Bourns Hall

Colloquium

David J. Steigmann Department of Mechanical Engineering University of California-Berkeley Puncturing a Thin Elastic Sheet Abstract Membrane theory is used to analyze the puncturing of a thin solid circular isotropic elastic sheet by a rigid axisymmetric indenter. A solution is obtained in which a hole is formed at the center of the sheet with an interior annulus in frictionless contact with the cylindrical surface. The contacting part is in a state of pure hoop stress with the corresponding hoop stretch exhibiting a strong singularity at the origin. Conditions are given ensuring that the solution has finite total energy and it is shown to be energetically favored over unpunctured states for transverse indenter displacements exceeding a finite critical value. It is found that puncturing is indicated even in materials for which conventional cavitation induced by boundary data alone is not possible. This finding is in accord with empirical observations for typical elastomers. Biosketch Dr. Steigmann received his Ph.D. in 1988 from Brown University, his M.Sc. in 1982 from MIT and his B.Sc. in 1979 from U. of Michigan. Currently he is an Associate Professor in the Department of Mechanical Engineering at UC Berkeley. Prior to joining UC Berkeley, Dr. Steigmann was a Professor in the Department of Mechanical Engineering at the University of Alberta, Canada. His current research interests are in the area of mechanics of thin films and thin-film/substrate systems, near-surface wave propagation and energy flux, electromagnetic phenomena in solid mechanics, applications to thin-film/substrate problems, surface stress, capillary phenomena, biological cell membranes, surfactant films in multi-phase fluid emulsions, finite elasticity, variational methods and elastic stability, tensile (membrane) structures, continuum mechanics, nonlinear three-dimensional mechanics of fabrics, numerical analysis of ill-conditioned structural problems and thin shells. Friday, April 15, 2005 Bourns Hall A265 3:10 p.m.-4:00 p.m. (Refreshments will be served at 3:00 p.m.)