Quasistatic crack growth in elasto-plastic materials with hardening: The antiplane case

References

[1] L. Ambrosio, A compactness theorem for a new class of functions of bounded variation, Boll. Un. Mat. Ital. B (7) 3 (1989), no. 4, 857–881. Suche in Google Scholar

[2] L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Math. Monogr., Oxford University, New York, 2000. 10.1093/oso/9780198502456.001.0001Suche in Google Scholar

[3] V. Barbu and T. Precupanu, Convexity and Optimization in Banach Spaces, 4th ed., Springer Monogr. Math., Springer, Dordrecht, 2012. 10.1007/978-94-007-2247-7Suche in Google Scholar

[4] B. Bourdin, G. A. Francfort and J.-J. Marigo, The variational approach to fracture, J. Elasticity 91 (2008), no. 1–3, 5–148. 10.1007/s10659-007-9107-3Suche in Google Scholar

[5] H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Math. Stud. 5, North-Holland, Amsterdam, 1973. Suche in Google Scholar

[6] M. Brokate and P. Krejčí, Wellposedness of kinematic hardening models in elastoplasticity, RAIRO Modél. Math. Anal. Numér. 32 (1998), no. 2, 177–209. 10.1051/m2an/1998320201771Suche in Google Scholar

[7] H. Bruno, G. Barros, I. F. M. Menezes and L. F. Martha, Return-mapping algorithms for associative isotropic hardening plasticity using conic optimization, Appl. Math. Model. 78 (2020), 724–748. 10.1016/j.apm.2019.10.006Suche in Google Scholar

[8] A. Chambolle and V. Crismale, Equilibrium configurations for nonhomogeneous linearly elastic materials with surface discontinuities, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) (2022), 10.2422/2036-2145.202006_002. 10.2422/2036-2145.202006_002Suche in Google Scholar

[9] G. Dal Maso, G. A. Francfort and R. Toader, Quasistatic crack growth in nonlinear elasticity, Arch. Ration. Mech. Anal. 176 (2005), no. 2, 165–225. 10.1007/s00205-004-0351-4Suche in Google Scholar

[10] G. Dal Maso and R. Toader, A model for the quasi-static growth of brittle fractures: Existence and approximation results, Arch. Ration. Mech. Anal. 162 (2002), no. 2, 101–135. 10.1007/s002050100187Suche in Google Scholar

[11] G. Dal Maso and R. Toader, Quasistatic crack growth in elasto-plastic materials: The two-dimensional case, Arch. Ration. Mech. Anal. 196 (2010), no. 3, 867–906. 10.1007/s00205-009-0258-1Suche in Google Scholar

[12] J. Desai, G. Allaire, F. Jouve and C. Mang, Topology optimization in quasi-static plasticity with hardening using a level-set method, Struct. Multidiscip. Optim. 64 (2021), no. 5, 3163–3191. 10.1007/s00158-021-03034-7Suche in Google Scholar

[13] D. C. Drucker, Stress-strain relations for strain hardening materials: Discussion and proposed experiments, Proceedings of Symposia in Applied Mathematics Vol. I, American Mathematical Society, Providence (1949), 181–187. 10.1090/psapm/001/0030425Suche in Google Scholar

[14] D. C. Drucker, Some implications of work hardening and ideal plasticity, Quart. Appl. Math. 7 (1950), 411–418. 10.1090/qam/34210Suche in Google Scholar

[15] H. Federer, Geometric Measure Theory, Grundlehren Math. Wiss. 153, Springer, New York, 1969. Suche in Google Scholar

[16] G. A. Francfort and C. J. Larsen, Existence and convergence for quasi-static evolution in brittle fracture, Comm. Pure Appl. Math. 56 (2003), no. 10, 1465–1500. 10.1002/cpa.3039Suche in Google Scholar

[17] G. A. Francfort and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids 46 (1998), no. 8, 1319–1342. 10.1016/S0022-5096(98)00034-9Suche in Google Scholar

[18] G. A. Francfort and U. Stefanelli, Quasi-static evolution for the Armstrong–Frederick hardening-plasticity model, Appl. Math. Res. Express. AMRX 2 (2013), 297–344. 10.1093/amrx/abt001Suche in Google Scholar

[19] J. Frehse and D. Löbach, Regularity results for three-dimensional isotropic and kinematic hardening including boundary differentiability, Math. Models Methods Appl. Sci. 19 (2009), no. 12, 2231–2262. 10.1142/S0218202509004108Suche in Google Scholar

[20] M. Friedrich, A compactness result in GSBV p and applications to Γ-convergence for free discontinuity problems, Calc. Var. Partial Differential Equations 58 (2019), no. 3, Paper No. 86. 10.1007/s00526-019-1530-3Suche in Google Scholar

[21] A. Giacomini and M. Ponsiglione, A Γ-convergence approach to stability of unilateral minimality properties in fracture mechanics and applications, Arch. Ration. Mech. Anal. 180 (2006), no. 3, 399–447. 10.1007/s00205-005-0392-3Suche in Google Scholar

[22] M. E. Gurtin, E. Fried and L. Anand, The Mechanics and Thermodynamics of Continua, Cambridge University, Cambridge, 2010. 10.1017/CBO9780511762956Suche in Google Scholar

[23] W. Han and B. D. Reddy, Plasticity. Mathematical Theory and Numerical Analysis, Interdiscip. Appl. Math. 9, Springer, New York, 1999. Suche in Google Scholar

[24] C. Johnson, On plasticity with hardening, J. Math. Anal. Appl. 62 (1978), no. 2, 325–336. 10.1016/0022-247X(78)90129-4Suche in Google Scholar

[25] J. Lemaitre and J.-L. Chaboche, Mechanics of Solid Materials, Cambridge University, Cambridge, 1990. 10.1017/CBO9781139167970Suche in Google Scholar

[26] G. A. Maugin, The Thermomechanics of Plasticity and Fracture, Cambridge Texts Appl. Math., Cambridge University, Cambridge, 1992. 10.1017/CBO9781139172400Suche in Google Scholar

[27] A. Mielke and T. Roubíček, Rate-Independent Systems. Theory and Application, Appl. Math. Sci. 193, Springer, New York, 2015. 10.1007/978-1-4939-2706-7Suche in Google Scholar

[28] W. Prager, Strain hardening under combined stresses, J. Appl. Phys. 16 (1945), 837–840. 10.1063/1.1707548Suche in Google Scholar

[29] W. Prager, Recent developments in the mathematical theory of plasticity, J. Appl. Phys. 20 (1949), 235–241. 10.1063/1.1698348Suche in Google Scholar

[30] U. Stefanelli, A variational principle for hardening elastoplasticity, SIAM J. Math. Anal. 40 (2008), no. 2, 623–652. 10.1137/070692571Suche in Google Scholar