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L'utilisation de limiteurs de localisation est nécessaire pour prendre en compte l'apparition de macro-fissures lors de la simulation de l'évolution des dégradations dans les matériaux composites stratifiés en accord avec des expérimentations. Ceux-ci introduisent un paramètre qui peut être relié à une longueur, ou un temps caractéristique, qui peut alors être identifié. L'approche introduite au LMT-Cachan consiste, dans le cadre dynamique, à utiliser un modèle d'endommagement retardé. Elle est basée sur le fait qu'une fissure ne peut pas apparaître instantanément. Ce modèle donne d'excellents résultats en restant dans le cadre de la dynamique et a l'avantage d'être local en espace. Cependant il requiert une discrétisation temporelle de la taille du temps caractéristique introduit (de l'ordre de la microseconde pour les composites), qui le rend inexploitable pour des simulations de chargement en quasi-statique. Les simulations dans ces cas de chargement nécessitent donc l'utilisation d'un temps caractéristique différent de celui identifié qui ne permet plus de maintenir un résultat en accord avec l'expérience. On cherche alors à adapter les paramètres de la loi d'évolution de l'endommagement afin d'obtenir une propagation de la macro-fissure dans la zone localisée qui soit compatible énergétiquement avec la mécanique de la rupture en contrôlant le taux de restitution d'énergie. Ce travail est dédié à maintenir l'objectivité de la solution et à adapter l'énergie dissipé à la mécanique de la rupture afin de pouvoir utiliser un temps caractéristique exploitable lors de simulations d'éprouvettes en composites sous un chargement quasi-statique. / The use of localization limiters is needed to take into account the apparition of macro-cracks during the simulation of the evolution of degradations in laminated composite materials with respect to experiments. Those introduce a parameter which can be related to a characteristic length, or a characteristic time, and therefore be identified. The approach introduced at LMT-Cachan is, in dynamics, to use a delayed damage model. It's based on the fact that a crack can't appear instantaneously. This model gives excellent results in dynamics and has the advantage to be local in space. Unfortunately, it requires a time discretization related to the characteristic time introduced (of the order of a microsecond for composites), which is far too computationally expensive for quasi-static simulations. Simulations in these loading cases need the use of a different characteristic time from the one identified which can't maintain anymore a result in accordance to experiments. We then adapt the parameters of the damage evolution law to obtain a propagation of a macro-crack in the localized zone that is energetically compatible with fracture mechanics by controlling the strain energy release rate. This work is dedicated to maintain the objectivity of the solution and to adapt the dissipated energy to fracture mechanics to be able to use a characteristic time exploitable for the simulation of composite samples under quasi-static loading.

El texto completo de este trabajo no está disponible en el Repositorio Académico UPC por restricciones de la casa editorial donde ha sido publicado. / In this paper, a three-dimensional numerical solution for the bending study of laminated composite doubly-curved shells is presented. The partial differential equations are solved analytically by the Navier summation for the midsurface variables; this method is only valid for shells with constant curvature where boundary conditions are considered simply supported. The partial differential equations present different coefficients, which depend on the thickness coordinates. A semi-analytical solution and the so-called Differential Quadrature Method are used to calculate an approximated derivative of a certain function by a weighted summation of the function evaluated in a certain grin domain. Each layer is discretized by a grid point distribution such as: Chebyshev-Gauss-Lobatto, Legendre, Ding and Uniform. As part of the formulation, the inter-laminar continuity conditions of displacements and transverse shear stresses between the interfaces of two layers are imposed. The proper traction conditions at the top and bottom of the shell due to applied transverse loadings are also considered. The present results are compared with other 3D solutions available in the literature, classical 2D models, Layer-wise models, etc. Comparison of the results show that the present formulation correctly predicts through-the-thickness distributions for stresses and displacements while maintaining a low computational cost. / Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica

Unlike published shell theories, the main two parts of this thesis are devoted to the asymptotic construction of a refined theory for composite laminated shells valid over a wide range of frequencies and wavelengths. The resulting theory is applicable to shells each layer of which is made of materials with monoclinic symmetry. It enables one to analyze shell dynamic responses within both long-wavelength, low- and high-frequency vibration regimes. It also leads to energy functionals that are both positive definiteness and sufficient simplicity for all wavelengths. This whole procedure was first performed analytically. From the insight gained from the procedure, a finite element version of the analysis was then developed; and a corresponding computer program, DVAPAS, was developed. DVAPAS can obtain the generalized 2-D constitutive law and recover accurately the 3-D results for stress and strain in composite shells. Some independent works will be needed to develop the corresponding 2-D surface analysis associated with the present theory and to continue towards full verification and validation of the present process by comparison with available published works.

A finite element model based on the layer-wise theory and the von Kármán type nonlinear strains is used to analyze damage in laminated composite beams. In the formulation, the Heaviside step function is employed to express the discontinuous interlaminar displacement field at the delaminated interfaces. Two types of the most common damage modes in composite laminates are investigated for cross-ply laminated beams using a numerical approach. First, a multi-scale analysis approach to determine the influence of transverse cracks on a laminate is proposed. In the meso-scale model, the finite element model based on the classical laminate theory provides the material stiffness reduction in terms of the crack density by computing homogenized material properties of the cracked ply. The multiplication of transverse cracks is predicted in a macro-scale beam model under bending loads. In particular, a damage analysis based on nonlinear strain fields in contrast to the linear case is carried out for a moderately large deformation. Secondly, the effect of delamination in a cross-ply laminated beam under bending loads is studied for various boundary conditions with various cross-ply laminate lay-ups. The crack growth of delamination is predicted through investigating the strain energy release rate. Finally, the interactions of a transverse crack and delamination are considered for beams of different configurations. The relationships between the two different damage modes are described through the density of intralaminar cracks and the length of the interlaminar crack. It is found that geometric nonlinearity plays an important role in progression of interlaminar cracks whereas growth of intralaminar cracks is not significantly influenced. This study also shows that the mixture of fracture mode I and II should be considered for analysis of delamination under bending loads and the fracture mode leading delamination changes as the damage develops. The growth of delamination originated from the tip of the transverse crack is found to strongly depend on the thickness of 90- degree layers as well as the transverse crack density. Further, the effect of interfacial crack growth on the transverse cracking can be quatitatively determined by the delamination length, the thickness of 90-degree layers and the transverse crack density.

We analyze by the finite element method transient deformations of a helmet mounted on a Roma Plastilina #1 clay-filled rigid and stationary headform. The helmet is made of a unidirectional fiber reinforced composite that is modeled as a linear elastic orthotropic material. Hashin's criteria are used to simulate the fiber and the matrix failure. The clay (impactor) is modeled as an elastic-plastic (elastic-viscoplastic), isotropic and homogeneous material. The problem is numerically solved by using the commercial software, ABAQUS, with built-in algorithms to simulate contact between distinct materials (e.g., the clay, the helmet, and the penetrator), and to delete elements whose material has failed. We have verified capabilities of the software for analyzing the penetration problems by solving a few impact problems that have been previously studied by others either experimentally or numerically. The effect of the number of layers in the helmet and the crater formed in the clay due to the impact of the projectile on the helmet has been delineated. It is believed that the crater size in the clay will provide useful information regarding the head injury trauma caused by the impact of a projectile on the helmet. / Master of Science

Doctor of Philosophy / Department of Civil Engineering / Hayder A. Rasheed / Thin-walled structures are major components in many engineering applications. When a thin-walled slender beam is subjected to lateral loads, causing moments, the beam may buckle by a combined lateral bending and twisting of cross-section, which is called lateral-torsional buckling. A generalized analytical approach for lateral-torsional buckling of anisotropic laminated, thin-walled, rectangular cross-section composite beams under various loading conditions (namely, pure bending and concentrated load) and boundary conditions (namely, simply supported and cantilever) was developed using the classical laminated plate theory (CLPT), with all considered assumptions, as a basis for the constitutive equations. Buckling of such type of members has not been addressed in the literature. Closed form buckling expressions were derived in terms of the lateral, torsional and coupling stiffness coefficients of the overall composite. These coefficients were obtained through dimensional reduction by static condensation of the 6x6 constitutive matrix mapped into an effective 2x2 coupled weak axis bending-twisting relationship. The stability of the beam under different geometric and material parameters, like length/height ratio, ply thickness, and ply orientation, was investigated. The analytical formulas were verified against finite element buckling solutions using ABAQUS for different lamination orientations showing excellent accuracy.

Theoretical formulations, analytical solutions, and finite element solutions for laminated composite plate and shell structures with smart material laminae are presented in the study. A unified third-order shear deformation theory is formulated and used to study vibration/deflection suppression characteristics of plate and shell structures. The von K??rm??n type geometric nonlinearity is included in the formulation. Third-order shear deformation theory based on Donnell and Sanders nonlinear shell theories is chosen for the shell formulation. The smart material used in this study to achieve damping of transverse deflection is the Terfenol-D magnetostrictive material. A negative velocity feedback control is used to control the structural system with the constant control gain. The Navier solutions of laminated composite plates and shells of rectangular planeform are obtained for the simply supported boundary conditions using the linear theories. Displacement finite element models that account for the geometric nonlinearity and dynamic response are developed. The conforming element which has eight degrees of freedom per node is used to develop the finite element model. Newmark's time integration scheme is used to reduce the ordinary differential equations in time to algebraic equations. Newton-Raphson iteration scheme is used to solve the resulting nonlinear finite element equations. A number of parametric studies are carried out to understand the damping characteristics of laminated composites with embedded smart material layers.

The objective of the present work is to investigate the behavior of laminated fiber -reinforced polymer matrix composite shell structures under bending load with the help of a modified finite element computer code which was previously developed for the analysis of pseudo-layered single material shells. The laminates are assumed to be orthotropic and the formulation is adapted to first order shear deformation theory. The aim is to determine the large deformation characteristics numerically, and to predict the modes of failure by the illustration of the critical elements of the model. Therefore, several failure theories are also integrated to the code to detect first ply failure. Triangular shell elements are used and all the related data are generated from the mid-plane. Laminates under transverse loading are analyzed through several boundary conditions and ply orientations. To verify the numerical results obtained, a commercial finite element program is used to compare the outputs of the study, and the comparison is found to have shown good agreement. The onset of damage is investigated by using different failure criteria consisting of maximum stress, Tsai-Wu, and Tsai- Hill theories and close results are obtained.

Theoretical formulations, analytical solutions, and finite element solutions for laminated composite plate and shell structures with smart material laminae are presented in the study. A unified third-order shear deformation theory is formulated and used to study vibration/deflection suppression characteristics of plate and shell structures. The von K??rm??n type geometric nonlinearity is included in the formulation. Third-order shear deformation theory based on Donnell and Sanders nonlinear shell theories is chosen for the shell formulation. The smart material used in this study to achieve damping of transverse deflection is the Terfenol-D magnetostrictive material. A negative velocity feedback control is used to control the structural system with the constant control gain. The Navier solutions of laminated composite plates and shells of rectangular planeform are obtained for the simply supported boundary conditions using the linear theories. Displacement finite element models that account for the geometric nonlinearity and dynamic response are developed. The conforming element which has eight degrees of freedom per node is used to develop the finite element model. Newmark's time integration scheme is used to reduce the ordinary differential equations in time to algebraic equations. Newton-Raphson iteration scheme is used to solve the resulting nonlinear finite element equations. A number of parametric studies are carried out to understand the damping characteristics of laminated composites with embedded smart material layers.