This dissertation presents applications of the finite element method in studying the durability of components used in aerospace (composites) and medical (hip implants) industries. In the first part of the dissertation the response of a fiber-reinforced composite material, subjected to loads that activate a number of micromechanisms of failure, is investigated in details. A composite material is heterogeneous in nature and generally exhibits local failures before final catastrophic failure at the structural level. The failure mechanisms in this class of materials generally span a number of length scales. Thus, local failure occurs at the micro-level in the form of fiber fracture, fiber buckling, matrix cracking, fiber-matrix debonding, and radial cracks at fiber-matrix interface. At the laminate level, failure occurs in the form of (i) intralaminar cracks in planes parallel and perpendicular to the fiber direction, and (ii) interlaminar cracks between two plies of a laminate; the latter resulting in delamination of the plies. A number of experimental studies aimed at understanding the failure mechanisms under different loading conditions have been reported in the literature. Simultaneously, various analytical and numerical models have also been developed to predict the different failure mechanisms. Such models match experimental data to varying degrees of accuracy. It is generally very difficult to consider all the different failure mechanisms that are observed in experiments, in a single numerical model. This area of research is still in progress. In this study, we focus on simultaneously capturing two major modes of failure that occur in fiber reinforced composites subjected to tensile loading. These are the splitting (intralaminar) and the delamination (interlaminar) modes of failure, respectively. Experimental observations suggest that these failure mechanisms typically occur in conjunction. The objective of this study is to model these experimental observations using tools available in the commercial finite element code, ABAQUS. Two different failure criteria, following the work by Hashin and Linde, respectively, are utilized to predict the intralaminar failure mechanisms. The interlaminar failure mechanisms, on the other hand, are modeled using cohesive elements that are based on a traction-separation law used to characterize the constitutive response of the interfaces between the plies. The predictions based on the numerical simulations are compared to experiments and other available data from the literature, and provide useful insights towards the combined modeling of the above-mentioned failure modes. In the second part of this dissertation an artificial hip implant is investigated from a durability point of view. The advent of artificial hip implants has restored mobility to a lot of patients in recent years, and total hip replacement surgeries are being performed routinely over the past few decades. In 2005 approximately 208,600 surgeries were performed and it is estimated to increase by approximately 174% by 2030. Given such a trend, it is important to ensure that the implant performs as flawlessly as possible, and as closely as possible to the real hip joint. This has led to studies seeking a detailed understanding of the mechanistic and biological aspects of hip implants. In this work, we develop a finite element model of the implant including the femoral ball, and analyze its mechanical response under a single stance phase of gait. The long term durability is investigated based on the computed stresses. In addition, the responses of two-dimensional models are compared to that of a corresponding three-dimensional model, with the aim of determining the applicability of simpler two-dimensional models towards making accurate predictions of the stress and deformation states in the implant. Some other aspects that are also investigated include: (i) the variations of the stress distribution in the implant with femoral ball size, (ii) the nature of the contact interactions between the femoral ball and the implant, and (iii) the influence of the details of the loading and the boundary conditions on the response of the implant. An analytical model is developed to validate the results from the two-dimensional model. The results suggest that the stresses in the neck region of the femoral stem are higher when a smaller sized femoral ball is used. However, the stresses in the region of contact between the ball and the stem appear to be higher for a larger sized femoral ball.
