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Galerkin finite element methods for semilinear elliptic differential inclusions
Modelling of wheatflour dough mixing as an openloop 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 wheatflour dough during mixing,, in, (2000), 391. 
[2] 
R. S. Anderssen, I. G. Gotz and K. H. Hoffmann, The global behavior of elastoplastic and viscoelastic materials with hysteresistype state equations,, SIAM J. Appl. Math., 58 (1998), 703. 
[3] 
R. S. Anderssen, P. W. Gras and F. MacRitchie, Linking mathematics to data from the testing of wheatflour dough,, Chem. in Aust., 64 (1997), 3. 
[4] 
R. S. Anderssen, P. W. Gras and F. MacRitchie, The rateindependence of the mixing of wheatflour dough to peak dough development,, J. Cereal Sci., 27 (1998), 167. 
[5] 
B. Appelbe, D. Flynn, H. McNamara,P. O'Kane, A. Pimenov, A. Pokrovskii, D. Rachinskii and A. Zhezherun, Rateindependent hysteresis in terrestrial hydrologya vegetated soil model with preisach hysteresis,, IEEE Control Syst. Mag., 29 (2009), 44. 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. 
[7] 
Z. P. Bažant and M. Jirásek, Nonlocal integral formulation of plasticity and damage: A survey of progress,, J. Engrg. Mech., 128 (2002), 1119. doi: 10.1061/(ASCE)07339399(2002)128:11(1119). 
[8] 
C. Carstensen, K. Hackl and A. Mielke, Nonconvex potentials and microstructures in finitestrain plasticity,, Proc. Roy. Soc. Lond. A, 458 (2002), 299. 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. 
[10] 
P. G. Ciarlet and J. Ne\vcas, Injectivity and selfcontact in nonlinear elasticity,, Arch. Ration. Mech. Anal., 19 (1987), 171. 
[11] 
G. Francfort and A. Mielke, Existence results for a class of rateindependent material models with nonconvex elastic energies,, J. reine angew. Math., 595 (2006), 55. 
[12] 
P. W. Gras, H. C. Carpenter and R. S. Anderssen, Modelling the developmental rheology of wheatflour dough using extension tests,, J. Cereal Sci., 31 (2000), 1. doi: 10.1006/jcrs.1999.0293. 
[13] 
M. E. Gurtin, On the plasticity of single crystals: Free energy, microforces, plasticstrain gradients,, J. Mech. Phys. Solids, 48 (2000), 989. doi: 10.1016/S00225096(99)000599. 
[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. 
[15] 
J. Kratochvíl, M. Kružík and R. Sedláček, Energetic approach to strain gradient plasticity,, Zeit. Angew. Math. Mech., 90 (2010), 122. 
[16] 
M. Kružík and J. Zimmer, A model of shape memory alloys accounting for plasticity,, IMA J. Appl. Math., 76 (2011), 193. 
[17] 
A. Mainik and A. Mielke, Existence results for energetic models for rateindependent systems,, Calc. Var. Partial Differential Equations, 22 (2005), 73. 
[18] 
A. Mainik and A. Mielke, Global existence for rateindependent gradient plasticity at finite strain,, J. Nonlinear Sci., 19 (2009). 
[19] 
A. Mielke, Energetic formulation of multiplicative elastoplasticity using dissipation distances.,, Cont. Mech. Thermodyn., 15 (2002), 351. 
[20] 
A. Mielke, Evolution of rateindependent systems,, in, II (2005), 461. 
[21] 
A. Mielke and T. Roubíček, A rateindependent model for inelastic behavior of shapememory alloys,, Multiscale Model. Simul., 1 (2003), 571. doi: 10.1137/S1540345903422860. 
[22] 
A. Mielke and T. Roubíček, Numerical approaches to rateindependent processes and applications in inelasticity,, ESAIM Math. Mod. Num. Anal., 43 (2009), 399. doi: 10.1051/m2an/2009009. 
[23] 
A. Mielke and F. Theil, A mathematical model for rateindependent phase transformations with hysteresis,, in, (1999), 117. 
[24] 
A. Mielke, F. Theil and V. I. Levitas, A variational formulation of rateindependent phase transformations using an extremum principle,, Arch. Ration. Mech. Anal., 162 (2002), 137. 
[25] 
T. S. K. Ng, G. H. McKinley and M. Padmanabhan, Linear to nonlinear rheology of wheat flour dough,, Applied Rheology, 16 (2006), 265. 
[26] 
N. PhanThien, M. SafariArdi and A. MoralesPatino, Oscillatory and simple shear flows of a flourwater dough: A constitutive model,, Rheol. Acta, 36 (1997), 38. 
[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 wheatflour dough during mixing,, in, (2000), 391. 
[2] 
R. S. Anderssen, I. G. Gotz and K. H. Hoffmann, The global behavior of elastoplastic and viscoelastic materials with hysteresistype state equations,, SIAM J. Appl. Math., 58 (1998), 703. 
[3] 
R. S. Anderssen, P. W. Gras and F. MacRitchie, Linking mathematics to data from the testing of wheatflour dough,, Chem. in Aust., 64 (1997), 3. 
[4] 
R. S. Anderssen, P. W. Gras and F. MacRitchie, The rateindependence of the mixing of wheatflour dough to peak dough development,, J. Cereal Sci., 27 (1998), 167. 
[5] 
B. Appelbe, D. Flynn, H. McNamara,P. O'Kane, A. Pimenov, A. Pokrovskii, D. Rachinskii and A. Zhezherun, Rateindependent hysteresis in terrestrial hydrologya vegetated soil model with preisach hysteresis,, IEEE Control Syst. Mag., 29 (2009), 44. 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. 
[7] 
Z. P. Bažant and M. Jirásek, Nonlocal integral formulation of plasticity and damage: A survey of progress,, J. Engrg. Mech., 128 (2002), 1119. doi: 10.1061/(ASCE)07339399(2002)128:11(1119). 
[8] 
C. Carstensen, K. Hackl and A. Mielke, Nonconvex potentials and microstructures in finitestrain plasticity,, Proc. Roy. Soc. Lond. A, 458 (2002), 299. 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. 
[10] 
P. G. Ciarlet and J. Ne\vcas, Injectivity and selfcontact in nonlinear elasticity,, Arch. Ration. Mech. Anal., 19 (1987), 171. 
[11] 
G. Francfort and A. Mielke, Existence results for a class of rateindependent material models with nonconvex elastic energies,, J. reine angew. Math., 595 (2006), 55. 
[12] 
P. W. Gras, H. C. Carpenter and R. S. Anderssen, Modelling the developmental rheology of wheatflour dough using extension tests,, J. Cereal Sci., 31 (2000), 1. doi: 10.1006/jcrs.1999.0293. 
[13] 
M. E. Gurtin, On the plasticity of single crystals: Free energy, microforces, plasticstrain gradients,, J. Mech. Phys. Solids, 48 (2000), 989. doi: 10.1016/S00225096(99)000599. 
[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. 
[15] 
J. Kratochvíl, M. Kružík and R. Sedláček, Energetic approach to strain gradient plasticity,, Zeit. Angew. Math. Mech., 90 (2010), 122. 
[16] 
M. Kružík and J. Zimmer, A model of shape memory alloys accounting for plasticity,, IMA J. Appl. Math., 76 (2011), 193. 
[17] 
A. Mainik and A. Mielke, Existence results for energetic models for rateindependent systems,, Calc. Var. Partial Differential Equations, 22 (2005), 73. 
[18] 
A. Mainik and A. Mielke, Global existence for rateindependent gradient plasticity at finite strain,, J. Nonlinear Sci., 19 (2009). 
[19] 
A. Mielke, Energetic formulation of multiplicative elastoplasticity using dissipation distances.,, Cont. Mech. Thermodyn., 15 (2002), 351. 
[20] 
A. Mielke, Evolution of rateindependent systems,, in, II (2005), 461. 
[21] 
A. Mielke and T. Roubíček, A rateindependent model for inelastic behavior of shapememory alloys,, Multiscale Model. Simul., 1 (2003), 571. doi: 10.1137/S1540345903422860. 
[22] 
A. Mielke and T. Roubíček, Numerical approaches to rateindependent processes and applications in inelasticity,, ESAIM Math. Mod. Num. Anal., 43 (2009), 399. doi: 10.1051/m2an/2009009. 
[23] 
A. Mielke and F. Theil, A mathematical model for rateindependent phase transformations with hysteresis,, in, (1999), 117. 
[24] 
A. Mielke, F. Theil and V. I. Levitas, A variational formulation of rateindependent phase transformations using an extremum principle,, Arch. Ration. Mech. Anal., 162 (2002), 137. 
[25] 
T. S. K. Ng, G. H. McKinley and M. Padmanabhan, Linear to nonlinear rheology of wheat flour dough,, Applied Rheology, 16 (2006), 265. 
[26] 
N. PhanThien, M. SafariArdi and A. MoralesPatino, Oscillatory and simple shear flows of a flourwater dough: A constitutive model,, Rheol. Acta, 36 (1997), 38. 
[27] 
I. Tsagrakis and E. C. Aifantis, Recent developments in gradient plasticity,, J. Engrg. Mater. Tech., 124 (2002). 
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