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1. | SISSA, International School of Advanced Studies, Via Bonomea 265, 34136 Trieste |
2. | Institute of Information Theory and Automation of the ASCR, Pod vodárenskou věží 4, 182 08 Prague |
References:
[1] |
G. Alberti and A. DeSimone, Quasistatic evolution of sessile drops and contact angle hysteresis, Arch. Rat. Mech. Anal., 202 (2011), 295-348.
doi: 10.1007/s00205-011-0427-x. |
[2] |
L. Ambrosio, Metric space valued functions of bounded variations, Ann. Scuola Normale Sup. Pisa Cl. Sci. (4), 17 (1990), 439-478. |
[3] |
S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), 67-90. |
[4] |
S. Baldo and G. Belletini, $\Gamma$-convergence and numerical analysis: An application to the minimal partition problem, Ricerche Mat., 40 (1991), 33-64. |
[5] |
H. Ben Belgacem, S. Conti, A. DeSimone and S. Müller, Rigorous bounds for the Föppl-von Kármán theory of isotropically compressed plates, Journal of Nonlinear Science, 10 (2000), 661-683.
doi: 10.1007/s003320010007. |
[6] |
B. Benešová, Global optimization numerical strategies for rate-independent processes, J. Global Optim., 50 (2011), 197-220.
doi: 10.1007/s10898-010-9560-6. |
[7] |
W. F. Brown, Virtues and weaknesses of the domain concept, Revs. Mod. Physics, 17 (1945), 15-19. |
[8] |
R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, A limited memory algorithm for bound constrained optimization, SIAM J. Scientific Computing, 16 (1995), 1190-1208.
doi: 10.1137/0916069. |
[9] |
C. Collins, D. Kinderlehrer and M. Luskin, Numerical approximation of the solution of a variational problem with a double well potential, SIAM J. Num. Anal., 28 (1991), 321-332.
doi: 10.1137/0728018. |
[10] |
R. Conti, C. Tamagnini and A. DeSimone, Critical softening in Cam-Clay plasticity: Adaptive viscous regularization, dilated time and numerical integration across stress-strain jump discontinuities, Comput. Methods Appl. Mech. Engrg., 258 (2013), 118-133.
doi: 10.1016/j.cma.2013.02.002. |
[11] |
J. Cooper, "Working Analysis," Elsevier Academic Press, 2005.
doi: 10.1249/00005768-199205001-00495. |
[12] |
G. Dal Maso, "An Introduction to $\Gamma$-Convegence," Progress in Nonlinear Differential Equations and their Applications, 8, Birkhäuser Boston, Inc., Boston, MA, 1993.
doi: 10.1007/978-1-4612-0327-8. |
[13] |
G. Dal Maso and A. DeSimone, Quasistatic evolution for Cam-Clay plasticity: Examples of spatially homogeneous solutions, Math. Model. Meth. Appl. Sci., 19 (2009), 1643-1711.
doi: 10.1142/S0218202509003942. |
[14] |
G. Dal Maso, A. DeSimone, M. G. Mora and M. Morini, A vanishing viscosity approach to quasistatic evolution in plasticity with softening, Arch. Rat. Mech. Anal., 189 (2008), 469-544.
doi: 10.1007/s00205-008-0117-5. |
[15] |
G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: A weak formulation via viscoplastic regularization and time rescaling, Calc. Var. PDE, 40 (2011), 125-181.
doi: 10.1007/s00526-010-0336-0. |
[16] |
G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solutions, Calc. Var. PDE, 44 (2012), 495-541.
doi: 10.1007/s00526-011-0443-6. |
[17] |
R. Delville, R. D. James, U. Salman, A. Finel and D. Schryvers, Transmission electron microscopy study of low-hysteresis shape memory alloys, in "Proceedings of ESOMAT 2009," 2009.
doi: 10.1051/esomat/200902005. |
[18] |
A. DeSimone, Hysteresis and imperfection sensitivity in small ferromagnetic particles, Meccanica, 30 (1995), 591-603.
doi: 10.1007/BF01557087. |
[19] |
A. DeSimone, N. Grunewald and F. Otto, A new model for contact angle hysteresis, Netw. Heterog. Media, 2 (2007), 211-225.
doi: 10.3934/nhm.2007.2.211. |
[20] |
A. DeSimone and L. Teresi, Elastic energies for nematic elastomers, Europ. Phys. J. E, 29 (2009), 191-204.
doi: 10.1140/epje/i2009-10467-9. |
[21] |
L. C. Evans and R. F. Gariepy, "Measure Theory and Fine Properties of Functions," Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. |
[22] |
H. Garcke, "On Mathematical Models for Phase Separation in Elastically Stressed Solids," Habilitation Thesis, University of Bonn, Bonn, 2000. |
[23] |
P. Germain, Q. Nguyen and P. Suquet, Continuum thermodynamics, J. Applied Mechanics, 50 (1983), 1010-1020.
doi: 10.1115/1.3167184. |
[24] |
L. Fedeli, A. Turco and A. DeSimone, Metastable equilibria of capillary drops on solid surfaces: A phase field approach, Cont. Mech. Thermodyn., 23 (2011), 453-471.
doi: 10.1007/s00161-011-0189-6. |
[25] |
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.
doi: 10.1515/CRELLE.2006.044. |
[26] |
R. D. James, Hysteresis in phase transformations, in "ICIAM 95" (Hamburg, 1995), Math. Res., 87, Akademie Verlag, Berlin, (1996), 133-154. |
[27] |
L. Juhász, H. Andrä and O. Hesebeck, A simple model for shape memory alloys under multi-axial non-proportional loading, in "Smart Materials" (ed. K.-H. Hoffmann), Proceedings of the 1st Caesarium, Springer, Berlin, (2000), 51-66. |
[28] |
M. Kružík and M. Luskin, The computation of martensitic microstructure with piecewise laminates, Journal of Scientific Computing, 19 (2003), 293-308.
doi: 10.1023/A:1025364227563. |
[29] |
M. Kružík, A. Mielke and T. Roubíček, Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi, Meccanica, 40 (2005), 389-418.
doi: 10.1007/s11012-005-2106-1. |
[30] |
M. Kružík and F. Otto, A phenomenological model for hysteresis in polycrystalline shape memory alloys, ZAMM Z. Angew. Math. Mech., 84 (2004), 835-842.
doi: 10.1002/zamm.200310139. |
[31] |
S. Leclerq, G. Bourbon and C. Lexcellent, Plasticity like model of martensite phase transition in shape memory alloys, J. Physique IV France, 5 (1995), 513-518.
doi: 10.1051/jp4:1995279. |
[32] |
S. Leclerq and C. Lexcellent, A general macroscopic description of thermomechanical behavior of shape memory alloys, J. Mech. Phys. Solids, 44 (1996), 953-980.
doi: 10.1016/0022-5096(96)00013-0. |
[33] |
C. Lexcellent, S. Moyne, A. Ishida and S. Miyazaki, Deformation behavior associated with stress-induced martensitic transformation in Ti-Ni thin films and their thermodynamical modelling, Thin Solid Films, 324 (1998), 184-189.
doi: 10.1016/S0040-6090(98)00352-6. |
[34] |
A. Mielke, T. Roubíček and U. Stefanelli, $\Gamma$-limits and relaxations for rate-independent evolutionary problems, Calc. Var., 31 (2008), 387-416.
doi: 10.1007/s00526-007-0119-4. |
[35] |
A. Mielke and F. Theil, Mathematical model for rate-independent phase transformations, in "Proceedings of the Workshop on Models of Continuum Mechanics in Analysis and Engineering" (eds. H.-D. Alber, R. Balean and R. Farwig), Shaker-Verlag, Aachen, (1999), 117-129. |
[36] |
A. Mielke and F. Theil, On rate-independent hysteresis models, Nonlin. Diff. Eq. Appl., 11 (2004), 151-189.
doi: 10.1007/s00030-003-1052-7. |
[37] |
A. Mielke, F. Theil and V. Levitas, A variational formulation of rate-independent phase transformations using extremum principle, Arch. Rat. Mech. Anal., 162 (2002), 137-177.
doi: 10.1007/s002050200194. |
[38] |
I. Müller, Modelling and simulation of phase transition in shape memory metals, in "Smart Materials" (ed. K.-H. Hoffmann), Proceedings of the 1st Caesarium, Springer, Berlin, (2000), 97-114. |
[39] |
F. Nishimura, T. Hayashi, C. Lexcellent and K. Tanaka, Phenomenological analysis of subloops and cyclic behavior in shape memory alloys under mechanical and/or thermal loads, Mech. of Mat., 19 (1995), 281-292. |
[40] |
T. Roubíček, Evolution model for martensitic phase transformation in shape-memory alloys, Interfaces and Free Boundaries, 4 (2002), 111-136.
doi: 10.4171/IFB/55. |
[41] |
Y. C. Shu and J. H. Yen, Multivariant model of martensitic microstructure in thin films, Acta Materialia, 56 (2008), 3969-3981.
doi: 10.1016/j.actamat.2008.04.018. |
[42] |
M. Thomas, Quasistatic damage evolution with spatial BV-regularization, Discr. Cont. Dyn. Syst. Ser. S, 6 (2013), 235-255.
doi: 10.3934/dcdss.2013.6.235. |
[43] |
J. M. T. Thomson and G. W. Hunt, "Elastic Instability Phenomena," J. Wiley and Sons, Chichester, 1984. |
show all references
References:
[1] |
G. Alberti and A. DeSimone, Quasistatic evolution of sessile drops and contact angle hysteresis, Arch. Rat. Mech. Anal., 202 (2011), 295-348.
doi: 10.1007/s00205-011-0427-x. |
[2] |
L. Ambrosio, Metric space valued functions of bounded variations, Ann. Scuola Normale Sup. Pisa Cl. Sci. (4), 17 (1990), 439-478. |
[3] |
S. Baldo, Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7 (1990), 67-90. |
[4] |
S. Baldo and G. Belletini, $\Gamma$-convergence and numerical analysis: An application to the minimal partition problem, Ricerche Mat., 40 (1991), 33-64. |
[5] |
H. Ben Belgacem, S. Conti, A. DeSimone and S. Müller, Rigorous bounds for the Föppl-von Kármán theory of isotropically compressed plates, Journal of Nonlinear Science, 10 (2000), 661-683.
doi: 10.1007/s003320010007. |
[6] |
B. Benešová, Global optimization numerical strategies for rate-independent processes, J. Global Optim., 50 (2011), 197-220.
doi: 10.1007/s10898-010-9560-6. |
[7] |
W. F. Brown, Virtues and weaknesses of the domain concept, Revs. Mod. Physics, 17 (1945), 15-19. |
[8] |
R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, A limited memory algorithm for bound constrained optimization, SIAM J. Scientific Computing, 16 (1995), 1190-1208.
doi: 10.1137/0916069. |
[9] |
C. Collins, D. Kinderlehrer and M. Luskin, Numerical approximation of the solution of a variational problem with a double well potential, SIAM J. Num. Anal., 28 (1991), 321-332.
doi: 10.1137/0728018. |
[10] |
R. Conti, C. Tamagnini and A. DeSimone, Critical softening in Cam-Clay plasticity: Adaptive viscous regularization, dilated time and numerical integration across stress-strain jump discontinuities, Comput. Methods Appl. Mech. Engrg., 258 (2013), 118-133.
doi: 10.1016/j.cma.2013.02.002. |
[11] |
J. Cooper, "Working Analysis," Elsevier Academic Press, 2005.
doi: 10.1249/00005768-199205001-00495. |
[12] |
G. Dal Maso, "An Introduction to $\Gamma$-Convegence," Progress in Nonlinear Differential Equations and their Applications, 8, Birkhäuser Boston, Inc., Boston, MA, 1993.
doi: 10.1007/978-1-4612-0327-8. |
[13] |
G. Dal Maso and A. DeSimone, Quasistatic evolution for Cam-Clay plasticity: Examples of spatially homogeneous solutions, Math. Model. Meth. Appl. Sci., 19 (2009), 1643-1711.
doi: 10.1142/S0218202509003942. |
[14] |
G. Dal Maso, A. DeSimone, M. G. Mora and M. Morini, A vanishing viscosity approach to quasistatic evolution in plasticity with softening, Arch. Rat. Mech. Anal., 189 (2008), 469-544.
doi: 10.1007/s00205-008-0117-5. |
[15] |
G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: A weak formulation via viscoplastic regularization and time rescaling, Calc. Var. PDE, 40 (2011), 125-181.
doi: 10.1007/s00526-010-0336-0. |
[16] |
G. Dal Maso, A. DeSimone and F. Solombrino, Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solutions, Calc. Var. PDE, 44 (2012), 495-541.
doi: 10.1007/s00526-011-0443-6. |
[17] |
R. Delville, R. D. James, U. Salman, A. Finel and D. Schryvers, Transmission electron microscopy study of low-hysteresis shape memory alloys, in "Proceedings of ESOMAT 2009," 2009.
doi: 10.1051/esomat/200902005. |
[18] |
A. DeSimone, Hysteresis and imperfection sensitivity in small ferromagnetic particles, Meccanica, 30 (1995), 591-603.
doi: 10.1007/BF01557087. |
[19] |
A. DeSimone, N. Grunewald and F. Otto, A new model for contact angle hysteresis, Netw. Heterog. Media, 2 (2007), 211-225.
doi: 10.3934/nhm.2007.2.211. |
[20] |
A. DeSimone and L. Teresi, Elastic energies for nematic elastomers, Europ. Phys. J. E, 29 (2009), 191-204.
doi: 10.1140/epje/i2009-10467-9. |
[21] |
L. C. Evans and R. F. Gariepy, "Measure Theory and Fine Properties of Functions," Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. |
[22] |
H. Garcke, "On Mathematical Models for Phase Separation in Elastically Stressed Solids," Habilitation Thesis, University of Bonn, Bonn, 2000. |
[23] |
P. Germain, Q. Nguyen and P. Suquet, Continuum thermodynamics, J. Applied Mechanics, 50 (1983), 1010-1020.
doi: 10.1115/1.3167184. |
[24] |
L. Fedeli, A. Turco and A. DeSimone, Metastable equilibria of capillary drops on solid surfaces: A phase field approach, Cont. Mech. Thermodyn., 23 (2011), 453-471.
doi: 10.1007/s00161-011-0189-6. |
[25] |
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.
doi: 10.1515/CRELLE.2006.044. |
[26] |
R. D. James, Hysteresis in phase transformations, in "ICIAM 95" (Hamburg, 1995), Math. Res., 87, Akademie Verlag, Berlin, (1996), 133-154. |
[27] |
L. Juhász, H. Andrä and O. Hesebeck, A simple model for shape memory alloys under multi-axial non-proportional loading, in "Smart Materials" (ed. K.-H. Hoffmann), Proceedings of the 1st Caesarium, Springer, Berlin, (2000), 51-66. |
[28] |
M. Kružík and M. Luskin, The computation of martensitic microstructure with piecewise laminates, Journal of Scientific Computing, 19 (2003), 293-308.
doi: 10.1023/A:1025364227563. |
[29] |
M. Kružík, A. Mielke and T. Roubíček, Modelling of microstructure and its evolution in shape-memory-alloy single-crystals, in particular in CuAlNi, Meccanica, 40 (2005), 389-418.
doi: 10.1007/s11012-005-2106-1. |
[30] |
M. Kružík and F. Otto, A phenomenological model for hysteresis in polycrystalline shape memory alloys, ZAMM Z. Angew. Math. Mech., 84 (2004), 835-842.
doi: 10.1002/zamm.200310139. |
[31] |
S. Leclerq, G. Bourbon and C. Lexcellent, Plasticity like model of martensite phase transition in shape memory alloys, J. Physique IV France, 5 (1995), 513-518.
doi: 10.1051/jp4:1995279. |
[32] |
S. Leclerq and C. Lexcellent, A general macroscopic description of thermomechanical behavior of shape memory alloys, J. Mech. Phys. Solids, 44 (1996), 953-980.
doi: 10.1016/0022-5096(96)00013-0. |
[33] |
C. Lexcellent, S. Moyne, A. Ishida and S. Miyazaki, Deformation behavior associated with stress-induced martensitic transformation in Ti-Ni thin films and their thermodynamical modelling, Thin Solid Films, 324 (1998), 184-189.
doi: 10.1016/S0040-6090(98)00352-6. |
[34] |
A. Mielke, T. Roubíček and U. Stefanelli, $\Gamma$-limits and relaxations for rate-independent evolutionary problems, Calc. Var., 31 (2008), 387-416.
doi: 10.1007/s00526-007-0119-4. |
[35] |
A. Mielke and F. Theil, Mathematical model for rate-independent phase transformations, in "Proceedings of the Workshop on Models of Continuum Mechanics in Analysis and Engineering" (eds. H.-D. Alber, R. Balean and R. Farwig), Shaker-Verlag, Aachen, (1999), 117-129. |
[36] |
A. Mielke and F. Theil, On rate-independent hysteresis models, Nonlin. Diff. Eq. Appl., 11 (2004), 151-189.
doi: 10.1007/s00030-003-1052-7. |
[37] |
A. Mielke, F. Theil and V. Levitas, A variational formulation of rate-independent phase transformations using extremum principle, Arch. Rat. Mech. Anal., 162 (2002), 137-177.
doi: 10.1007/s002050200194. |
[38] |
I. Müller, Modelling and simulation of phase transition in shape memory metals, in "Smart Materials" (ed. K.-H. Hoffmann), Proceedings of the 1st Caesarium, Springer, Berlin, (2000), 97-114. |
[39] |
F. Nishimura, T. Hayashi, C. Lexcellent and K. Tanaka, Phenomenological analysis of subloops and cyclic behavior in shape memory alloys under mechanical and/or thermal loads, Mech. of Mat., 19 (1995), 281-292. |
[40] |
T. Roubíček, Evolution model for martensitic phase transformation in shape-memory alloys, Interfaces and Free Boundaries, 4 (2002), 111-136.
doi: 10.4171/IFB/55. |
[41] |
Y. C. Shu and J. H. Yen, Multivariant model of martensitic microstructure in thin films, Acta Materialia, 56 (2008), 3969-3981.
doi: 10.1016/j.actamat.2008.04.018. |
[42] |
M. Thomas, Quasistatic damage evolution with spatial BV-regularization, Discr. Cont. Dyn. Syst. Ser. S, 6 (2013), 235-255.
doi: 10.3934/dcdss.2013.6.235. |
[43] |
J. M. T. Thomson and G. W. Hunt, "Elastic Instability Phenomena," J. Wiley and Sons, Chichester, 1984. |
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