0388861 20240103202136.920130207235959.9 000312737100002 10.3934/dcdsb.2013.18.283 11 s. cav_un_epca*02578451531-3492182 (2013)283-293AIMS Press Dissipation Dough mixing Rate-independent systems cav_un_auth*0289083 Anderssen R. AU cav_un_auth*0101142 Kružík Martin Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2013/MTR/kruzik-modelling of wheat-flour dough mixing as an open-loop hysteretic process.pdf IAA100750802 GA AV ČR cav_un_auth*0241214 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 /emph{„energetic solution“} /cite{mtl} 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 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. 2013 BA 2 http://hdl.handle.net/11104/0217941 MATHEMATICSAPPLIED 0.937 0.206 5.0 0.00627 0.665 962 131 0.847 ScienceCitationIndex Q2 54.739 33.665 Q2 Q2 2013 000312737100002 WOS cav_un_epca*0257845 Discrete and Continuous Dynamical Systems-Series B 1531-3492 1553-524X Roč. 18 č. 2 2013 283 293 AIMS Press