Simulations using the Finite Element Method (FEM) play an increasingly important role in the design process of joints and fasteners in the aerospace industry. In order to utilize the potential of such adhesive bonding, there is an increasing need for effective and accurate computational methods. The geometry and the nature of an adhesive joint are, however, not so simple to describe effectively using standard FEM-codes. To overcome this difficulty, special FEM-elements can be developed that provide a material surface treatment of the adhesive and the joined parts. In order to create a model that reflects the above features, one may introduce proper scalings on the geometry and on the material properties in terms of a perturbation parameter. Within the framework of three-dimensional elasticity, together with an asymptotic expansion method, a material surface model is obtained through a systematic procedure. In such a derivation, no a priori assumptions for the displacements or stress fields are needed. The final result is a variational equation posed over a single reference surface which forms the basis of a structural element for the compound joint. Through the usage of continuum damage mechanics and the framework of a generalized standard material, the linear elastic model is extended to include an elastic-plastic material model with damage for the adhesive. The model is FE-discretized and an important implication is that the (quasi-static) propagation of the local failure zone in the adhesive layer can be simulated. The failure load is obtained as a computational result and consequently no postulated failure criterion is needed. The derived FE-method opens up the possibility to efficiently model and analyze the mechanical behavior of large bonded structures. / At the time the thesis was defended paper I. was in fact two manuscripts, which later were combined to give the published article.

A Mecânica do Dano Contínuo é atualmente uma poderosa ferramenta para se modelar o comportamento não-linear de vários materiais decorrente da evolução de um processo de microfissuração. A perda de rigidez causada pelo processo físico tem sido considerada em modelos constitutivos através de variáveis de dano escalar, vetorial ou tensorial. Quando o carregamento é proporcionalmente crescente as deformações residuais podem ser ignoradas e relações constitutivas simples podem ser obtidas, onde os efeitos do dano aparecem por uma penalização direta das propriedades elásticas. Por outro lado, efeitos de dano podem ser acoplados com deformações residuais levando a relações constitutivas mais gerais. Esse trabalho está relacionado a esses tipos de modelos assumindo que o meio ideal apresenta um comportamento elástico linear com danificação ou elastoplástico com danificação. Um dos principais aspectos discutido relaciona-se à formulação variacional, a qual está baseada em conceitos de Análise Convexa e Não-Convexa. Explorando o fato que a evolução do dano tem correspondência com a idealização de regime de encruamento negativo, a teoria de localização de deformação é abordada e um estudo da condição necessária de singularidade ou perda da condição de elipticidade é realizado. Na sequência, uma proposta preliminar para uma análise de pós-singularidade, baseada na Teoria de Bifurcação, é feita no sentido de caracterizar pontos limite ou pontos de bifurcação de solução, em sistemas conservativos. / Continuum Damage Mechanics is nowadays a powerful tool to model the non-linear behaviour of several materials due to evolution of a microcracking process. The lost of rigidity caused by such physical process has been accounted in the constitutive models through a scalar, vectorial or tensorial damage variables. When proportional loading is considered the residuals strains can be ignored and simple constitutive relations can be obtained in which damage effects appear by direct penalization of the elastic properties. On the other hand, damage effects can be coupled with residual strains leading to more general constitutive relations. This work is related to such kind of models assuming that the ideal medium presents a linear elastic-damage or an elastoplastic-damage behaviour. One of the main topics discussed is related to the variational formulation which is based on Convex and Non-Convex Analysis concepts. Exploring the fact that damage evolution has correspondence with a softening idealised regime, the strain localization theory is treated and a study of a necessary condition for singularity or ellipticity tose condition is developed. In the sequence, a introductory poscritical analysis is proposed, based in the bifurcation theory and aiming to detect if the singularity corresponds to a limit or a bifurcation point solution, in conservative systems.

Le principal objectif de ce travail est l'étude de la fragmentation d'enveloppes métalliques. Cette thèse est divisée en quatre parties : la construction d'un modèle d'endommagement, l'implémentation numérique, la calibration des paramètres du modèle en utilisant des données expérimentales, et des travaux analytiques.Tout d'abord, nous avons considéré des modèles qui couplent les modèles d'endommagement classiques avec la plasticité et la dynamique. En utilisant l'énergie et l'action du système, nous avons obtenu toutes les équations qui décrivent le modèle dynamique et ductile : l'équation de la dynamique, le critère de plasticité et le critère d'endommagement. Nous avons ensuite détaillé l'implémentation numérique de ces modèles.Des résultats qualitatifs ont ensuite pu être obtenus, comme le nombre et la direction des fissures, ainsi que la convergence vers le modèle quasi-statique.Afin de mieux comprendre l'influence de chaque paramètre du modèle, nous avons étudié analytiquement le problème. A partir de l'observation de l'amplitude des perturbations, nous avons pu décrire comment obtenir une approximation analytique du nombre de fissures dans le cas d'un anneau en expansion.Cependant, pour être capable de simuler des problèmes réalistes, il est nécessaire de calibrer les paramètres du modèle. Nous nous sommes intéressés plus particulièrement au cas des matériaux fragiles. Les données expérimentales ont été obtenues par une série d'expériences réalisée par le CEA.Afin d'empêcher la localisation de la déformation plastique dans des bandes d'épaisseur nulle, d'autres formes de régularisation ont été étudiées, comme par exemple, l'utilisation des propriétés dissipatives du champ de température.Enfin, nous avons conclu ce travail en proposant des modèles de plasticité où l'énergie dépend aussi du gradient de la déformation plastique (modèles de plasticité à gradient). / The main objective of this work was the study of the fragmentation of a metallic shell. This thesis is divided into four parts: construction of a damage model, numerical implementation, calibration of the model parameters using experimental data and analytical works.In this work, we considered a model that couples the standard gradient damage models with plasticity and dynamics. Using the energy and the action of the system, we could obtain all the equations necessary to describe the dynamic ductile model: the equations of dynamics, the plasticity criterion and the damage criterion. We then detail the numerical implementation of these models.Some qualitative behaviours are then obtained, such as the number and the direction of cracks, and the convergence to the quasi-static model.In order to better understand the influence of the parameters, we studied the problem analytically. By studying the amplitude of the perturbations, we describe how to obtain an analytic approximation for the number of cracks in a ring under expansion.In order to run realistic simulations, it is needed to calibrate the material parameters. We focus here on a simple case of brittle materials. The experimental data were obtained in a series of shockless spalling tests performed by the CEA.We also study other forms of regularization, now applied to the plastic strain, avoiding localization in zero-thickness bands.We considered using the dissipative properties of the temperature field to regularize the model. Finally, we conclude with plasticity models where we add a term depending on the gradient of the plastic strain (gradient plasticity models).

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Dentre os materias comumente utilizados hà um destaque especial para os materiais compÃsitos polimÃricos, desde a fabricaÃÃo de brinquedos a artÃficios bÃlicos. Dessa forma faz-se necessÃrio uma investigaÃÃo ampla sobre todos os aspectos referentes a esses materiais. Assim, a presente pesquisa objetiva avaliar os processos de danificaÃÃo de um compÃsito polimÃrico ( polimetil metacrilato â PMMA, reforÃado com fibra de vidro) atravÃs de um modelo matemÃtico para a tensÃo normal. Primeiramente, foi realizada uma bateria de ensaios de traÃÃo e simulados numericamente, onde foram encontrados os parÃmetros matemÃticos caracterÃsticos deste material, foram apresentados tambÃm, os aspectos relativos a caracterizaÃÃo quÃmica e metalogrÃfica. A seguir foi realizado AnÃlises Computacionais pelo mÃtodo dos elementos finitos em um cÃdigo de cÃlculo internacionalmente conhecido, com o objetivo de verificar a relaÃÃo existente entre o comprimento de trincas e o valor da variÃvel dano. De posse destes dados foram determinados os valores para a variÃvel D0, e os intervalos de validade da expressÃo apresentada. Finalmente concluÃmos a importÃncia de estudos como este a fim de que se possa obter histÃricos de degradaÃÃo do material, para posterior anÃlise de vida remanescente do mesmo. Ainda nesta tÃnica determinou-se a relaÃÃo dano x comprimento da trinca, algo original em nossa literatura nacional, alÃm da apresentaÃÃo de sugestÃes para novos trabalhos, relacionados com a mecÃnica do dano em diversos materiais. / Dentre os materias comumente utilizados hà um destaque especial para os materiais compÃsitos polimÃricos, desde a fabricaÃÃo de brinquedos a artÃficios bÃlicos. Dessa forma faz-se necessÃrio uma investigaÃÃo ampla sobre todos os aspectos referentes a esses materiais. Assim, a presente pesquisa objetiva avaliar os processos de danificaÃÃo de um compÃsito polimÃrico ( polimetil metacrilato â PMMA, reforÃado com fibra de vidro) atravÃs de um modelo matemÃtico para a tensÃo normal. Primeiramente, foi realizada uma bateria de ensaios de traÃÃo e simulados numericamente, onde foram encontrados os parÃmetros matemÃticos caracterÃsticos deste material, foram apresentados tambÃm, os aspectos relativos a caracterizaÃÃo quÃmica e metalogrÃfica. A seguir foi realizado AnÃlises Computacionais pelo mÃtodo dos elementos finitos em um cÃdigo de cÃlculo internacionalmente conhecido, com o objetivo de verificar a relaÃÃo existente entre o comprimento de trincas e o valor da variÃvel dano. De posse destes dados foram determinados os valores para a variÃvel D0, e os intervalos de validade da expressÃo apresentada. Finalmente concluÃmos a importÃncia de estudos como este a fim de que se possa obter histÃricos de degradaÃÃo do material, para posterior anÃlise de vida remanescente do mesmo. Ainda nesta tÃnica determinou-se a relaÃÃo dano x comprimento da trinca, algo original em nossa literatura nacional, alÃm da apresentaÃÃo de sugestÃes para novos trabalhos, relacionados com a mecÃnica do dano em diversos materiais.

A danificaÃÃo e a falha do concreto sÃo largamente investigadas no ramo da MecÃnica do Dano em Meios ContÃnuos. VÃrios modelos existem na literatura e descrevem muito bem uma variedade de fenÃmenos observados, dependendo de sua complexidade. O principal objetivo deste trabalho à investigar e modelar os efeitos da corrosÃo no dano e falha das propriedades do concreto. Inicialmente, foram feitos ensaios de traÃÃo e de compressÃo em alguns corpos-de- prova intactos sem que tivessem sido submetidos a nenhuma corrosÃo para determinar o comportamento mecÃnico do concreto. Outros foram submetidos a uma cÃmara de corrosÃo acelerada Salt Spray ( durante perÃodos de tempo diferentes) para determinar esse comportamento considerando a corrosÃo. Para o ensaio de traÃÃo, foi desenvolvido um dispositivo composto de peÃas de aÃo, onde se pode realizar esse ensaio de tal maneira a se obter os grÃficos de tensÃo deformaÃÃo utilizando corpos-de-prova cilÃndricos iguais aos usados para a compressÃo. Com esses resultados experimentais, utilizando a MecÃnica do Dano em Meios ContÃnuos, um modelo elÃstico aclopado ao dano à usado para modelar o comportamento do concreto. Em um primeiro estÃgio, a elasticidade isotrÃpica e o dano isotrÃpico ( somente com uma variÃvel escalar D) sÃo usados, mas incluindo-se os efeitos da corrosÃo. Nos resultados, à analisada a evoluÃÃo do dano no concreto em relaÃÃo ao tempo de exposiÃÃo dos corpos-de-prova na cÃmara de corrosÃo acelerada Salt Spray e em funÃÃo dos carregamentos mecÃnicos. / A danificaÃÃo e a falha do concreto sÃo largamente investigadas no ramo da MecÃnica do Dano em Meios ContÃnuos. VÃrios modelos existem na literatura e descrevem muito bem uma variedade de fenÃmenos observados, dependendo de sua complexidade. O principal objetivo deste trabalho à investigar e modelar os efeitos da corrosÃo no dano e falha das propriedades do concreto. Inicialmente, foram feitos ensaios de traÃÃo e de compressÃo em alguns corpos-de- prova intactos sem que tivessem sido submetidos a nenhuma corrosÃo para determinar o comportamento mecÃnico do concreto. Outros foram submetidos a uma cÃmara de corrosÃo acelerada Salt Spray ( durante perÃodos de tempo diferentes) para determinar esse comportamento considerando a corrosÃo. Para o ensaio de traÃÃo, foi desenvolvido um dispositivo composto de peÃas de aÃo, onde se pode realizar esse ensaio de tal maneira a se obter os grÃficos de tensÃo deformaÃÃo utilizando corpos-de-prova cilÃndricos iguais aos usados para a compressÃo. Com esses resultados experimentais, utilizando a MecÃnica do Dano em Meios ContÃnuos, um modelo elÃstico aclopado ao dano à usado para modelar o comportamento do concreto. Em um primeiro estÃgio, a elasticidade isotrÃpica e o dano isotrÃpico ( somente com uma variÃvel escalar D) sÃo usados, mas incluindo-se os efeitos da corrosÃo. Nos resultados, à analisada a evoluÃÃo do dano no concreto em relaÃÃo ao tempo de exposiÃÃo dos corpos-de-prova na cÃmara de corrosÃo acelerada Salt Spray e em funÃÃo dos carregamentos mecÃnicos.

The problem of damage accumulation in laminated composite materials hasreceived much attention due to their widespread application in the aerospace, automotive,civil, and sports industries. In the aerospace industry, composites are usedto make light weight and efficient structural components. In the Boeing 787, forexample, more than 50% of the structure is made of composite materials. Althoughthere have been significant developments in analyzing cross-ply laminates, none ofthe present approaches provides reasonable predictions for multidirectional laminatesin which intralaminar cracks may form in multiple orientations. Nevertheless, theprediction of damage accumulation and its effect on structural performance is a verydifficult problem due to complexity of the cracking processes.This study presents a synergistic damage mechanics (SDM) methodology to analyzedamage behavior in multidirectional composite laminates with intralaminarcracks in plies of multiple orientations. SDM combines the strengths of micro-damagemechanics (MDM) and continuum damage mechanics (CDM) in predicting the stiffness degradation due to these cracks. The micromechanics is performed on a representativeunit cell using a three-dimensional finite element analysis to calculate thecrack opening displacement accounting for the influence of the surrounding plies, theso-called constraint effect. This information is then incorporated in the CDM formulationdealing with laminates containing cracks in different ply orientations through a `constraint parameter'. Following CDM, a separate damage mode is defined for eachtype of crack and the expressions for engineering moduli of the damaged laminateare then derived in terms of crack density and the constraint parameter. The SDMmethodology is implemented for [0m/±θn/0m/2]s laminates containing cracks in ±θplies. It is then extended to [0m/±θn/90r]s and [0m/90r/±θn]s laminates with cracksadditionally in the 90°-plies. The predictions agree well with published experimentaldata as well as independent FE computations. Limited parametric studies areperformed to show usability of SDM for more general laminates.To predict the initiation and growth of intralaminar cracks, an energy basedmodel is proposed in which these cracks initiate and multiply when the work requiredto form new set of cracks exceeds a laminate dependent critical energy release rate.The approach requires determination of average crack opening and sliding displacementsat varying crack spacing. This task is performed through a suitable 3-D FEanalysis. In case of off-axis ply cracking, a mixed mode fracture criterion is utilized,where the critical energy release rates in normal and shear modes are determinedby fitting the damage model with the experimental data for a reference laminate.The predictions from the model for [0/± θ4/01/2]s and [0/90/ ± 45]s laminates showremarkable agreement with the experimental results.The methodology and the results covered in this dissertation will be of interest tomechanics of materials researchers as well as to engineers in industry where compositematerials for structural applications are of interest.

In-service inspections of high temperature pressureequipment show that weldments are prone to creep and fatiguedamage. It is not uncommon that severely damaged weldments arefound even before the design life of the component has beenreached. In order to improve this situation action has beentaken during the last decades, both from industry, universitiesand research institutes, aiming at an enhanced understanding ofthe weldment response. The work presented in this thesis focuses on numericalsimulation of weldment creep response. For a more profoundunderstanding of the evolution of creep damage in mismatchedlow alloy weldments, simulations are performed using thecontinuum damage mechanics, CDM, concept. Both design and lifeassessment aspects are addressed. The possibility to assessseam welded pipes using results from tests of cross-weldspecimens taken out from the seam is investigated. It is foundthat the larger the cross-weld specimen the better thecorrelation. The advantage to use the CDM concept prior to aregular creep analysis is also pointed out. In order to developthe CDM analysis, a modified Kachanov-Rabotnov constitutivemodel is implemented into ABAQUS. Using this model, a secondredistribution of stresses is revealed as the tertiary creepstage is reached in the mismatched weldment. Creep crack growth, CCG, in cross-weld compact tension, CT,specimens is investigated numerically where a fracturemechanics concept is developed in two steps. In the first one,the C*value and an averaged constraint parameter areused for characterising the fields in the process zone, whilein the second step, the creep deformation rate perpendicular tothe crack plane and a constraint parameter ahead of the cracktip, are used as characterising parameters. The influence oftype and degree of mismatch, location of starter notch as wellas size of CT specimen, is investigated. Results show that notonly the material properties of the weldment constituentcontaining the crack, but also the deformation properties ofthe adjacent constituents, influence the CCG behaviour.Furthermore, the effect of size is influenced by the mismatchof the weldment constituents. A circumferentially cracked girth weld with differentmismatch is assessed numerically by use of the fracturemechanics concept developed. The results show that type anddegree of mismatch have a great influence on the CCG behaviourand that C*alone cannot characterise crack tip fields.Corresponding R5 assessments are also performed. Comparisonwith the numerical investigation shows that the assumption ofplane stress or plane strain conditions in the R5 analysis isessential for the agreement of the results. Assuming the formerresults in a relatively good agreement for the axial stressdominated cases while for the hoop stress dominated cases, R5predicts higher CCG rates by an order of magnitude. <b>Keywords:</b>ABAQUS, constraint effect, continuum damagemechanics, creep, creep crack growth, design, design code,finite element method, fracture mechanics, life assessment,mismatch, numerical simulation, weldment

The present work focuses on the formulation of a Continuum Damage Mechanics model for nonlinear analysis of masonry structural elements. The material is studied at the macro-level, i.e. it is modelled as a homogeneous orthotropic continuum. The orthotropic behaviour is simulated by means of an original methodology, which is based on nonlinear damage constitutive laws and on the concept of mapped tensors from the anisotropic real space to the isotropic fictitious one. It is based on establishing a one-to-one mapping relationship between the behaviour of an anisotropic real material and that of an isotropic fictitious one. Therefore, the problem is solved in the isotropic fictitious space and the results are transported to the real field. The application of this idea to strain-based Continuum Damage Models is rather innovative. The proposed theory is a generalization of classical theories and allows us to use the models and algorithms developed for isotropic materials. A first version of the model makes use of an isotropic scalar damage model. The adoption of such a simple constitutive model in the fictitious space, together with an appropriate definition of the mathematical transformation between the two spaces, provides a damage model for orthotropic materials able to reproduce the overall nonlinear behaviour, including stiffness degradation and strain-hardening/softening response. The relationship between the two spaces is expressed in terms of a transformation tensor which contains all the information concerning the real orthotropy of the material. A major advantage of this working strategy lies in the possibility of adjusting an arbitrary isotropic criterion to the particular behaviour of the orthotropic material. Moreover, orthotropic elastic and inelastic behaviours can be modelled in such a way that totally different mechanical responses can be predicted along the material axes. The aforementioned approach is then refined in order to account for different behaviours of masonry in tension and compression. The aim of studying a real material via an equivalent fictitious solid is achieved by means of the appropriate definitions of two transformation tensors related to tensile or compressive states, respectively. These important assumptions permit to consider two individual damage criteria, according to different failure mechanisms, i.e. cracking and crushing. The constitutive model adopted in the fictitious space makes use of two scalar variables, which monitor the local damage under tension and compression, respectively. Such a model, which is based on a stress tensor split into tensile and compressive contributions that allows the model to contemplate orthotropic induced damage, permits also to account for masonry unilateral effects. The orthotropic nature of the Tension-Compression Damage Model adopted in the fictitious space is demonstrated. This feature, both with the assumption of two distinct damage criteria for tension and compression, does not permit to term the fictitious space as “isotropic”. Therefore, the proposed formulation turns the original concept of “mapping the real space into an isotropic fictitious one” into the innovative and more general one of “mapping the real space into a favourable (or convenient) fictitious one”. Validation of the model is carried out by means of comparisons with experimental results on different types of orthotropic masonry. The model is fully formulated for the 2-dimensional case. However, it can be easily extended to the 3-dimensional case. It provides high algorithmic efficiency, a feature of primary importance when analyses of even large scale masonry structures are carried out. To account for this requisite it adopts a strain-driven formalism consistent with standard displacement-based finite element codes. The implementation in finite element programs is straightforward. Finally, a localized damage model for orthotropic materials is formulated. This is achieved by means of the implementation of a crack tracking algorithm, which forces the crack to develop along a single row of finite elements. Compared with the smeared cracking approach, such an approach shows a better capacity to predict realistic collapsing mechanisms. The resulting damage in the ultimate condition appears localized in individual cracks. Moreover, the results do not suffer from spurious mesh-size or mesh-bias dependence. The numerical tool is finally validated via a finite element analysis of an in-plane loaded masonry shear wall.

This dissertation proposes a finite element procedure for evaluating the high order strain derivatives in nonlocal computational mechanics. The superconvergent second derivative recovery methods used are proven to be effective in evaluating the Laplacian of the equivalent strain based on low order (linear) elements. Current nonlocal finite element techniques with linear elements are limited to structured meshes, while the new technique can deal with unstructured meshes with various element types. Other superconvergent patch recovery (SCP) based nonlocal approaches, such as the patch projection techniques only utilize nodal based patches to evaluate the first derivatives of the strain. The SCP technique has not yet been used for recovery of higher order strain derivatives. The proposed technique is capable of evaluating the Laplacian of the equivalent strain and has the potential for even higher order derivative recovery. The same patches can be easily utilized for error estimation and adaptive meshing for nonlocal problems. We employ two super-convergent patch options: the element based patch with all neighbors or only facing neighbors. The nonlocal strain derivatives can be recovered through either a mesh nodal averaging process or directly at the patch element quadrature points after the patch least square fitting problems are solved. Numerical examples for both strain gradient damage mechanics and strain gradient plasticity problems are given. In summary, the new finite element nonlocal computational technique based on the superconvergent second derivative recovery methods is proven to be robust in evaluating the high order strain derivatives with low order element unstructured meshes.

The problem of damage accumulation in laminated composite materials hasreceived much attention due to their widespread application in the aerospace, automotive,civil, and sports industries. In the aerospace industry, composites are usedto make light weight and efficient structural components. In the Boeing 787, forexample, more than 50% of the structure is made of composite materials. Althoughthere have been significant developments in analyzing cross-ply laminates, none ofthe present approaches provides reasonable predictions for multidirectional laminatesin which intralaminar cracks may form in multiple orientations. Nevertheless, theprediction of damage accumulation and its effect on structural performance is a verydifficult problem due to complexity of the cracking processes.This study presents a synergistic damage mechanics (SDM) methodology to analyzedamage behavior in multidirectional composite laminates with intralaminarcracks in plies of multiple orientations. SDM combines the strengths of micro-damagemechanics (MDM) and continuum damage mechanics (CDM) in predicting the stiffness degradation due to these cracks. The micromechanics is performed on a representativeunit cell using a three-dimensional finite element analysis to calculate thecrack opening displacement accounting for the influence of the surrounding plies, theso-called constraint effect. This information is then incorporated in the CDM formulationdealing with laminates containing cracks in different ply orientations through a `constraint parameter'. Following CDM, a separate damage mode is defined for eachtype of crack and the expressions for engineering moduli of the damaged laminateare then derived in terms of crack density and the constraint parameter. The SDMmethodology is implemented for [0m/±θn/0m/2]s laminates containing cracks in ±θplies. It is then extended to [0m/±θn/90r]s and [0m/90r/±θn]s laminates with cracksadditionally in the 90°-plies. The predictions agree well with published experimentaldata as well as independent FE computations. Limited parametric studies areperformed to show usability of SDM for more general laminates.To predict the initiation and growth of intralaminar cracks, an energy basedmodel is proposed in which these cracks initiate and multiply when the work requiredto form new set of cracks exceeds a laminate dependent critical energy release rate.The approach requires determination of average crack opening and sliding displacementsat varying crack spacing. This task is performed through a suitable 3-D FEanalysis. In case of off-axis ply cracking, a mixed mode fracture criterion is utilized,where the critical energy release rates in normal and shear modes are determinedby fitting the damage model with the experimental data for a reference laminate.The predictions from the model for [0/± θ4/01/2]s and [0/90/ ± 45]s laminates showremarkable agreement with the experimental results.The methodology and the results covered in this dissertation will be of interest tomechanics of materials researchers as well as to engineers in industry where compositematerials for structural applications are of interest.