Cohesive Dynamics and Brittle Fracture

We formulate a nonlocal cohesive model for calculating the deformation state inside a cracking body. In this model a more complete set of physical properties including elastic and softening behavior are assigned to each point in the medium. We work within the small deformation setting and use the peridynamic formulation. Here strains are calculated as difference quotients. The constitutive relation is given by a nonlocal cohesive law relating force to strain. At each instant of the evolution we identify a process zone where strains lie above a threshold value. Perturbation analysis shows that jump discontinuities within the process zone can become unstable and grow. We derive an explicit inequality that shows that the size of the process zone is controlled by the ratio given by the length scale of nonlocal interaction divided by the characteristic dimension of the sample. The process zone is shown to concentrate on a set of zero volume in the limit where the length scale of nonlocal interaction vanishes with respect to the size of the domain. In this limit the dynamic evolution is seen to have bounded linear elastic energy and Griffith surface energy. The limit dynamics corresponds to the simultaneous evolution of linear elastic displacement and the fracture set across which the displacement is discontinuous. We conclude illustrating how the approach developed here can be applied to limits of dynamics associated with other energies that $\Gamma$- converge to the Griffith fracture energy.Comment: 38 pages, 4 figures, typographical errors corrected, removed section 7 of previous version and added section 8 to the current version, changed title to Cohesive Dynamics and Brittle Fracture. arXiv admin note: text overlap with arXiv:1305.453

University Scholar Series: Scott Myers-Lipton

Rebuild America: Solving the Economic Crisis through Civic Works On October 13, 2010, Scott Myers-Lipton spoke in the University Scholar Series hosted by Provost Gerry Selter at the Dr. Martin Luther King, Jr. Library. Scott Myers-Lipton is a Professor in the Sociology Department at SJSU. His recent book, titled Rebuild America: Solving the Economic Crisis through Civic Works, analyzes the history of U.S. public works and explores the federal government\u27s new emphasis to create jobs and build infrastructure.https://scholarworks.sjsu.edu/uss/1004/thumbnail.jp

Reviving Reliance

This Article explores the misalignment between the disclosure requirements of the federal securities laws and the private causes of action available to investors to enforce those requirements. Historically, federally mandated disclosures were designed to allow investors to set an appropriate price for publicly traded securities. Today’s disclosures, however, also enable stockholders to participate in corporate governance and act as a check on managerial misbehavior. To enforce these requirements, investors’ chief option is a claim under the general antifraud statute, section 10(b) of the Securities Exchange Act of 1934. But courts are deeply suspicious of investors’ attempts to use the Act to hold corporations liable for false statements related to governance. As this Article demonstrates, judicial skepticism can be traced to the functional elimination of the element of reliance from private investors’ claims. Without the element of reliance, courts cannot discriminate between deception, which section 10(b) prohibits, and poor managerial decisionmaking, to which section 10(b) does not speak. Doctrines that courts developed to distinguish between the two now have the perverse effect of devaluing disclosures intended to facilitate shareholder participation in corporate governance. More troublingly, they enforce a normative viewpoint that shareholders do not, or should not, have interests beyond the short-term maximization of a firm’s stock price. This interpretation of shareholder preferences undermines modern regulatory initiatives that employ shareholders as a restraining force on antisocial corporate conduct. This Article proposes that courts adopt new interpretations of section 10(b) that reestablish the centrality of reliance. By doing so, courts can facilitate shareholders’ participation in the corporate governance structure and reward investors who inhabit the role of corporate monitor