סמינר מחלקתי ביה"ס להנדסה מכאנית Prof. Greg Rodin
School of Mechanical Engineering Seminar
Wednesday, January 4, 2016 at 15:00
Wolfson Building of Mechanical Engineering, Room 206
ON ELASTIC INTERACTIONS WITHIN REPRESENTATIVE VOLUME ELEMENTS CONTAINING INHOMOGENEITIES
Prof. Gregory J. Rodin
Institute for Computational Engineering and Sciences
University of Texas at Austin
Interactions in linear elastic composites containing inhomogeneities are examined using integral equations. Two types of elastic interactions are identified: (i) many-body interactions among inhomogeneities and (ii) collective interactions between the entire population of inhomogeneities and the boundary data. It is shown that for large specimens the latter interactions can be expressed in terms of macroscopic quantities. A simple approximation for the effective stiffness tensor is developed by assuming that the many-body interactions among inhomogeneities are negligible. The new approximation coincides with the Mori-Tanaka approximation for basic cases, but should be more accurate in general, as it is based on a less restrictive assumption. An integral equation is also used to examine the underlying assumptions of the Kanaun-Levin and Ponte-
-Willis approximations. Connections with Maxwell's approximation are established.
