Abstract: This talk will examine how in several different types of complex materials, geometrical effects at the local level are closely related to their macro-scale properties. The talk will begin by examining flow in dense granular materials: due to strong heterogeneities in forces at the level of a single particle, this regime has long-resisted a complete continuum description. A simple model based upon local rearrangements of groups of particles will be presented, which can be used to recapitulate microscopic particle mixing in granular drainage. It will also be shown how examining local groups of particles in large-scale discrete-element simulations can be used to probe continuum quantities like plastic yield and mixing. As part of this work, a free software library for computing the Voronoi tessellation was developed which will be briefly discussed.
The talk will then describe the development of a continuum simulation of the shear transformation zone theory of Falk and Langer. The theory, motivated by local geometrical considerations, can be used to derive a continuum model of flow in amorphous media. Simulations employing finite differences and the level set method will be presented, to investigate the necking instability in a bar being stretched.
Time permitting, some preliminary results examining the forces between cells will be presented. Recent studies have suggested that mechanical feedback between cells can play an important role in the development of cancer. Simulations using a three-dimensional level set and hyperelastic finite difference framework will be presented, and compared to force response measurements of mammalian acini under compression. The simulations can provide insight on how forces will propagate through groups of cells in different geometries.
Bio: Chris Rycroft is a Morrey Assistant Professor in the UC Berkeley Mathematics Department and the Department of Mathematics at LBNL. He is interested in computational applied mathematics, and works on developing parallel and high-performance simulation methods to address problems in solid and fluid mechanics.
Currently he is collaborating on a number of research projects at different institutions, working with physicists at UC Santa Barbara and the Weizmann Institute on developing computational methods to study deformation in glassy materials. At LBL, he is using his Voronoi software library to automatically screen databases of zeolites to analyze their porosity properties. Chris also works with the Laboratory for Thermal-Hydraulics at the Paul Scherrer Institute, on designing a scaled-down engineering facility to study graphite wear at high temperatures. For more information about Chri's current work you can see his personal website at http://math.berkeley.edu/~chr/
Host: Prof. Frederic Gibou