Browsing by Subject "Phase-field modeling"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item Characterization and modeling of mixed-mode I+III fracture in brittle materials(2015-12) Pham, Khai Hong; Ravi-Chandar, K.; Landis, Chad M; Liechti, Kenneth M; Mear, Mark E; Marder, Michael PMixed-mode I+III fracture in brittle materials presents spectacular, scale-independent pattern formation in nature and engineering applications; and it is one of the last remaining puzzles in linear elastic fracture mechanics. This problem has received much attention in the literature over the past few decades both from experiments and analysis, but there are still open challenges that remain. Specifically, the existence of a threshold ratio of mode III to mode I loading below which fragmentation of the crack front (formation of daughter cracks) does not occur and the length scale associated with the spacing of the fragments when they do occur are still under debate. The continued growth of cracks under remote mode I + III loading is also of interest; it is observed that in some cases the fragmented cracks coalesce, while in others they maintain their independent development. We approach this problem through carefully designed experiments to examine the physical aspects of crack initiation and growth. This is then explored further through numerical simulations of the stress state that explore the influence of perturbations on the formation of daughter cracks. We show that a parent crack subjected to combined modes I+III loading exhibits fragmentation of the crack front into daughter cracks without any threshold. The distance between the daughter cracks is dictated by the length scale corresponding to the decay of the elastic field; this decay depends on the characteristic dimension of the parent crack from which the daughter cracks are nucleated. As the daughter cracks continue growing, they coarsen in spacing also through elastic shielding. As the daughter cracks grow farther, the parent crack, pinned at the original position, experiences increased stress intensity factor and the bridging regions begin to crack and the parent crack front advances towards the daughter cracks. This establishes a steady state condition for the system of parent crack with equally spaced daughter cracks to continue growing together. Finally, direct numerical simulation of crack initiation and growth is explored using a phase-field model. The model is first validated for in-plane modes I + II through comparison to experiments, and then used to explore combined modes I + III in order to study the above mechanism of mixed-mode I + III crack growth.Item A continuum modeling approach for the deposition of enamel(2015-12) Kuang, Ye; Landis, Chad M.; Mear, Mark EIn this report continuum methods to analyze organogenesis on curved surfaces is devised. This initial study will investigate a basic system. Dental enamel is the example system used to study the simulation of organogenesis as well as pattern formation. It is observed that dental enamel is created by a number of ameloblast cells migrating generally outward from the dental enamel junction (DEJ). These cells also rearrange locally within the surface that they reside. In this report, the simulations are based on the postulate that the cell motion arises from changes in the local strain environment as the cells migrate. As opposed to a passive movement driven by external driving forces or energy gradients, this theory hypothesizes that motion can arise internally due to the migration of the individual cell influenced by the local cell density and the velocity of the cell relative to its contacting neighbors. To model this kinematically driven approach we first develop a set of continuum equations to describe the velocity of the cells. This consists of two components, one the governs the in-plane rearrangements of the cells based on local strain cues, and a second that governs the velocity of the cells normal to the DEJ, which depends upon if the cells are actively secreting or not. This second feature requires the knowledge of the location of the boundary between secretory and non-secretory cells, which we is called the commencement front. On the secretory side of the commencement front the normal velocity of the cells is a specified quantity, while on the non-secretory side the normal velocity is zero. In order to track the evolution of the commencement front a phase-field description is utilized that treats this boundary as a diffuse instead of a sharp interface. The numerical method that is used to solve the equations is described, and some initial preliminary results for simple surface geometries are presented.Item Phase-field modeling of piezoelectrics and instabilities in dielectric elastomer composites(2011-12) Li, Wenyuan, 1982-; Landis, Chad M.; Huang, Rui; Mear, Mark; Tassoulas, John L.Ferroelectric ceramics are broadly used in applications including actuators, sensors and information storage. An understanding of the microstructual evolution and domain dynamics is vital for predicting the performance and reliability of such devices. The underlying mechanism responsible for ferroelectric constitutive response is ferroelectric domain wall motion, domain switching and the interactions of domain walls with other material defects. In this work, a combined theoretical and numerical modeling framework is developed to investigate the nucleation and growth of domains in a single crystal of ferroelectric material. The phase-field approach, applying the material electrical polarization as the order parameter, is used as the theoretical modeling framework to allow for a detailed accounting of the electromechanical processes. The finite element method is used for the numerical solution technique. In order to obtain a better understanding of the energetics of fracture within the phase-field setting, the J-integral is modified to include the energies associated with the order parameter. Also, the J- integral is applied to determine the crack-tip energy release rate for common sets of electromechanical crack-face boundary conditions. The calculations confirm that only true equilibrium states exhibit path-independence of J, and that domain structures near crack tips may be responsible for allowing positive energy release rate during purely electrical loading. The small deformation assumption is prevalent in the phase-field modeling approach, and is used in the previously described calculations. The analysis of large deformations will introduce the concept of Maxwell stresses, which are assumed to be higher order effects that can be neglected in the small deformation theory. However, in order to investigate the material response of soft dielectric elastomers undergoing large mechanical deformation and electric field, which are employed in electrically driven actuator devices, manipulators and energy harvesters, a finite deformation theory is incorporated in the phase-field model. To describe the material free energy, compressible Neo-Hookean and Gent models are used. The Jaumann rate of the polarization is used as the objective polarization rate to make the description of the dissipation frame indifferent. To illustrate the theory, electromechanical instabilities in composite materials with different inclusions will be studied using the finite element methods.