Fiber-reinforced rubberlike materials (FRRM) commonly used in tires undergo large deformations, and exhibit different response in tension and compression along the fiber direction. Assuming that the response of a fiber-reinforced rubberlike material can be modeled as transversely isotropic with the fiber direction as the axis of transverse isotropy, we express the stored energy function, W, in terms of the five invariants of the right Cauchy-Green strain tensor and the fiber direction, and account for different response in tension and compression along the fiber direction. It has been shown in the literature that in shear-dominated deformations, the 5th invariant, I5, significantly contribution to the stress-strain curve. We have implemented the constitutive relation in the commercial software, LS-DYNA. The numerical solutions of several boundary value problems studied here agree with their analytical solutions derived by using Ericksen's inverse approach, in which a part of the solution is assumed and unknowns in the presumed solution are then found by analyzing the pertinent boundary value problem. However, computed results have not been compared with experimental findings. For W of the FRRMs an expression that is a complete quadratic function of the five invariants is also examined. Homogeneous deformations such as simple extension, simple shear, and biaxial loading problems are studied to delineate the mechanical behaviors of FRRMs. Consistency with the infinitesimal deformation theory requires that linear terms in the 4th and 5th invariants, I4 and I5, be included in the expression for W. Stability analysis of deformations reveals the qualitative changes triggered by the second order terms of the quadratic function. Analytical solutions for inflation, extension and twist deformations caused by internal pressure, end torque, and axial force for a pressurized cylindrical laminate are derived using Ericksen's inverse method. Effects of fiber orientations on the mechanical behaviors of a +/-α angle-ply cylindrical tube are investigated using the derived analytical solutions. The T-peel test, widely used for characterizing adhesion across a plethora of adhesives, adherends, and geometries, results in a range of responses that may complicate meaningful interpretation of the test data. This research effort, involving several specific specimen types, was undertaken to investigate concerns that commonly used configurations may not always result in plateaus in the force-displacement response. We experimentally and numerically study debonding of T-peel specimens having 75 mm bond length and 0.81 mm thick adherends made of either 6061 aluminum (Al) or one of the three steels (G70 70U hot dip galvanized, E60 elctrogalvanized (EGZ), 1010 cold-rolled steel (CRS) bonded with either LORD® 406 or Maxlok™ acrylic adhesive. For the EGZ and the Al adherends, specimens with a bond length of 250 mm and adherend thickness of 1.60 mm are also examined. Effects of adherend materials and thicknesses, bond lengths, and adhesives on test results are examined using three metrics to interpret the T-peel bond performance. We find a limited correlation between the commonly used "T-peel strength" and the energy dissipated per unit debond area. For those two metrics, the relative performances of the CRS and the Al specimens are quite different. Quasi-static plane strain deformations of the test specimens are analyzed by the finite element method (FEM) and a cohesive zone model using the commercial software, ABAQUS, to help interpret the test data. Numerical results provided energies required to elastically and plastically deform the adherends, and help determine the transition from non-self-similar to self-similar debonding. The FE simulations also facilitate determination of the fraction of the crosshead displacement at which self-similar debonding occurs. Results reported herein should help practitioners select appropriate specimen dimensions for extracting meaningful data for adhesive performance. / Ph. D.

Cette thèse présente une approche globale de la modélisation du comportement thermomécanique et cyclique des alliages à mémoire de forme (AMF) en grandes déformations. Cette approche s’articule en trois étapes : i) La généralisation du modèle ZM de comportement des AMF en grandes déformations dans le cadre de la thermodynamique des processus irréversibles. Pour ce faire, le gradient de la transformation totale est décomposé sous la forme du produit de trois gradients : le gradient de transformation lié à la déformation élastique, le gradient lié au changement de phase et le gradient de transformation lié à la réorientation de la martensite. Cette décomposition permet ainsi la modélisation de la réponse des structures en AMF dans le cas de chargements multiaxiaux non-proportionnels en transformations fi nies. ii) La prise en compte du couplage thermomécanique en transformations fi nies. Pour ce faire, la déformation de Henckya été introduite. Le modèle obtenu intègre trois caractéristiques thermomécaniques importantes des AMF, à savoir l’effet de la coexistence de l’austénite et de deux variantes de martensites distinctes, la variation de la taille de la boucle d’hystérésis avec la température et la transition du processus de changement de phase, d’abrupt à doux. iii) Enfin, en vue de prédire la réponse des structures en AMF sous chargement thermomécanique cyclique, le modèle développé dans la deuxième étape est généralisé pour décrire la pseudoélasticité cyclique des AMF polycristallins. Le modèle obtenu permet la prise en compte de quatre caractéristiques fondamentales liées au comportement cyclique des AMF : la déformation résiduelle accumulée, la dégénérescence de la boucle d’hystérésis, l’évolution de la transformation de phase, d’abrupte à douce. La mise en œuvre numérique de ces modèles s’appuie sur des algorithmes d’intégration appropriés. Des exemples numériques on été traités pour valider chaque étape. / Shape Memory Alloys (SMAs) are a class of smart materials that possess two salient features known as pseudoelasticity (PE) and shape memory effect(SME). In industrial applications, SMA structures are typically subjected to complex service conditions, such as large deformations, thermomechanically coupled boundaries and loadings, and cyclic loadings. The reliability and durability analysis of these SMA structures requires a good understanding of constitutive behavior in SMAs. To this end, this work develops a comprehensive constitutive modeling approach to investigate thermomechanical and cyclic behavior of SMAs in fi nite deformations. The work is generally divided into three steps. First, to improve accuracy of SMA model infinite deformation regime, the ZM model proposed by Zaki and Moumni (2007b) is extended within a fi nite-strain thermodynamic framework. Moreover, the transformation strain is decomposed into phase transformation and martensite reorientation components to capture multi-axial non-proportional response. Secondly, in addition to the fi nite deformation, thermomechanical coupling effect is taken into account by developing a new fi nite-strain thermomechanical constitutive model. A more straightforward approach is obtained by using the fi nite Hencky strain. This model incorporates three important thermomechanical characteristics, namely the coexistence effect between austenite and two distinct martensite variants, the variation with temperature of hysteresis size, and the smooth transition at initiation and completion of phase transformation. Finally, with a view to studying SMA behavior under cyclic loading, the model developed in the second step is generalized to describe cyclic pseudoelasticity of polycrystalline SMAs. The generalized model captures four fundamental characteristics related to the cyclic behavior of SMAs: large accumulated residual strain, degeneration of pseudoelasticity and hysteresis loop, rate dependence, and evolution of phase transformation from abrupt to smooth transition. Numerical implementation of these models are realized by introducing proper integration algorithms. Finite element simulations, including orthodontic archwire, helical and torsion spring actuators, are carried out using the proposed models. The future directions of this work mainly involve plasticity and fatigue analysis of SMA structures.

The goal of this thesis is to develop a hybrid _nite element formulation to carry out stress analysis of arteries. To the best of our knowledge, a hybrid _nite element impel mentation of the Holzapfel-Ogden artery model has not been carried out before. Since arteries are thin `shell-type' structures, they are subjected to membrane, shear and volumetric locking in case when standard _nite elements are used. Since hybrid _nite elements are known to overcome these problems, we develop hybrid hexahedral element formulations (both lower and higher-order) for artery analysis. We demonstrate The better coarse mesh accuracy of hybrid elements, which are based on a two-_eld variational formulation, over conventional displacement based elements. Typically, wend that three or four extra levels of renement are required with conventional elements to achieve the ame accuracy as hybrid elements. The recently proposed Holzapfel-Ogden constitutive model for the artery and its implementation both within the conventional and hybrid _nite element frameworks is discussed. The numerical implementation is particularly challenging due to the presence of _bers which can only take tensile loads. The mathematically exact tangent stiness matrix that we have derived in this work is crucial in ensuring convergence of the numerical strategy.

Synthetic vascular grafts are useful to bypass diseased arteries. The long-term failure of synthetic grafts is primarily due to intimal hyperplasia at the anastomotic sites. The accelerated intimal hyperplasia may stem from a compliance mismatch between the host artery and the graft since commercially available synthetic conduits are much stiffer than an artery. The objective of this thesis is to design a method for fabricating a vascular graft that mechanically matches the patients native artery over the expected physiologic range of pressures. The creation of an optimized mechanical graft will hopefully lead to an improvement in patency rates. The mechanical equivalency between the graft and the host artery is defined locally by several criteria including the diameter upon inflation, the elasticity at mean pressure, and axial force. A single parameter mathematical for a thin-walled tube is used to describe of the final mechanical behavior of a synthetic graft. For the general problem, the objective would be to fabricate a mechanics-matching vascular graft for each host artery. Typically, fabrication parameters are set initially and the properties of the fabricated graft are measured. However, by modeling the entire fabrication process and final mechanical properties, it is possible to invert the situation and let the typical output mechanical values be used to define the fabrication parameters. The resultant fabricated graft will then be mechanically matching. As a proof-of-concept, several prototype synthetic grafts were manufactured and characterized by a single Invariant to match a canine artery. The resultant graft equaled the diameter upon inflation, the elasticity at mean pressure, and axial force of the native canine artery within 6%. An alternative to making an individual graft for each artery is also presented. A surgeon may choose the best graft from a set of pre-manufactured grafts, using a computer program algorithm for best fit using two parameters in a neighborhood. The design optimization problem was solved for both canine carotid and human coronary arteries. In conclusion, the overall process of design, fabrication and selection of a mechanics matching synthetic vascular graft is shown to be reliable and robust.