Micromechanics modeling of deformation, fracture growth in structural and biological materials

This dissertation consists of original work in two research areas: mechanics of composite materials and biomechanics of living tissues. A series of four theoretical studies has been carried out on deformation, fracture and growth in structural and biological materials. These are: (1) Delamination cracking in functionally graded coating/metal substrate systems, (2) Crack bridging in functionally graded coating/metal substrate systems, (3) Effective stiffness of biodegradable polymer matrix composites, and (4) A strain-gradient model for bone surface remodeling.; To provide quantitative guidance for optimal composites design, a number of micromechanics models have been developed based on basic mechanics concepts and theories, such as mixed-mode linear fracture mechanics, nonlinear thin-plate theory, position-dependent crack bridging mechanism, and time-dependent constitutive laws, etc., these models have applied to solve the fracture related problems such as delamination cracking and multiple cracking with bridging in functionally graded coating/substrate systems and to derive the effective stiffness of biodegradable polymer matrix composites used for bone fixation devices. Original results include: (1) Generic expressions of the stress intensity factors for an edge delamination crack in a FGM (functionally graded material) coating. (2) Finite element results for fracture mode mixity as a function of coating gradation, coating thickness and crack location for an edge delamination crack. (3) General expressions for the energy release rate and the critical temperature drop for a buckle-driven delamination crack as a function of material gradation, thermomechanical parameters of ceramic and metal phase, and location and length of crack. (4) The necessary increase in coating thickness owing to the material gradation in order to keep the temperature in the substrate within the limiting temperature. (5) A finite element model for computing the crack-tip energy release rate of multiple bridged cracks in a functionally graded coating. (6) Analytical expressions for the time-dependent effective stiffness of biodegradable polymer matrix composites with various types of reinforcement options, including spherical particles, aligned fibers and randomly oriented fibers.; In addition, a phenomenological model relating the applied strain gradient to the bone surface growth rate is also presented. The application of this model to quantitative studies of the adaption of bone structures, straightening of a slightly curved bone, and loosening of bone-implant interface shows a consistent picture with experimental observations.