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.

Computational prediction of the influence of crosslink distribution on the thermo-mechanical properties of epoxies

Experimental studies on epoxies report that the microstructure consists of highly crosslinked localized regions connected with a dispersed phase of low crosslink density. The various thermo-mechanical properties of epoxies might be affected by the crosslink distribution. But as experiments cannot report the exact number of crosslinked covalent bonds present in the structure, molecular dynamics is thus being used in this work to determine the influence of crosslink distribution on thermo-mechanical properties. Molecular dynamics and molecular mechanics simulations are used to establish wellequilibrated molecular models of EPON 862-DETDA epoxy system with a range of crosslink densities and various crosslink distributions. Crosslink distributions are being varied by forming differently crosslinked localized clusters and then by forming different number of crosslinks interconnecting the clusters. Simulations are subsequently used to predict the volume shrinkage, thermal expansion coefficients, and elastic properties of each of the crosslinked systems. The results indicate that elastic properties increase with increasing levels of overall crosslink density and the thermal expansion coefficient decreases with overall crosslink density, both above and below the glass transition temperature. Elastic moduli and coefficients of linear thermal expansion values were found to be different for systems with same overall crosslink density but having different crosslink distributions, thus indicating an effect of the epoxy nanostructure on physical properties. The values of thermo-mechanical properties for all the crosslinked systems are within the range of values reported in literature.

Model to describe the mode I fracture of steel fiber reinforced ultra-high performance concrete

Ultra-high performance fiber reinforced concrete (UHPFRC) has arisen from the implementation of a variety of concrete engineering and materials science concepts developed over the last century. This material offers superior strength, serviceability, and durability over its conventional counterparts. One of the most important differences for UHPFRC over other concrete materials is its ability to resist fracture through the use of randomly dispersed discontinuous fibers and improvements to the fiber-matrix bond. Of particular interest is the materials ability to achieve higher loads after first crack, as well as its high fracture toughness. In this research, a study of the fracture behavior of UHPFRC with steel fibers was conducted to look at the effect of several parameters related to the fracture behavior and to develop a fracture model based on a non-linear curve fit of the data. To determine this, a series of three-point bending tests were performed on various single edge notched prisms (SENPs). Compression tests were also performed for quality assurance. Testing was conducted on specimens of different cross-sections, span/depth (S/D) ratios, curing regimes, ages, and fiber contents. By comparing the results from prisms of different sizes this study examines the weakening mechanism due to the size effect. Furthermore, by employing the concept of fracture energy it was possible to obtain a comparison of the fracture toughness and ductility. The model was determined based on a fit to P-w fracture curves, which was cross referenced for comparability to the results. Once obtained the model was then compared to the models proposed by the AFGC in the 2003 and to the ACI 544 model for conventional fiber reinforced concretes.

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.