Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion
- Volume: 45, Issue: 3, page 477-504
- ISSN: 0764-583X
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] C. Agelet de Saracibar, M. Cervera and M. Chiumenti, On the formulation of coupled thermoplastic problems with phase-change. Int. J. Plasticity15 (1999) 1–34. Zbl1054.74035
- [2] J. Alberty, C. Carstensen and S.A. Funken, Remarks around 50 lines of Matlab: short finite element implementation. Numer. Algorithms20 (1999) 117–137. Zbl0938.65129MR1709562
- [3] S. Bartels and T. Roubíček, Thermoviscoplasticity at small strains. ZAMM88 (2008) 735–754. Zbl1153.74011MR2488604
- [4] L. Boccardo, A. Dall'aglio, T. Gallouët and L. Orsina, Nonlinear parabolic equations with measure data. J. Funct. Anal.147 (1997) 237–258. Zbl0887.35082MR1453181
- [5] L. Boccardo and T. Gallouët, Non-linear elliptic and parabolic equations involving measure data. J. Funct. Anal.87 (1989) 149–169. Zbl0707.35060
- [6] L. Boccardo and T. Gallouët, Summability of the solutions of nonlinear elliptic equations with right hand side measures. J. Convex Anal.3 (1996) 361–365. Zbl0869.35108MR1448062
- [7] B.A. Boley and J.H. Weiner, Theory of thermal stresses. J. Wiley (1960), Dover edition (1997). Zbl1234.74001MR112414
- [8] S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods. Springer, second edition, New York (2002). Zbl1135.65042MR1894376
- [9] O. Bruhns and J. Mielniczuk, Zur Theorie der Verzweigungen nicht-isothermer elastoplastischer Deformationen. Ing.-Arch. 46 (1977) 65–74. Zbl0357.73034
- [10] M. Canadija and J. Brnic, Associative coupled thermoplasticity at finite strain with temperature-dependent material parameters. Int. J. Plasticity20 (2004) 1851–1874. Zbl1066.74515
- [11] C. Carstensen and R. Klose, Elastoviscoplastic finite element analysis in 100 lines of Matlab. J. Numer. Math.10 (2002) 157–192. Zbl1099.74544MR1935965
- [12] G. Dal Maso, G.A. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity. Arch. Rational Mech. Anal.176 (2005) 165–225. Zbl1064.74150MR2186036
- [13] G. Dal Maso, A. DeSimone and M.G. Mora, Quasistatic evolution problems for linearly elastic-perfectly plastic materials. Arch. Ration. Mech. Anal.180 (2006) 237–291. Zbl1093.74007MR2210910
- [14] C. Eck, J. Jarušek and M. Krbec, Unilateral Contact Problems. Chapman & Hall/CRC, Boca Raton (2005). Zbl1079.74003MR2128865
- [15] G. Francfort and A. Mielke, An existence result for a rate-independent material model in the case of nonconvex energies. J. reine angew. Math. 595 (2006) 55–91. Zbl1101.74015MR2244798
- [16] P. Hakansson, M. Wallin and M. Ristinmaa, Comparison of isotropic hardening and kinematic hardening in thermoplasticity. Int. J. Plasticity21 (2005) 1435–1460. Zbl1229.74027
- [17] S. Hu and N.S. Papageorgiou, Handbook of Multivalued Analysis. Kluwer, Dordrecht, Part I (1997), Part II (2000). Zbl0887.47001
- [18] D. Knees, On global spatial regularity and convergence rates for time dependent elasto-plasticity. Math. Models Methods Appl. Sci. (2010) DOI: 10.1142/S0218202510004805. Zbl1207.35083MR2735915
- [19] G.A. Maughin, The Thermomechanics of Plasticity and Fracture. Cambridge Univ. Press, Cambridge (1992). Zbl0753.73001MR1173212
- [20] C. Miehe, A theory of large-strain isotropic thermoplasticity based on metric transformation tensor. Archive Appl. Mech.66 (1995) 45–64. Zbl0844.73027
- [21] A. Mielke, Evolution of rate-independent systems, in Handbook of Differential Equations: Evolut. Diff. Eqs., C. Dafermos and E. Feireisl Eds., Elsevier, Amsterdam (2005) 461–559. Zbl1120.47062MR2182832
- [22] A. Mielke and T. Roubíček, Numerical approaches to rate-independent processes and applications in inelasticity. ESAIM: M2AN 43 (2009) 399–428. Zbl1166.74010MR2527399
- [23] A. Mielke and and F. Theil, A mathematical model for rate-independent phase transformations with hysteresis, in Models of continuum mechanics in analysis and engineering, H.-D. Alber, R. Balean and R. Farwing Eds., Shaker Ver., Aachen (1999) 117–129.
- [24] A. Mielke and F. Theil, On rate-independent hysteresis models. Nonlin. Diff. Eq. Appl.11 (2004) 151–189. Zbl1061.35182MR2210284
- [25] A. Mielke, T. Roubíček and U. Stefanelli, Γ-limits and relaxations for rate-independent evolutionary problems. Calc. Var. PDE31 (2008) 387–416. Zbl1302.49013MR2366131
- [26] T.D.W. Nicholson, Large deformation theory of coupled thermoplasticity including kinematic hardening. Acta Mech.142 (2000) 207–222. Zbl1027.74010
- [27] P. Rosakis, A.J. Rosakis, G. Ravichandran and J. Hodowany, A thermodynamic internal variable model for the partition of plastic work into heat and stored energy in metals. J. Mech. Phys. Solids48 (2000) 581–607. Zbl1005.74004
- [28] T. Roubíček, Nonlinear Partial Differential Equations with Applications. Birkhäuser, Basel (2005). Zbl1270.35005
- [29] T. Roubíček, Thermo-visco-elasticity at small strains with L1-data. Quart. Appl. Math.67 (2009) 47–71. Zbl1160.74011MR2495071
- [30] T. Roubíček, Rate independent processes in viscous solids at small strains. Math. Methods Appl. Sci.32 (2009) 825–862. Zbl1194.35226MR2507935
- [31] T. Roubíček, Thermodynamics of rate independent processes in viscous solids at small strains. SIAM J. Math. Anal.42 (2010) 256–297. Zbl1213.35279MR2596554
- [32] A. Srikanth and N. Zabaras, A computational model for the finite element analysis of thermoplasticity coupled with ductile damage at fonite strains. Int. J. Numer. Methods Eng.45 (1999) 1569–1605. Zbl0943.74073
- [33] Q. Yang, L. Stainier and M. Ortiz, A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids. J. Mech. Phys. Solids54 (2006) 401–424. Zbl1120.74367MR2192499
- [34] H. Ziegler, A modification of Prager's hardening rule. Quart. Appl. Math.17 (1959) 55–65. Zbl0086.18704MR104405