# American Institute of Mathematical Sciences

March  2013, 18(2): 283-293. doi: 10.3934/dcdsb.2013.18.283

## Modelling of wheat-flour dough mixing as an open-loop hysteretic process

 1 CSIRO Mathematics, Informatics and Statistics, North Road, ANU Campus, Acton ACT, GPO Box 664, Canberra, ACT 2601, Australia 2 Institute of Information Theory and Automation of the ASCR, Pod vodárenskou věží 4, 182 08 Prague, Czech Republic

Received  October 2011 Revised  July 2012 Published  November 2012

Motivated by the fact that various experimental results yield strong confirmatory support for the hypothesis that the mixing of a wheat-flour dough is essentially a rate-independent process'', this paper examines how the mixing can be modelled using the rigorous mathematical framework developed to model an incremental time evolving deformation of an elasto-plastic material. Initially, for the time evolution of a rate-independent elastic process, the concept is introduced of an "energetic solution'' [24] as the characterization for the rate-independent deformations occurring. The framework in which it is defined is formulated in terms of a polyconvex stored energy density and a multiplicative decomposition of large deformations into elastic and nonelastic (plastic or viscous) components. The mixing of a dough to peak dough development is then modelled as a sequence of incremental elasto-nonelastic deformations. For such incremental processes, the existence of Sobolev solutions is guaranteed. Finally, the limit passage to vanishing time increment leads to the existence of an energetic solution to our problem.
Citation: Robert S. Anderssen, Martin Kružík. Modelling of wheat-flour dough mixing as an open-loop hysteretic process. Discrete & Continuous Dynamical Systems - B, 2013, 18 (2) : 283-293. doi: 10.3934/dcdsb.2013.18.283
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