Mathematics Colloquium
Date:Lincoln NE 68508
Affiliation: Kansas State University
Local Host: Petronela Radu
Title: A role of surface energy in modeling of fracture
Additional Public Info:
It has been shown that taking into account surface mechanics is extremely important for accurate modeling of many physical phenomena such as those arising in nanoscience, fracture propagation and contact mechanics. In this talk we will discuss three models which incorporate surface energy of the boundary into the modeling of fracture, namely, those proposed by Gurtin-Murdoch, Slattery et al, and Steigmann-Ogden. All of these models are based on a physically valid assumption that behavior of molecules near a surface of a material is significantly different from that in the bulk. This phenomenon can be modeled by incorporating a local curvature and a local stretch of the material surface into the boundary conditions. The theory will be presented through the problems for straight and curvilinear interface and noninterface plane fractures. It will be shown that taking surface effects on the boundary into account results in elimination of the power and oscillating singularities at the crack tips which are predicted by linear elastic fracture mechanics. The mechanical problems will be reduced to the systems of singular integro-differential equations. The regularization and numerical solution of these systems will be addressed and numerical examples will be presented. Similarities and differences of the models will be studied. Potential directions for future research and connections with experimental results will be discussed.
Refreshments will be served 3:30-4:00 in 348 Avery. The talk is free and open to the public.