Advanced mechanics of materials with microstructure

The study of advanced materials aimed at improving human life has been performed since time immemorial. Such studies have created everlasting and greatly revered monuments and have helped revolutionize transportation by ushering the age of lighter–than–air flying machines. Hence a study of the mechanical behavior of advanced materials can pave way for their use for mankind’s benefit. In this school of thought, the aim of this dissertation is to broadly perform two investigations. First, an efficient modeling approach is established to predict the elastic response of cellular materials with distributions of cell geometries. Cellular materials find important applications in structural engineering. The approach does not require complex and time-consuming computational techniques usually associated with modeling such materials. Unlike most current analytical techniques, the modeling approach directly accounts for the cellular material microstructure. The approach combines micropolar elasticity theory and elastic mixture theory to predict the elastic response of cellular materials. The modeling approach is applied to the two dimensional balsa wood material. Predicted properties are in good agreement with experimentally determined properties, which emphasizes the model’s potential to predict the elastic response of other cellular solids, such as open cell and closed cell foams. The second topic concerns intraneural ganglion cysts which are a set of medical conditions that result in denervation of the muscles innervated by the cystic nerve leading to pain and loss of function. Current treatment approaches only temporarily alleviate pain and denervation which, however, does not prevent cyst recurrence. Hence, a mechanistic understanding of the pathogenesis of intraneural ganglion cysts can help clinicians understand them better and therefore devise more effective treatment options. In this study, an analysis methodology using finite element analysis is established to investigate the pathogenesis of intraneural ganglion cysts. Using this methodology, the propagation of these cysts is analyzed in their most common site of occurrence in the human body i.e. the common peroneal nerve. Results obtained using finite element analysis show good correlation with clinical imaging patterns thereby validating the promise of the method to study cyst pathogenesis.

Development of a continuum mechanics model of passive skeletal muscle

Skeletal muscle force evaluation is difficult to implement in a clinical setting. Muscle force is typically assessed through either manual muscle testing, isokinetic/isometric dynamometry, or electromyography (EMG). Manual muscle testing is a subjective evaluation of a patient’s ability to move voluntarily against gravity and to resist force applied by an examiner. Muscle testing using dynamometers adds accuracy by quantifying functional mechanical output of a limb. However, like manual muscle testing, dynamometry only provides estimates of the joint moment. EMG quantifies neuromuscular activation signals of individual muscles, and is used to infer muscle function. Despite the abundance of work performed to determine the degree to which EMG signals and muscle forces are related, the basic problem remains that EMG cannot provide a quantitative measurement of muscle force. Intramuscular pressure (IMP), the pressure applied by muscle fibers on interstitial fluid, has been considered as a correlate for muscle force. Numerous studies have shown that an approximately linear relationship exists between IMP and muscle force. A microsensor has recently been developed that is accurate, biocompatible, and appropriately sized for clinical use. While muscle force and pressure have been shown to be correlates, IMP has been shown to be non-uniform within the muscle. As it would not be practicable to experimentally evaluate how IMP is distributed, computational modeling may provide the means to fully evaluate IMP generation in muscles of various shapes and operating conditions. The work presented in this dissertation focuses on the development and validation of computational models of passive skeletal muscle and the evaluation of their performance for prediction of IMP. A transversly isotropic, hyperelastic, and nearly incompressible model will be evaluated along with a poroelastic model.

Quantification of relativistic perturbation forces on spacecraft trajectories

The intent of the work presented in this thesis is to show that relativistic perturbations should be considered in the same manner as well known perturbations currently taken into account in planet-satellite systems. It is also the aim of this research to show that relativistic perturbations are comparable to standard perturbations in speciffc force magnitude and effects. This work would have been regarded as little more then a curiosity to most engineers until recent advancements in space propulsion methods { e.g. the creation of a artiffcial neutron stars, light sails, and continuous propulsion techniques. These cutting-edge technologies have the potential to thrust the human race into interstellar, and hopefully intergalactic, travel in the not so distant future. The relativistic perturbations were simulated on two orbit cases: (1) a general orbit and (2) a Molniya type orbit. The simulations were completed using Matlab's ODE45 integration scheme. The methods used to organize, execute, and analyze these simulations are explained in detail. The results of the simulations are presented in graphical and statistical form. The simulation data reveals that the speciffc forces that arise from the relativistic perturbations do manifest as variations in the classical orbital elements. It is also apparent from the simulated data that the speciffc forces do exhibit similar magnitudes and effects that materialize from commonly considered perturbations that are used in trajectory design, optimization, and maintenance. Due to the similarities in behavior of relativistic versus non-relativistic perturbations, a case is made for the development of a fully relativistic formulation for the trajectory design and trajectory optimization problems. This new framework would afford the possibility of illuminating new more optimal solutions to the aforementioned problems that do not arise in current formulations. This type of reformulation has already showed promise when the previously unknown Space Superhighways arose as a optimal solution when classical astrodynamics was reformulated using geometric mechanics.