Levich Institute Seminar Announcement, 01/31/2006

Tuesday, 01/31/2006
2:00 PM
Steinman Hall, Room #312
(Chemical Engineering Conference Room)

Professor Stephen Cowin
City College of CUNY
Department of Mechanical Engineering

"Some Continuum Models of Materials with Flow or Deformation Dependent Microstructures"


The objective of this talk is to review the use of tensors to approximately characterize the local microstructure of solids or fluids in a continuum model. Two material models that employ such tensors, and also postulate constitutive equations for the evolution of the tensorial measures of microstructure during deformation, will be described. A transversely isotropic fluid is the first example and the second example is a model of the strain or strain-rate sensitive adaptation of the trabecular architecture of living cancellous bone. In the transversely isotropic fluid model a unit vector is used to represent the significant microstructure in a polymeric fluid. Second rank tensors are used to represent the significant aspects of microstructure in the cancellous bone model and in the characterization of local structure in quasi-statically deforming granular materials. Such second rank structural tensors are called "fabric" tensors. In highly porous cancellous bone the architecture of the porous solid matrix volume may be characterized by fabric tensors formed from various quantitative stereological measures (mean intercept length, volume orientation, star volume). In granular materials fabric tensors may be formed from contact normal data, from particle shape data or from pore volume orientation data and again represent certain, but different, aspects of the local structure. These tensors represent, approximately, the microstructure of the material in the material model and they endow the continuum model with a particular material symmetry.