Acknowledgments I would like to thank my family, friends, and colleagues who provided me with their friendship and support during my time in graduate school. My parents and family were, and continue to be, a constant source of encouragement. They inspired me to set ambitious goals for myself, and they heartened me when those goals seemed distant. The members of the GVU Center, especially the ot...

Fragility fractures, including neck of femur fractures, result from reductions in the amount, quality and architecture of bone. The aim of this study was to compare the cancellous bone structure, and static indices of bone turnover, in female patients who had sustained fragility fracture at the femoral neck, with age-matched females without fragility fracture. Bone samples were taken from the i...

The present work is concerned with the verification and validation of an implementation of the eigenfracture scheme of Schmidt et al. (SIAM J Multiscale Model Simul 7:1237–1266, 2009) based on material-point erosion, which we refer to as eigenerosion. Eigenerosion is derived from the general eigenfracture scheme by restricting the eigendeformations in a binary sense: they can be either zero, in...

Biomechanical tests are widely used in animal studies on osteoporotic fracture healing. However, the biomechanical recovery process is still unknown, leading to difficulty in choosing time points for biomechanical tests and in correctly assessing osteoporotic fracture healing. To determine the biomechanical recovery process during osteoporotic fracture healing, studies on osteoporotic femur fra...

This paper focuses on the analysis of the partial differential equations arising from a new approach to modeling brittle fracture based on an extension of continuum mechanics to the nanoscale. It is shown that ascribing constant surface tension to the fracture surfaces and using the appropriate crack surface boundary condition given by the jump momentum balance, leads to a sharp crack opening p...