Les opérations de hernies abdominales sont l’une des chirurgies les plus répandues dans le monde. Pourtant, malgré des progrès considérables en particulier dans le développement des textiles prosthétiques pour consolider la paroi abdominale, le taux de récurrence reste très élevé. Il apparaît donc nécessaire de développer des modèles numériques patient-spécifiques de la paroi abdominale afin de mesurer puis améliorer l’impact des solutions de soins. Les tissus assurant la cohésion et la stabilité de la paroi abdominale sont les gaines rectusiennes antérieure et postérieure et la ligne blanche, qui sont des tissus conjonctifs. Leur structure particulière, composée d’un entremêlement de fibres de collagène et d’élastine sont au cœur de cette étude.Ce mémoire a permis de mettre en évidence la relation entre architecture microscopique et comportement macroscopique des tissus fibreux. Grâce à des campagnes expérimentales combinant essais mécaniques et observations microscopiques, la structure des tissus a pu être identifiée et corrélée aux paramètres mécaniques. Des outils d’analyse d’images tridimensionnelles ont été développés afin d’estimer automatiquement l’anisotropie d’une texture. Les informations recueillies ont alors menées au développement d’un modèle constitutif anisotrope hypo-paramétré. Basé sur une description tridimensionnelle du réseau fibrillaire, le modèle a été écrit de manière à décorréler les paramètres liés à la structure et ceux relatifs à la nature même du matériau. En considérant les paramètres matériau similaires pour tous les individus, le modèle a démontré sa capacité à prédire le comportement mécanique à partir d’informations texturales / Abdominal hernia operations are one of the most common surgeries in the world. However, despite considerable progress, particularly in the development of prosthetic textiles to strengthen the abdominal wall, the recurrence rate remains very high. It therefore appears necessary to develop patient-specific numerical models of the abdominal wall in order to measure and improve the impact of care solutions. The tissues that ensure the cohesion and stability of the abdominal wall are the anterior and posterior rectus sheaths and the linea alba, which are connective tissues. Their particular structure, composed of an intertwining of collagen and elastin fibers, is at the heart of this study. This thesis highlighted the relationship between microscopic architecture and macroscopic behaviour of fibrous tissues. Thanks to experimental campaigns combining mechanical tests and microscopic observations, the structure of tissues has been identified and correlated to mechanical parameters. Three-dimensional image analysis tools have been developed to automatically estimate the anisotropy of a texture. The collected information then led to the development of a hypo-parameterized anisotropic constitutive model. Based on a three-dimensional description of the fibrillary network, the model was written in such a way as to uncorrelate the parameters related to the structure and those related to the nature of the material. By considering similar material parameters for every individual, the model demonstrated its ability to predict mechanical behaviour based on textural information

There is a high demand for implementing simulations in the design and product devel-opment processes, avoiding the execution of costly tests on prototypes and giving thechance of discarding unsuitable designs, as well as exploring possible ones without much cost added.This project assignment is to find a suitable way to simulate drop tests on two typesof PMMA sheets, a material widely used on luminaire covers. Therefore, it becomesnecessary to study the mechanical behavior of these materials, using experimental tests,in order to calibrate the material models used in the simulations.During the experimental testing, common polymer behaviors were found on the twostudied materials, such as rate dependence, non-linear elasticity, viscoelasticity and vis-coplasticy. Behaviors which presented several challenges regarding the choice and cali-bration of the material models.The two di?erent polymers were calibrated for the simulations using two di?erentmaterial models. An elastic-plastic (Drucker Prager Plasticity) model was used for oneof the materials, whereas an hyperelastic-viscoelastic model was used for the other one.Finally, several drop tests simulations were conducted and compared with experimentaltests

Tato práce je zaměřena na problematiku výpočtového a experimentálního modelování deformačně napjatostních stavů měkkých tkání se zaměřením na riziko ruptury u výdutě břišní aorty (AAA). V první části (kap. 1) je stručně nastíněn současný stav dané problematiky. Tato část shrnuje důležité poznatky publikované v dostupné literatuře. Pozornost je věnována zejména klíčovým faktorům pro stanovení rizika ruptury AAA. V další kapitole (kap. 2) je stručně popsána histologie cévní stěny a její výsledné mechanické chování, jakož i její patologie, především AAA. Druhá část práce (kap.3) je věnována experimentálnímu vyhodnocování deformačně napjatostního chování měkkých tkání, které je nutným předpokladem k věrohodnému výpočtovému modelování tohoto chování. V této kapitole je stručně popsáno experimentální zařízení speciálně vyvinuté pro testování měkkých tkání a typy zkoušek, které lze na tomto zařízení provádět. Dále jsou shrnuty klíčové faktory ovlivňující deformačně napjatostní chování měkkých tkání a experimentální ověření těchto faktorů na vzorcích z prasečích hrudních aort. V závěru této kapitoly jsou shrnuty nové poznatky vyplývající z experimentálního testování. Třetí část disertační práce (kap.4) je zaměřena na matematický popis deformačně napjatostního chování měkkých tkání, stručný popis používaných konstitutivních vztahu a postup při identifikaci parametrů pro tyto konstitutivní modely určované na základě provedených experimentálních zkoušek. Poslední část disertační práce (kap.5) je věnována výpočtovému modelování deformačně napjatostního chování AAA. V této kapitole jsou nejdříve shrnuty klíčové faktory a předpoklady pro vytváření modelů a pro vyhodnocování výsledku a dále jsou uvedeny materiálové parametry pro konstitutivní modely implementované do programu ANSYS. Byly provedeny testovací výpočty při použití hypotetické zjednodušené geometrie AAA, na kterých byly vyhodnoceny vlivy změny geometrie a vliv změny konsitutivního modelu na extrémní napětí ve stěně AAA. U reálné geometrie AAA byla navržena a otestována metoda výpočtu nezatížené geometrie z reálných CT snímků. Dále byl testován vliv zvýšení vnitřního tlaku jako rizika ruptury AAA. V závěru práce jsou shrnuty poznatky a možnosti výpočtového modelování a návrhy na další práce.

Tato práce se zabývá výpočtovými simulacemi zkoušek jednoosým tahem a tříbodovým ohybem kompozitního vzorku složeného z elastomerové matrice a ocelových výztužných vláken orientovaných pod různými úhly, jakož i jejich experimentální verifikací. Simulace byly provedeny pomocí dvou různých modelů - bimateriálového a unimateriálového výpočtového modelu. Při použití bimateriálového modelu, který detailně zohledňuje strukturu kompozitu, tzn. pracuje s matricí a jednotlivými vlákny, je zapotřebí vytvořit model každého vlákna obsaženého v kompozitu, což přináší řadu nevýhod (pracná tvorba výpočtového modelu, řádově větší množství elementů potřebných k diskretizaci v MKP systémech a delší výpočetní časy). Na druhé straně v unimateriálovém modelu se nerozlišují jednotlivá vlákna, pracuje se pouze s kompozitem jako celkem tvořeným homogenním materiálem a výztužný účinek vláken je zahrnut v měrné deformační energii. Porovnání experimentů se simulacemi ukázalo, že bimateriálový model je v dobré shodě s experimenty, na rozdíl od unimateriálového modelu, který je schopen poskytnou odpovídající výsledky pouze v případě tahového namáhání. Z tohoto důvodu byl hledán způsob, který by umožnil rozšířit unimateriálový model o ohybovou tuhost výztužných vláken. V roce 2007 Spencer a Soldatos publikovali rozšířený unimateriálový model, který je schopen pracovat nejen s tahovou, ale i ohybovou tuhostí vlákna. Představený obecný model je však založen na Cosseratově teorii kontinua a jeho praktické využití je pro jeho složitost nemožné. Proto byl vytvořen zjednodušený model (částečně podle Spencera a Soldatose) s vlastní navrženou formou měrné deformační energie. Za účelem ověření nového unimateriálového modelu s ohybovou tuhostí vláken byly odvozeny všechny potřebné rovnice a byl napsán vlastní konečno-prvkový řešič. Tento řešič je založen na Cosseratově teorii kontinua a obsahuje zmíněný anizotropní hyperelastický unimateriálový model zahrnující ohybovou tuhost vláken. Vzhledem k tomu, že v případě Cosseratovy teorie jsou při výpočtu potřebné i druhé derivace posuvů, bylo nutné použít tzv. C1 prvky, které mají spojité jak pole posuvů, tak jejich prvních derivací. Nakonec byly provedeny nové simulace s využitím vlastního řešiče, které ukazují, že tuhost vláken lze u nového unimateriálového modelu řídit odpovídající materiálovou konstantou. V závěru práce je pak diskutováno, zda je nový unimateriálový model s ohybovou tuhostí schopen poskytnout stejné výsledky jako model bimateriálový, a to jak při tahovém tak i ohybovém namáhání kompozitního vzorku.

[pt] O design otimizado de estruturas considerando não-linearidades tem sido amplamente pesquisado nas décadas recentes. A análise de elementos finitos aplicada à otimização topológica é prejudicada pela deformação excessiva de elementos de baixa densidade sob alta compressão, o que impede o processo de encontrar uma solução ótima. Dois métodos, o esquema Interpolação de Energia e a técnica de Hiperelasticidade Aditiva, são implementados para superar essa dificuldade no problema de minimização da flexibilidade, e modelos de materiais hiperelásticos são usados para investigar suas influências na topologia otimizada. O Método das Assíntotas Móveis é usado para atualizar as variáves de projeto cujas sensibilidades foram calculadas pelo método adjunto. A equação de estado é resolvida através do método de Newton-Raphson com um incremento de carga ajustável para reduzir o custo computacional. Resultados de dois problemas de referência são comparado com aqueles já estabelecidos na literatura. O uso de diferentes modelos hiperelásticos apresentou pouca influência no design final da estrutura. O método de Interpolação de Energia foi capaz de convergir para cargas muito maiores que o método padrão, enquanto a Hiperelasticidade Aditiva apresentou dificuldades de convergência em estado plano de deformação. / [en] The optimized design of structures considering nonlinearities has been widely researched in the recent decades. The finite element analysis applied to topology optimization is jeopardized by the excessive deformation of low-density elements under high compression, which hinders the process of finding an optimal solution. Two methods, the Energy Interpolation scheme and the Additive Hyperelasticity technique, are implemented to overcome this difficulty in the minimum compliance problem, and hyperelastic material models are used to investigate their influence on the optimized topology. The Method of Moving Asymptotes is used to update the design variables whose sensitivities were calculated from the adjoint method. The state equation is solved through the Newton-Raphson method with an adjusting load step to reduce computational cost. Results for two benchmark problems are compared with those already established in the literature. The use of different hyperelastic models presented little influence on the final design of the structure. The Energy Interpolation method was able to converge for much higher loads than the default method, while the Additive Hyperelasticity presented convergence difficulties in plane strain.

Neste trabalho apresenta-se uma formulação para modelagem não linear geométrica e não linear elástica de materiais compósitos através da imersão de elementos finitos de barra simples em elementos finitos triangulares do tipo chapa utilizando uma formulação inovadora do método dos elementos finitos baseada em posições. Essa formulação posicional utiliza funções de forma para aproximar grandezas definidas na Teoria da Elasticidade Não Linear e propõe que a energia específica de deformação e o potencial das cargas externas sejam escritos em função das posições nodais definidas a partir de uma função mudança de configuração. Assumindo as posições nodais valores atuais em cada nó, esse método considera naturalmente a não linearidade geométrica, ao passo que relações não lineares entre tensão e deformação podem ser consideradas através de uma teoria elástica não linear denominada hiperelasticidade que permite obter leis constitutivas linearizadas em formato variacional. Utilizando malhas independentes para os elementos de barras e chapa, a técnica para a imersão das barras adota funções de forma para escrever a posição de qualquer ponto de um elemento de barra em função dos nós dos elementos de chapa, não ocorrendo, portanto, nem o aumento do número de graus de liberdade nem a necessidade de que os nós dos elementos de barra coincidam com os nós dos elementos de chapa. Além disso, nesse trabalho propõe-se também uma formulação posicional para os elementos de barra simples que utiliza uma medida de deformação chamada de não linear de engenharia, a qual permite introduzir facilmente um comportamento tanto ativo quanto viscoso nos elementos de barra imersos. As formulações propostas são idealizadas para a modelagem de tecidos musculares, não estando, no entanto, limitadas somente a esse tipo de aplicação. Os quatro primeiro exemplos escolhidos são casos simples, alguns inclusive com soluções analíticas, e são destinados principalmente à validação das formulações apresentadas. Através da modelagem de uma estrutura formada por braço e antebraço, o quinto e último exemplo demonstra as potencialidades dos conceitos trabalhados e das formulações propostas durante este trabalho. / This work presents a formulation for material and geometrical nonlinear analysis of composite materials by immersion of truss finite elements into triangular 2D solid ones using a novel formulation of the finite element method based on positions. This positional formulation uses the shape functions to approximate some quantities defined in the Nonlinear Theory of Elasticity and proposes to describe the specific strain energy and the potential of the external loads as function of nodal positions which are set from a deformation function. Because the nodal positions have current values in each node, this method naturally considers the geometric nonlinearities while the nonlinear relationships between stress and strain may be considered by a pure nonlinear elastic theory called hyperelasticity which allows to obtain linearized constitutive laws in its variational form. If independent meshes are used for the truss elements and for the 2D solid elements, the immersion technique of the trusses adopts shape functions to write the position of any point of a truss as a function of the nodal positions of the 2D solid elements, therefore there is neither an increase in the number of degrees of freedom nor the need that the nodes of the trusses elements coincide with the nodes of the 2D solid elements. Moreover, this work also proposes a positional formulation for the truss elements using a so called nonlinear engineering strain which allows to easily introduce both active and viscous behavior in the immersed truss elements. The proposed formulations are idealized for muscle tissue modeling, however they are not limited only to this type of application. The first 4 chosen examples are simple cases, some of them even with analytical solutions, mainly for validation purposes of the presented formulations. By modeling a structure formed by an arm and an forearm, the 5th and last example shows the potentialities of the concepts and proposed formulations during this work.

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.

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 trabalho apresenta-se uma formulação para modelagem não linear geométrica e não linear elástica de materiais compósitos através da imersão de elementos finitos de barra simples em elementos finitos triangulares do tipo chapa utilizando uma formulação inovadora do método dos elementos finitos baseada em posições. Essa formulação posicional utiliza funções de forma para aproximar grandezas definidas na Teoria da Elasticidade Não Linear e propõe que a energia específica de deformação e o potencial das cargas externas sejam escritos em função das posições nodais definidas a partir de uma função mudança de configuração. Assumindo as posições nodais valores atuais em cada nó, esse método considera naturalmente a não linearidade geométrica, ao passo que relações não lineares entre tensão e deformação podem ser consideradas através de uma teoria elástica não linear denominada hiperelasticidade que permite obter leis constitutivas linearizadas em formato variacional. Utilizando malhas independentes para os elementos de barras e chapa, a técnica para a imersão das barras adota funções de forma para escrever a posição de qualquer ponto de um elemento de barra em função dos nós dos elementos de chapa, não ocorrendo, portanto, nem o aumento do número de graus de liberdade nem a necessidade de que os nós dos elementos de barra coincidam com os nós dos elementos de chapa. Além disso, nesse trabalho propõe-se também uma formulação posicional para os elementos de barra simples que utiliza uma medida de deformação chamada de não linear de engenharia, a qual permite introduzir facilmente um comportamento tanto ativo quanto viscoso nos elementos de barra imersos. As formulações propostas são idealizadas para a modelagem de tecidos musculares, não estando, no entanto, limitadas somente a esse tipo de aplicação. Os quatro primeiro exemplos escolhidos são casos simples, alguns inclusive com soluções analíticas, e são destinados principalmente à validação das formulações apresentadas. Através da modelagem de uma estrutura formada por braço e antebraço, o quinto e último exemplo demonstra as potencialidades dos conceitos trabalhados e das formulações propostas durante este trabalho. / This work presents a formulation for material and geometrical nonlinear analysis of composite materials by immersion of truss finite elements into triangular 2D solid ones using a novel formulation of the finite element method based on positions. This positional formulation uses the shape functions to approximate some quantities defined in the Nonlinear Theory of Elasticity and proposes to describe the specific strain energy and the potential of the external loads as function of nodal positions which are set from a deformation function. Because the nodal positions have current values in each node, this method naturally considers the geometric nonlinearities while the nonlinear relationships between stress and strain may be considered by a pure nonlinear elastic theory called hyperelasticity which allows to obtain linearized constitutive laws in its variational form. If independent meshes are used for the truss elements and for the 2D solid elements, the immersion technique of the trusses adopts shape functions to write the position of any point of a truss as a function of the nodal positions of the 2D solid elements, therefore there is neither an increase in the number of degrees of freedom nor the need that the nodes of the trusses elements coincide with the nodes of the 2D solid elements. Moreover, this work also proposes a positional formulation for the truss elements using a so called nonlinear engineering strain which allows to easily introduce both active and viscous behavior in the immersed truss elements. The proposed formulations are idealized for muscle tissue modeling, however they are not limited only to this type of application. The first 4 chosen examples are simple cases, some of them even with analytical solutions, mainly for validation purposes of the presented formulations. By modeling a structure formed by an arm and an forearm, the 5th and last example shows the potentialities of the concepts and proposed formulations during this work.

The analysis of wave propagation in hyperelastic waveguides has significant applications in various branches of engineering like Non-Destructive Testing and Evaluation, impact analysis, material characterization and damage detection. Linear elastic models are typically used for wave analysis since they are sufficient for many applications. However, certain solids exhibit inherent nonlinear material properties that cannot be adequately described with linear models. In the presence of large deformations, geometric nonlinearity also needs to be incorporated in the analysis. These two forms of nonlinearity can have significant consequences on the propagation of stress waves in solids. A detailed analysis of nonlinear wave propagation in solids is thus necessary for a proper understanding of these phenomena. The current research focuses on the development of novel algorithms for nonlinear finite element analysis of stress wave propagation in hyperelastic waveguides. A full three-dimensional(3D) finite element analysis of stress wave propagation in waveguides is both computationally difficult and expensive, especially in the presence of nonlinearities. By definition, waveguides are solids with special geometric features that channel the propagation of stress waves along certain preferred directions. This suggests the use of kinematic waveguide models that take advantage of the special geometric features of the waveguide. The primary advantage of using waveguide models is the reduction of the problem dimension and hence the associated computational cost. Elementary waveguide models like the Euler-Bernoulli beam model, Kirchoff plate model etc., which are developed primarily within the context of linear elasticity, need to be modified appropriately in the presence of material/geometric nonlinearities and/or loads with high frequency content. This modification, besides being non-trivial, may be inadequate for studying nonlinear wave propagation and higher order waveguide models need to be developed. However, higher order models are difficult to formulate and typically have complex governing equations for the kinematic modes. This reflects in the relatively scarce research on the development of higher order waveguide models for studying nonlinear wave propagation. The formulation is difficult primarily because of the complexity of both the governing equations and their linearization, which is required as part of a nonlinear finite element analysis. One of the primary contributions of this thesis is the development and implementation of a general, flexible and efficient framework for automating the finite element analysis of higher order kinematic models for nonlinear waveguides. A hierarchic set of higher order waveguide models that are compatible with this formulation are proposed for this purpose. This hierarchic series of waveguide models are similar in form to the kinematic assumptions associated with standard waveguide models, but are different in the sense that no conditions related to the stress distribution specific to a waveguide are imposed since that is automatically handled by the proposed algorithm. The automation of the finite element analysis is accomplished with a dexterous combination of a nodal degrees-of-freedom based assembly algorithm, automatic differentiation and a novel procedure for numerically computing the finite element matrices directly from a given waveguide model. The algorithm, however, is quite general and is also developed for studying nonlinear plane stress configurations and inhomogeneous structures that require a coupling of continuum and waveguide elements. Significant features of the algorithm are the automatic numerical derivation of the finite element matrices for both linear and nonlinear problems, especially in the context of nonlinear plane stress and higher order waveguide models, without requiring an explicit derivation of their algebraic forms, automatic assembly of finite element matrices and the automatic handling of natural boundary conditions. Full geometric nonlinearity and the hyperelastic form of material nonlinearity are considered in this thesis. The procedures developed here are however quite general and can be extended for other types of material nonlinearities. Throughout this thesis, It is assumed that the solids under investigation are homogeneous and isotropic. The subject matter of the research is developed in four stages: First, a comparison of different finite element discretization schemes is carried out using a simple rod model to choose the most efficient computational scheme to study nonlinear wave propagation. As part of this, the frequency domain Fourier spectral finite element method is extended for a special class of weakly nonlinear problems. Based on this comparative study, the Legendre spectral element method is identified as the most efficient computational tool. The efficiency of the Legendre spectral element is also illustrated in the context of a nonlinear Timoshenko beam model. Since the spectral element method is a special case of the standard nonlinear finite element Method, differing primarily in the choice of the element basis functions and quadrature rules, the automation of the standard nonlinear finite element method is undertaken next. The automatic finite element formulation and assembly algorithm that constitutes the most significant contribution of this thesis is developed as an efficient numerical alternative to study the physics of wave propagation in nonlinear higher order structural models. The development of this algorithm and its extension to a general automatic framework for studying a large class of problems in nonlinear solid mechanics forms the second part of this research. Of special importance are the automatic handling of nonlinear plane stress configurations, hierarchic higher order waveguide models and the automatic coupling of continuum and higher order structural elements using specially designed transition elements that enable an efficient means to study waveguides with local inhomogeneities. In the third stage, the automatic algorithm is used to study wave propagation in hyperelastic waveguides using a few higher order 1D kinematic models. Two variants of a particular hyperelastic constitutive law – the6-constantMurnaghanmodel(for rock like solids) and the 9-constant Murnaghan model(for metallic solids) –are chosen for modeling the material nonlinearity in the analysis. Finally, the algorithm is extended to study energy-momentum conserving time integrators that are derived within a Hamiltonian framework, thus illustrating the extensibility of the algorithm for more complex finite element formulations. In short, the current research deals primarily with the identification and automation of finite element schemes that are most suited for studying wave propagation in hyper-elastic waveguides. Of special mention is the development of a novel unified computational framework that automates the finite element analysis of a large class of problems involving nonlinear plane stress/plane strain, higher order waveguide models and coupling of both continuum and waveguide elements. The thesis, which comprises of 10 chapters, provides a detailed account of various aspects of hyperelastic wave propagation, primarily for 1D waveguides.