Sorin Mitran, University of North Carolina at Chapel Hill


Continuum-microscopic computation of constitutive laws for viscoelastic flow

Abstract: A method to compute continuum viscoelastic flows starting from spatially inhomogeneous microscopic models is presented. Adaptive mesh refinement is employed on the continuum level to dynamically locate areas of high flow property gradients. Areas so identified are sampled at a microscopic level in accordance with some microscopic model (e.g. Kelvin, Zener, Burgers) which features spatially varying properties. A hierarchical microscopic simulation is carried out in order to computationally identify statistical moments entering into the continuum level consitutive law. Dynamics from a finer level of microscopic simulation are analyzed through principal orthogonal decomposition and higher-order tensor decompositions in order to identify modes that are representable on a coarser level. Thermal background is captured through a multi-level heat equation. Applications especially related to rupture phenomena are presented.


Address: Applied Mathematics, CB #3250 Phillips Hall University of North Carolina at Chapel Hill Chapel Hill, NC  27599-3250.

                http://www.amath.unc.edu/Faculty/mitran/