid connections, as steel and precast concrete structures.

A reação álcali-agregado (RAA) é uma reação química complexa envolvendo os álcalis presentes no cimento Portland e minerais silicosos presentes em alguns tipos de agregados reativos. O produto dessa reação expande quando em contato com a água, causando fissuração e deformação, o que afeta a durabilidade e importantes propriedades mecânicas das estruturas de concreto. Entretanto, estruturas que estejam sob tensão de compressão, aplicada por carregamentos ou induzida pela presença de armadura, apresentam expansão reduzida na direção comprimida. Uma das ferramentas que se utiliza para a previsão da vida útil de estruturas afetadas pela RAA é a modelagem numérica da expansão do concreto, possibilitando a previsão e projeto de reparos necessários. Nesse contexto, modelos paramétricos combinam os principais fatores que influenciam a reação (reatividade dos constituintes, porosidade, temperatura, umidade e estado de tensões), possibilitando a determinação da distribuição e da taxa de expansão na estrutura. Nessa pesquisa foi desenvolvido um modelo paramétrico cujo principal interesse foi o estudo das tensões induzidas pela presença de fibras e armadura na expansão do concreto afetado pela RAA. O modelo implementado em elementos finitos tem como parâmetros nodais as posições, uma formulação alternativa ao método dos elementos finitos baseado em deslocamentos; a medida de deformação utilizada é a de Green e a lei constitutiva dos materiais é a de Saint-Venant-Kirchhoff. O material composto é discretizado por meio de uma matriz elástica bi-dimensional reforçado por fibras lineares perfeitamente aderidas à matriz. Comparações entre os resultados obtidos por meio do modelo desenvolvido e resultados de trabalhos experimentais comprovam a aplicabilidade e potencialidade do modelo numérico apresentado. / The alkali-aggregate reaction (AAR) is a complex chemical reaction involving alkalis present in the Portland cement paste and siliceous minerals present in some types of reactive aggregates. The product of this reaction expands in contact with water, causing cracking and deformation that affects durability and important mechanical properties of the concrete structures. However, structures under compressive stress, applied or induced by the presence of rebars, the expansion is reduced in the compressed direction. One of the tools used to predict the service life of structures affected by AAR is the numerical modeling of the concrete expansion, allowing prevision and projecting repairs needed. In this context, parametric models combine the main factors that influence the reaction (reactivity of the constituents, porosity, temperature, humidity and stress state), enabling the determination of distribution and rate of expansion in the structure. In this research was developed a parametric model whose main interest was the study of stresses induced by the presence of fibers and rebars in the expansion of concrete affected by AAR. The model implemented in finite element has as nodal parameters positions, an alternative formulation to the finite element method based on displacement; the deformation measurement used is Green and the material constitutive law is the Saint-Venant-Kirchhoff. The composite material is discretized by a two-dimensional elastic matrix reinforced by perfectly adherent linear fibers. Comparisons between the results obtained from the developed model and results of experimental studies demonstrate the applicability and potential of the numerical model presented.

A utilização de materiais compósitos tornou-se uma alternativa importante em muitas aplicações dentro de diversas áreas da engenharia, pois seus constituintes podem agregar propriedades mecânicas, térmicas e acústicas ao compósito, garantindo eficiência e baixo custo. Com isso, faz-se necessário um maior conhecimento do comportamento mecânico desses materiais diante das solicitações, principalmente no que diz respeito aos campos de deslocamento, deformações e tensões. O presente trabalho tem por finalidade a análise, em nível macroscópico, de estruturas bidimensionais elásticas constituídas de materiais compósitos particulados, utilizando formulação desenvolvida no contexto do Grupo de Mecânica Computacional (GMEC), do Departamento de Engenharia de Estruturas (SET), da Escola de Engenharia de São Carlos (EESC), da Universidade de São Paulo (USP), no qual se insere a presente pesquisa. A formulação utilizada baseia-se no Método dos Elementos Finitos Posicional (MEFP) e foi desenvolvida em nível mesoscópico por tratar da interação entre matriz e partículas. Tal formulação possibilita a consideração da interação partícula-matriz sem a necessidade de coincidência entre as malhas da matriz e das partículas e sem o aumento do número de graus de liberdade dos problemas, admitindo-se aderência perfeita entre as fases. A formulação considera material isotrópico e comportamento não-linear geométrico das fases. A aplicação da formulação foi aqui proposta com o intuito de avaliar a influência da geometria, tamanho, fração volumétrica, distribuição e propriedades mecânicas das partículas adotadas, no comportamento global da estrutura em nível macroscópico. Foram desenvolvidos e apresentados exemplos de aplicação, com comparação dos resultados numéricos das análises com resultados de ensaios experimentais encontrados na literatura, bem como com resultados de modelos matemáticos de homogeneização e modelos numéricos propostos por outros autores, que utilizaram o método dos elementos finitos e técnicas de homogeneização assintótica. / The use of composite materials has become an important alternative in many applications in different areas of engineering, because their constituents can add mechanical, thermal and acoustic properties to the composite, ensuring efficiency and low cost. Thus, it is necessary a better understanding of the mechanical behavior of these materials, mainly regarding displacement, stress and strain fields. This study aims to analyze, in macroscopic scale, two-dimensional elastic structures made of particulate composite materials, using formulation developed in the context of the Grupo de Mecânica Computacional (GMEC), of Departamento de Engenharia de Estruturas (SET), of Escola de Engenharia de São Carlos (EESC), of Universidade de São Paulo (USP). The formulation is based on the Positional Finite Element Method and was developed in mesoscopic level, considering the matrix-particles interaction and neglecting the interface, by means of kinematic relations used to ensure adherence of the particles to the matrix without introducing new degrees of freedom in the problem. The formulation considers isotropic material and geometric non-linear behavior of the composite phases. The application of the formulation was proposed in this work in order to evaluate the influence of geometry, size, volume fraction, distribution and mechanical properties of the particles adopted in the global behavior of the structure in macroscopic level. Numerical examples were developed and presented in order to compare the numerical results of the analysis with results obtained in experimental studies found in the literature, as well as results of mathematical models and numerical models using finite element method and the asymptotic homogenization technique.

Axolotl uniquely generates blastema cells as a pool of progenitor/stem cells to restore an entire limb, a particular property that other organisms, such as humans, do not have. What underlies these differences? Is the main difference that cells residing at the amputation plane (in the stump) undergo reprogramming processes to re-enter the embryonic program, which allows developmental patterning to start, or are there fundamental differences? There is also a significant debate about whether regeneration occurs via stem cell differentiation or by dedifferentiation of mature limb tissue. The aim of my thesis was to address following questions: Are the cells in the blastema reprogrammed or differentiated to regenerate? Are the blastema cells genetically reactivated de novo during regeneration? How does the amputated limb exactly know which part of the limb needs to be regenerate? Using a novel technique of long-term genetic fate mapping, my team demonstrated that dedifferentiation in regenerated axolotl muscle tissue does not occur. Instead, PAX7+ satellite cells indeed play an important role during muscle regeneration in the axolotl limb. Surprisingly, this is in contrast to the newt, which regenerates muscle cells through a dedifferentiation process. Therefore, there is a fundamental difference that underlies the regenerative mechanism ((Sandoval-Guzman et al., 2014) [KR1]). This demonstrates that there is an unexpected diversity and flexibility of cellular mechanims used during limb regeneration, even among two closely related species. Finally, if one salamander species uses a mammalian regenerative strategy (Cornelison and Wold, 1997; Collins et al., 2005) involving stem cells and another uses a dedifferentiative strategy, this raises the question of whether there are other fundamental aspects of regeneration that could also be anomalous. This hypothesis is promising since there could be more than one possible mechanism to induce mammalian regeneration. The process of limb regeneration in principle seems to be more similar to those of limb development as historically assumed. We showed molecularly that embryonic players are reused during regeneration by reactivating the position- and tissue-specific developmental gene programs by using the newly isolated Twist sequences as early blastema cell markers ((Kragl et al., 2013) [KR2]). To gain insights into the molecular mechanisms of the P/D limb patterning in general, it was crucial to study the early patterning events of the resident progenitor/stem cells by using the specific blastema cell marker HoxA as a positional marker along the proximo-distal axis. Our HOXA protein analysis using high molecular and cellular resolution as well as transplantation assays demonstrated for the first time that axolotl limb blastema cells acquire their positional identity in a proximal to distal sequence. We found a hierarchy of cellular restrictions in positional identities. Amputation at the level of the upper arm showed that the blastema harbors cells, which convert to lower arm and hand. We observed ((Roensch et al., 2013) [KR3]) for the first time that intercalation- the intermediate element (lower arm) arises later from an interaction between the proximal and distal cells identities- does not occur. Intercalation, which has been an accepted model for a long time, is not the patterning mechanism underlying normal (without any manipulation) limb regeneration that is unique to axolotl. We further demonstrated, using the Hox genes as markers that positional identity is cell-type specific since their effects were confirmed to be present in the lateral plate mesoderm- derived cells of the limb. As our knowledge about limb blastemas expands concerning cell composition and molecular events controlling patterning, the similarity to development is becoming more and more clear. My work has resolved many ambiguities surrounding the molecularly identification of different types of blastema cells and how P/D limb patterning occurs during regeneration in comparison to development. It has highlighted the importance of combining high-resolution methods, such as in situ hybridizations, single-cell PCR (sc-PCR) of individual dissociated blastema cells and genetic labeling methods with grafting experiments to map cell fates in vivo. In addition to understanding the processes of regeneration, another long-term goal in the regenerative medicine field is to identify key molecules that trigger the regeneration of tissues. Recently, my colleague Takuji Sugiura (Sugiura et al., 2016) observed that an early event of blastema formation is the secretion of molecules like MLP (MARCKS-like protein), which induces wound-associated cell cycle re-entry. Such findings further increase the enthusiasm of biologists to understand the underlying principles of regeneration. By building our knowledge of the molecules and pathways that are involved in tissue regeneration, we increase the possibility of identifying a way to ‘activate’ regenerative processes in humans and thus reach the final goal of regenerative medicine, which is to use the concepts of cellular reprogramming, stem cell biology and tissue engineering to repair complex body structures.

On considère des jeux stochastiques joués sur un graphe fini. La première partie s’intéresse aux jeux stochastiques à deux joueurs et information parfaite. Dans de tels jeux, les joueurs choisissent des actions dans ensemble fini, tour à tour, pour une durée infinie, produisant une histoire infinie. Le but du jeu est donné par une fonction d’utilité qui associe un réel à chaque histoire, la fonction est bornée et Borel-mesurable. Le premier joueur veut maximiser l’utilité espérée, et le deuxième joueur veut la minimiser. On démontre que si la fonction d’utilité est à la fois shift-invariant et submixing alors le jeu est semi-positionnel. C’est-à-dire le premier joueur a une stratégie optimale qui est déterministe et sans mémoire. Les deux joueurs ont information parfaite: ils choisissent leurs actions en ayant une connaissance parfaite de toute l’histoire. Dans la deuxième partie, on étudie des jeux de durée fini où le joueur protagoniste a zéro information. C’est-à-dire qu’il ne reçoit aucune information sur le déroulement du jeu, par conséquent sa stratégie est un mot fini sur l’ensemble des actions. Un automates probabiliste peut être considéré comme un tel jeu qui a un seul joueur. Tout d’abord, on compare deux classes d’automates probabilistes pour lesquelles le problème de valeur 1 est décidable: les automates leaktight et les automates simples. On prouve que la classe des automates simples est un sous-ensemble strict de la classe des automates leaktight. Puis, on considère des jeux semi-aveugles, qui sont des jeux à deux joueurs où le maximiseur a zéro information, et le minimiseur est parfaitement informé. On définit la classe des jeux semi-aveugles leaktight et on montre que le problème d’accessibilité maxmin est décidable sur cette classe. / We consider stochastic games that are played on finite graphs. The subject of the first part are two-player stochastic games with perfect information. In such games the two players take turns choosing actions from a finite set, for an infinite duration, resulting in an infinite play. The objective of the game is given by a Borel-measurable and bounded payoff function that maps infinite plays to real numbers. The first player wants to maximize the expected payoff, and the second player has the opposite objective, that of minimizing the expected payoff. We prove that if the payoff function is both shift-invariant and submixing then the game is half-positional. This means that the first player has an optimal strategy that is at the same time pure and memoryless. Both players have perfect information, so the actions are chosen based on the whole history. In the second part we study finite-duration games where the protagonist player has zero information. That is, he gets no feedback from the game and consequently his strategy is a finite word over the set of actions. Probabilistic finite automata can be seen as an example of such a game that has only a single player. First we compare two classes of probabilistic automata: leaktight automata and simple automata, for which the value 1 problem is known to be decidable. We prove that simple automata are a strict subset of leaktight automata. Then we consider half-blind games, which are two player games where the maximizer has zero information and the minimizer is perfectly informed. We define the class of leaktight half-blind games and prove that it has a decidable maxmin reachability problem.

Axolotl uniquely generates blastema cells as a pool of progenitor/stem cells to restore an entire limb, a particular property that other organisms, such as humans, do not have. What underlies these differences? Is the main difference that cells residing at the amputation plane (in the stump) undergo reprogramming processes to re-enter the embryonic program, which allows developmental patterning to start, or are there fundamental differences? There is also a significant debate about whether regeneration occurs via stem cell differentiation or by dedifferentiation of mature limb tissue. The aim of my thesis was to address following questions: Are the cells in the blastema reprogrammed or differentiated to regenerate? Are the blastema cells genetically reactivated de novo during regeneration? How does the amputated limb exactly know which part of the limb needs to be regenerate? Using a novel technique of long-term genetic fate mapping, my team demonstrated that dedifferentiation in regenerated axolotl muscle tissue does not occur. Instead, PAX7+ satellite cells indeed play an important role during muscle regeneration in the axolotl limb. Surprisingly, this is in contrast to the newt, which regenerates muscle cells through a dedifferentiation process. Therefore, there is a fundamental difference that underlies the regenerative mechanism ((Sandoval-Guzman et al., 2014) [KR1]). This demonstrates that there is an unexpected diversity and flexibility of cellular mechanims used during limb regeneration, even among two closely related species. Finally, if one salamander species uses a mammalian regenerative strategy (Cornelison and Wold, 1997; Collins et al., 2005) involving stem cells and another uses a dedifferentiative strategy, this raises the question of whether there are other fundamental aspects of regeneration that could also be anomalous. This hypothesis is promising since there could be more than one possible mechanism to induce mammalian regeneration. The process of limb regeneration in principle seems to be more similar to those of limb development as historically assumed. We showed molecularly that embryonic players are reused during regeneration by reactivating the position- and tissue-specific developmental gene programs by using the newly isolated Twist sequences as early blastema cell markers ((Kragl et al., 2013) [KR2]). To gain insights into the molecular mechanisms of the P/D limb patterning in general, it was crucial to study the early patterning events of the resident progenitor/stem cells by using the specific blastema cell marker HoxA as a positional marker along the proximo-distal axis. Our HOXA protein analysis using high molecular and cellular resolution as well as transplantation assays demonstrated for the first time that axolotl limb blastema cells acquire their positional identity in a proximal to distal sequence. We found a hierarchy of cellular restrictions in positional identities. Amputation at the level of the upper arm showed that the blastema harbors cells, which convert to lower arm and hand. We observed ((Roensch et al., 2013) [KR3]) for the first time that intercalation- the intermediate element (lower arm) arises later from an interaction between the proximal and distal cells identities- does not occur. Intercalation, which has been an accepted model for a long time, is not the patterning mechanism underlying normal (without any manipulation) limb regeneration that is unique to axolotl. We further demonstrated, using the Hox genes as markers that positional identity is cell-type specific since their effects were confirmed to be present in the lateral plate mesoderm- derived cells of the limb. As our knowledge about limb blastemas expands concerning cell composition and molecular events controlling patterning, the similarity to development is becoming more and more clear. My work has resolved many ambiguities surrounding the molecularly identification of different types of blastema cells and how P/D limb patterning occurs during regeneration in comparison to development. It has highlighted the importance of combining high-resolution methods, such as in situ hybridizations, single-cell PCR (sc-PCR) of individual dissociated blastema cells and genetic labeling methods with grafting experiments to map cell fates in vivo. In addition to understanding the processes of regeneration, another long-term goal in the regenerative medicine field is to identify key molecules that trigger the regeneration of tissues. Recently, my colleague Takuji Sugiura (Sugiura et al., 2016) observed that an early event of blastema formation is the secretion of molecules like MLP (MARCKS-like protein), which induces wound-associated cell cycle re-entry. Such findings further increase the enthusiasm of biologists to understand the underlying principles of regeneration. By building our knowledge of the molecules and pathways that are involved in tissue regeneration, we increase the possibility of identifying a way to ‘activate’ regenerative processes in humans and thus reach the final goal of regenerative medicine, which is to use the concepts of cellular reprogramming, stem cell biology and tissue engineering to repair complex body structures.

The Aim of this master`s thesis was creation of a digital cadastral map in the part of cadastre unit Vilantice, in Chotěborky. There is an analog cadastral map scale 1:2 880 in the cadastre unit Vilantice currently. Review and completion of the positional point field was done by technology of global navigation satellite system and terrestrial methods. Result of this master`s thesis were the documentation of the review and completion of the positional point field, mapping sketches and vector file of a digital cadastral map.

京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第18140号 / 医博第3860号 / 新制||医||1002(附属図書館) / 30998 / 京都大学大学院医学研究科医学専攻 / (主査)教授 富樫 かおり, 教授 伊達 洋至, 教授 武藤 学 / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM