[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.
|