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Preface
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 |
References:
[1] |
R. S. Anderssen and P. W. Gras, The hysteretic behaviour of wheat-flour dough during mixing, in "Wheat Gluten" (eds. P. R Schewry and A. S. Tatham), Royal Society of Chemistry Special Publications, (2000), 391-395. |
[2] |
R. S. Anderssen, I. G. Gotz and K. H. Hoffmann, The global behavior of elastoplastic and viscoelastic materials with hysteresis-type state equations, SIAM J. Appl. Math., 58 (1998), 703-723. |
[3] |
R. S. Anderssen, P. W. Gras and F. MacRitchie, Linking mathematics to data from the testing of wheat-flour dough, Chem. in Aust., 64 (1997), 3-5. |
[4] |
R. S. Anderssen, P. W. Gras and F. MacRitchie, The rate-independence of the mixing of wheat-flour dough to peak dough development, J. Cereal Sci., 27 (1998), 167-177. |
[5] |
B. Appelbe, D. Flynn, H. McNamara,P. O'Kane, A. Pimenov, A. Pokrovskii, D. Rachinskii and A. Zhezherun, Rate-independent hysteresis in terrestrial hydrologya vegetated soil model with preisach hysteresis, IEEE Control Syst. Mag., 29 (2009), 44-69.
doi: 10.1109/MCS.2008.930923. |
[6] |
J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal., 63 (1977), 337-403. |
[7] |
Z. P. Bažant and M. Jirásek, Nonlocal integral formulation of plasticity and damage: A survey of progress, J. Engrg. Mech., 128 (2002), 1119-1149.
doi: 10.1061/(ASCE)0733-9399(2002)128:11(1119). |
[8] |
C. Carstensen, K. Hackl and A. Mielke, Nonconvex potentials and microstructures in finite-strain plasticity, Proc. Roy. Soc. Lond. A, 458 (2002), 299-317.
doi: 10.1098/rspa.2001.0864. |
[9] |
M. N. Charalambides, L. Wanigasooriya and J. G. Williams, Biaxial deformation of dough using the bubble inflation technique. II. Numerical modelling, Rheol. Acta, 41 (2002), 541-548. |
[10] |
P. G. Ciarlet and J. Ne\vcas, Injectivity and self-contact in nonlinear elasticity, Arch. Ration. Mech. Anal., 19 (1987), 171-188. |
[11] |
G. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies, J. reine angew. Math., 595 (2006), 55-91. |
[12] |
P. W. Gras, H. C. Carpenter and R. S. Anderssen, Modelling the developmental rheology of wheat-flour dough using extension tests, J. Cereal Sci., 31 (2000), 1-13.
doi: 10.1006/jcrs.1999.0293. |
[13] |
M. E. Gurtin, On the plasticity of single crystals: Free energy, microforces, plastic-strain gradients, J. Mech. Phys. Solids, 48 (2000), 989-1036.
doi: 10.1016/S0022-5096(99)00059-9. |
[14] |
R. H. Kilborn and K. H. Tipples, Factors affecting mechanical dough development 1. Effect of mixing intensity and work input, Cereal Chem., 49 (1972), 34-47. |
[15] |
J. Kratochvíl, M. Kružík and R. Sedláček, Energetic approach to strain gradient plasticity, Zeit. Angew. Math. Mech., 90 (2010), 122-135. |
[16] |
M. Kružík and J. Zimmer, A model of shape memory alloys accounting for plasticity, IMA J. Appl. Math., 76 (2011), 193-216. |
[17] |
A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems, Calc. Var. Partial Differential Equations, 22 (2005), 73-99. |
[18] |
A. Mainik and A. Mielke, Global existence for rate-independent gradient plasticity at finite strain, J. Nonlinear Sci., 19 (2009). |
[19] |
A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances., Cont. Mech. Thermodyn., 15 (2002), 351-382. |
[20] |
A. Mielke, Evolution of rate-independent systems, in "Evolutionary equations, II, Handb. Differ. Equ.,'' Elsevier/North-Holland, Amsterdam, (2005), 461-559. |
[21] |
A. Mielke and T. Roubíček, A rate-independent model for inelastic behavior of shape-memory alloys, Multiscale Model. Simul., 1 (2003), 571-597.
doi: 10.1137/S1540345903422860. |
[22] |
A. Mielke and T. Roubíček, Numerical approaches to rate-independent processes and applications in inelasticity, ESAIM Math. Mod. Num. Anal., 43 (2009), 399-428.
doi: 10.1051/m2an/2009009. |
[23] |
A. Mielke and F. Theil, A mathematical model for rate-independent phase transformations with hysteresis, in "Models of Continuum Mechanics in Analysis and Engineering'' (eds. H.-D.Alder, R. Balean and R. Farwig), Shaker Verlag, Aachen, (1999), 117-129. |
[24] |
A. Mielke, F. Theil and V. I. Levitas, A variational formulation of rate-independent phase transformations using an extremum principle, Arch. Ration. Mech. Anal., 162 (2002), 137-177. |
[25] |
T. S. K. Ng, G. H. McKinley and M. Padmanabhan, Linear to non-linear rheology of wheat flour dough, Applied Rheology, 16 (2006), 265-274. |
[26] |
N. PhanThien, M. SafariArdi and A. MoralesPatino, Oscillatory and simple shear flows of a flour-water dough: A constitutive model, Rheol. Acta, 36 (1997), 38-48. |
[27] |
I. Tsagrakis and E. C. Aifantis, Recent developments in gradient plasticity, J. Engrg. Mater. Tech., 124 (2002). |
show all references
References:
[1] |
R. S. Anderssen and P. W. Gras, The hysteretic behaviour of wheat-flour dough during mixing, in "Wheat Gluten" (eds. P. R Schewry and A. S. Tatham), Royal Society of Chemistry Special Publications, (2000), 391-395. |
[2] |
R. S. Anderssen, I. G. Gotz and K. H. Hoffmann, The global behavior of elastoplastic and viscoelastic materials with hysteresis-type state equations, SIAM J. Appl. Math., 58 (1998), 703-723. |
[3] |
R. S. Anderssen, P. W. Gras and F. MacRitchie, Linking mathematics to data from the testing of wheat-flour dough, Chem. in Aust., 64 (1997), 3-5. |
[4] |
R. S. Anderssen, P. W. Gras and F. MacRitchie, The rate-independence of the mixing of wheat-flour dough to peak dough development, J. Cereal Sci., 27 (1998), 167-177. |
[5] |
B. Appelbe, D. Flynn, H. McNamara,P. O'Kane, A. Pimenov, A. Pokrovskii, D. Rachinskii and A. Zhezherun, Rate-independent hysteresis in terrestrial hydrologya vegetated soil model with preisach hysteresis, IEEE Control Syst. Mag., 29 (2009), 44-69.
doi: 10.1109/MCS.2008.930923. |
[6] |
J. M. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Arch. Rat. Mech. Anal., 63 (1977), 337-403. |
[7] |
Z. P. Bažant and M. Jirásek, Nonlocal integral formulation of plasticity and damage: A survey of progress, J. Engrg. Mech., 128 (2002), 1119-1149.
doi: 10.1061/(ASCE)0733-9399(2002)128:11(1119). |
[8] |
C. Carstensen, K. Hackl and A. Mielke, Nonconvex potentials and microstructures in finite-strain plasticity, Proc. Roy. Soc. Lond. A, 458 (2002), 299-317.
doi: 10.1098/rspa.2001.0864. |
[9] |
M. N. Charalambides, L. Wanigasooriya and J. G. Williams, Biaxial deformation of dough using the bubble inflation technique. II. Numerical modelling, Rheol. Acta, 41 (2002), 541-548. |
[10] |
P. G. Ciarlet and J. Ne\vcas, Injectivity and self-contact in nonlinear elasticity, Arch. Ration. Mech. Anal., 19 (1987), 171-188. |
[11] |
G. Francfort and A. Mielke, Existence results for a class of rate-independent material models with nonconvex elastic energies, J. reine angew. Math., 595 (2006), 55-91. |
[12] |
P. W. Gras, H. C. Carpenter and R. S. Anderssen, Modelling the developmental rheology of wheat-flour dough using extension tests, J. Cereal Sci., 31 (2000), 1-13.
doi: 10.1006/jcrs.1999.0293. |
[13] |
M. E. Gurtin, On the plasticity of single crystals: Free energy, microforces, plastic-strain gradients, J. Mech. Phys. Solids, 48 (2000), 989-1036.
doi: 10.1016/S0022-5096(99)00059-9. |
[14] |
R. H. Kilborn and K. H. Tipples, Factors affecting mechanical dough development 1. Effect of mixing intensity and work input, Cereal Chem., 49 (1972), 34-47. |
[15] |
J. Kratochvíl, M. Kružík and R. Sedláček, Energetic approach to strain gradient plasticity, Zeit. Angew. Math. Mech., 90 (2010), 122-135. |
[16] |
M. Kružík and J. Zimmer, A model of shape memory alloys accounting for plasticity, IMA J. Appl. Math., 76 (2011), 193-216. |
[17] |
A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems, Calc. Var. Partial Differential Equations, 22 (2005), 73-99. |
[18] |
A. Mainik and A. Mielke, Global existence for rate-independent gradient plasticity at finite strain, J. Nonlinear Sci., 19 (2009). |
[19] |
A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances., Cont. Mech. Thermodyn., 15 (2002), 351-382. |
[20] |
A. Mielke, Evolution of rate-independent systems, in "Evolutionary equations, II, Handb. Differ. Equ.,'' Elsevier/North-Holland, Amsterdam, (2005), 461-559. |
[21] |
A. Mielke and T. Roubíček, A rate-independent model for inelastic behavior of shape-memory alloys, Multiscale Model. Simul., 1 (2003), 571-597.
doi: 10.1137/S1540345903422860. |
[22] |
A. Mielke and T. Roubíček, Numerical approaches to rate-independent processes and applications in inelasticity, ESAIM Math. Mod. Num. Anal., 43 (2009), 399-428.
doi: 10.1051/m2an/2009009. |
[23] |
A. Mielke and F. Theil, A mathematical model for rate-independent phase transformations with hysteresis, in "Models of Continuum Mechanics in Analysis and Engineering'' (eds. H.-D.Alder, R. Balean and R. Farwig), Shaker Verlag, Aachen, (1999), 117-129. |
[24] |
A. Mielke, F. Theil and V. I. Levitas, A variational formulation of rate-independent phase transformations using an extremum principle, Arch. Ration. Mech. Anal., 162 (2002), 137-177. |
[25] |
T. S. K. Ng, G. H. McKinley and M. Padmanabhan, Linear to non-linear rheology of wheat flour dough, Applied Rheology, 16 (2006), 265-274. |
[26] |
N. PhanThien, M. SafariArdi and A. MoralesPatino, Oscillatory and simple shear flows of a flour-water dough: A constitutive model, Rheol. Acta, 36 (1997), 38-48. |
[27] |
I. Tsagrakis and E. C. Aifantis, Recent developments in gradient plasticity, J. Engrg. Mater. Tech., 124 (2002). |
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