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. / Tire belts, seals, and impact absorbing cushions are usually made of fiber-reinforced rubberlike materials (FRRMs), but are difficult to analyze because their response to complex loading situations is strongly dependent on a variety of material properties. Many biological soft tissues, such as tendons, ligaments and arteries are also typically modeled as FRRMs. We assume that a fiber-reinforced rubberlike material can be modeled as nonlinear, incompressible and directionally dependent, with different response in tension and compression along the fiber direction. For such a material, the stored energy functions, W, depends upon five invariant metrics of the imposed strain state and the fiber direction. Explicit expressions for the stresses are derived for two polynomial functions of the five invariants for W. Homogeneous deformations such as simple extension, simple shear, and biaxial loading problems, nonhomogeneous deformations such as plane strain bending of a rectangle beam into a circular one, and inflation, twist and extension of a pressurized cylindrical laminate, are analyzed to reveal the mechanical behaviors descried by the developed material models. To enable the numerical solutions, the developed material models are incorporated in the commercial software, LS-DYNA, as user-defined subroutines. The implementations have been verified by ensuring that the computed solutions of several boundary value problems agree well with the derived analytical solutions or those available in the literature. The work provides theoretical guidelines for using quadratic polynomial functions for material models of FRRM, and delivers the software (user-defined material subroutines) capable of numerically analyzing large deformations of FRRM with different responses in tension and compressions. Large elasto-plastic deformations of T-peel joints have been analyzed using the commercial software, ABAQUS, to delineate conditions that result in self-similar debonding, enabling one to appropriately partition the energy involved in bending the adherends and propagating a debond. Using experimentally measured fracture energies from separate double cantilever beam (DCB) tests, implemented in a traction-separation law, accurate estimates of required peel force, crosshead displacements at break, and plastically deformed peel arm shapes are made. The demonstrated success of predicting load-displacement curves, deformed shape, and various energy metrics by using the traction-separation law in ABAQUS provides us with a framework to use in the future assessment of T-peel configurations being addressed in this study.