The study of the propagation of multiple cracks is essential to modeling and predicting structural integrity. The interaction between two cracks depends on a number of factors such as the domain geometry, the relative crack sizes and the separation between the two crack tips. In this paper, we study the interaction between two dynamically propagating cracks. We use the phase field method to track the crack paths, since this method can handle complex crack behavior such as crack branching, without any ad hoc criteria for crack evolution. The results from our dynamic simulations indicate that, unlike crack inter- action under quasi-static or fatigue loading, the presence of another crack does not accelerate crack propagation when dynamic loads are applied. However, some similarities in the crack topologies are observed for both quasi-static and dynamic loading.
Several constitutive theories have been proposed in the literature to model the viscoelastic response of soft tissue, including widely used rheological constitutive models. These models are characterized by certain parameters (“time constants”) that define the time scales over which the tissue relaxes. These parameters are primarily obtained from stress relaxation experiments using curve-fitting techniques. However, the question of how best to estimate these time constants remains open.
As a step towards answering this question, we develop an optimal experimental design approach based on ideas from information geometry, namely Fisher information and Kullback-Leibler divergence. Tissue is modeled as a standard linear solid and described using a one- or two-term Prony series. Treating the time constants as unknowns, we develop expressions for the Fisher information and Kullback-Leibler divergence that allow us to maximize information gain from experimental data. Based on the results of this study, we propose that the largest time constant estimated from a stress relaxation experiment for a linear viscoelastic material should be at most one-fifth of the total time of the experiment in order to maximize information gain.
This is the iBook version of chapter one of five. It requires the iBooks app to read. The media is embedded so no internet connection is necessary after the book has been downloaded. It contains many interactive widgets and videos that are not found in the epub, pdf, and mobi versions. However, the file size for this format is much larger and requires the book to be broken into individual chapters. All the text can be read by clicking the Closed Caption (CC) button on each video. There are keywords on the right side of each page to enable word searches.
Cincinnati's struggle for fair housing has been a long and often contested one. A handful of neighborhoods in the Queen City and its metropolitan area are now stably racially integrated and more seem likely to join that number in the near future. Yet there is much more work to be done, as the metropolitan area as a whole remains one of the most segregated in the nation.
Science teachers are often charged with providing discipline-specific literacy instruction. However, little is known about the reading and writing genres, or text types, typically found in these classrooms. In particular, there is a lack of knowledge about what opportunities adolescents have to engage with the genres privileged in science to learn the discipline's specialized ways of making meaning and communicating knowledge. This article reports on a case study of the reading and writing genres found within four middle-grade science classrooms in one small all-female school. Results suggest that although a variety of text genres were present, there was little discussion of how and why science content was presented in particular ways. Notably, students also had far more opportunities to read than write extended nonfiction. Teachers can cultivate a more reciprocal relation between reading and writing in science by using genres that students read as models for their writing.
