title: A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic material.
abstract: A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stresses recently reported in R. Sainudiin, M. Moyers-Gonzalez and T. Burghelea, Soft Matter, 2015, 11(27), 5531-5545 is presented. The predictions of the model are in fair agreement with microscopic simulations and are in very good agreement with the micro-structural semi-empirical model reported in A. M. V. Putz and T. I. Burghelea, Rheol. Acta, 2009, 48, 673-689. With only two internal parameters, the nonlinear dynamical system model captures several key features of the solid-fluid transition observed in experiments: the effect of the interactions between microscopic constituents on the yield point, the abruptness of solid-fluid transition and the emergence of a hysteresis of the micro-structural states upon increasing/decreasing external forces. The scaling behaviour of the magnitude of the hysteresis with the degree of the steadiness of the flow is consistent with previous experimental observations. Finally, the practical usefulness of the approach is demonstrated by fitting a rheological data set measured with an elasto-viscoplastic material.
authors.affiliation: Université de Nantes, Nantes Atlantique Universités, CNRS, Laboratoire de Thermocinétique de Nantes, UMR 6607, La Chantrerie, Rue Christian Pauc, B.P. 50609, F-44306 Nantes Cedex 3, France. teodor.burghelea@univ-nantes.fr.
authors.forename: Teodor
authors.identifier: http://orcid.org/0000-0003-1631-9537
authors.initials: T
authors.lastname: Burghelea
authors.affiliation: School of Mathematics and Statistics, Private Bag 4800, University of Canterbury, Christchurch 8041, New Zealand. miguel.moyersgonzalez@canterbury.ac.nz.
authors.forename: Miguel
authors.initials: M
authors.lastname: Moyers-Gonzalez
authors.affiliation: Department of Mathematics, Uppsala University, Lägerhyddsvägen 1, Hus 1, 5 och 7, Box 480, 751 06 Uppsala, Sweden. raazesh.sainudiin@math.uu.se.
authors.forename: Raazesh
authors.initials: R
authors.lastname: Sainudiin