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A characterization of energetic and $BV$ solutions to one-dimensional rate-independent systems
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Some remarks on the viscous approximation of crack growth
Crack propagation by a regularization of the principle of local symmetry
1. | Dipartimento di Matematica, Università degli Studi di Pavia, Via A. Ferrata 1 - 27100 Pavia, Italy |
References:
[1] |
M. Amestoy and J. B. Leblond, Crack paths in plane situations. II. Detailed form of the expansion of the stress intensity factors, Internat. J. Solids Structures, 29 (1992), 465-501.
doi: 10.1016/0020-7683(92)90210-K. |
[2] |
A. Chambolle, G. A. Francfort and J.-J. Marigo, Revisiting energy release rates in brittle fracture, J. Nonlinear Sci., 20 (2010), 395-424.
doi: 10.1007/s00332-010-9061-2. |
[3] |
A. Chambolle, A. Giacomini and M. Ponsiglione, Crack initiation in elastic bodies, Arch. Ration. Mech. Anal., 188 (2008), 309-349.
doi: 10.1007/s00205-007-0080-6. |
[4] |
B. Cotterell, On brittle fracture paths, Internat. J. Fracture, 1 (1965), 96-103.
doi: 10.1007/BF00186747. |
[5] |
B. Cotterell and J. R. Rice, Slightly curved or kinked cracks, Int. J. Fracture, 16 (1980), 155-169.
doi: 10.1007/BF00012619. |
[6] |
G. Dal Maso, "An Introduction to $\Gamma$-Convergence," Birkhäuser, Boston, 1993.
doi: 10.1007/978-1-4612-0327-8. |
[7] |
A. Friedman and Y. Liu, Propagation of cracks in elastic media, Arch. Rational Mech. Anal., 136 (1996), 235-290.
doi: 10.1007/BF02206556. |
[8] |
R. V. Goldstein and R. L. Salganik, Brittle fracture of solids with arbitrary cracks, Internat. J. Fracture, 10 (1974), 507-523. |
[9] |
M. Gosz, J. Dolbow and B. Moran, Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks, Int. J. Solids Struct., 35 (1998), 1763-1783.
doi: 10.1016/S0020-7683(97)00132-7. |
[10] |
P. Grisvard, Singularités en elasticité, Arch. Rational Mech. Anal., 107 (1989), 157-180.
doi: 10.1007/BF00286498. |
[11] |
A. M. Khludnev, V. A. Kovtunenko and A. Tani., On the topological derivative due to kink of a crack with non-penetration. Anti-plane model, J. Math. Pures Appl., 94 (2010), 571-596.
doi: 10.1016/j.matpur.2010.06.002. |
[12] |
G. Lazzaroni and R. Toader, Energy release rate and stress intensity factor in antiplane elasticity, J. Math. Pures Appl., 95 (2011), 565-584.
doi: 10.1016/j.matpur.2011.01.001. |
[13] |
N. G. Meyers, An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa (3), 17 (1963), 189-206. |
[14] |
M. Negri, A comparative analysis on variational models for quasi-static brittle crack propagation, Adv. Calc. Var., 3 (2010), 149-212.
doi: 10.1515/acv.2010.008. |
[15] |
G. C. Sih and F. Erdogan, On the crack extension in plates under plane loading and transverse shear, J. Basic Engineering, 85 (1963), 519-527.
doi: 10.1115/1.3656897. |
[16] |
G. J. Williams and P. D. Ewing, Fracture under complex stress - the angled crack problem, Int. J. Fracture, 8 (1972), 441-446.
doi: 10.1007/BF00191106. |
[17] |
M. L. Williams, On the stress distribution at the base of a stationary crack, J. Appl. Mech., 24 (1957), 109-114. |
show all references
References:
[1] |
M. Amestoy and J. B. Leblond, Crack paths in plane situations. II. Detailed form of the expansion of the stress intensity factors, Internat. J. Solids Structures, 29 (1992), 465-501.
doi: 10.1016/0020-7683(92)90210-K. |
[2] |
A. Chambolle, G. A. Francfort and J.-J. Marigo, Revisiting energy release rates in brittle fracture, J. Nonlinear Sci., 20 (2010), 395-424.
doi: 10.1007/s00332-010-9061-2. |
[3] |
A. Chambolle, A. Giacomini and M. Ponsiglione, Crack initiation in elastic bodies, Arch. Ration. Mech. Anal., 188 (2008), 309-349.
doi: 10.1007/s00205-007-0080-6. |
[4] |
B. Cotterell, On brittle fracture paths, Internat. J. Fracture, 1 (1965), 96-103.
doi: 10.1007/BF00186747. |
[5] |
B. Cotterell and J. R. Rice, Slightly curved or kinked cracks, Int. J. Fracture, 16 (1980), 155-169.
doi: 10.1007/BF00012619. |
[6] |
G. Dal Maso, "An Introduction to $\Gamma$-Convergence," Birkhäuser, Boston, 1993.
doi: 10.1007/978-1-4612-0327-8. |
[7] |
A. Friedman and Y. Liu, Propagation of cracks in elastic media, Arch. Rational Mech. Anal., 136 (1996), 235-290.
doi: 10.1007/BF02206556. |
[8] |
R. V. Goldstein and R. L. Salganik, Brittle fracture of solids with arbitrary cracks, Internat. J. Fracture, 10 (1974), 507-523. |
[9] |
M. Gosz, J. Dolbow and B. Moran, Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks, Int. J. Solids Struct., 35 (1998), 1763-1783.
doi: 10.1016/S0020-7683(97)00132-7. |
[10] |
P. Grisvard, Singularités en elasticité, Arch. Rational Mech. Anal., 107 (1989), 157-180.
doi: 10.1007/BF00286498. |
[11] |
A. M. Khludnev, V. A. Kovtunenko and A. Tani., On the topological derivative due to kink of a crack with non-penetration. Anti-plane model, J. Math. Pures Appl., 94 (2010), 571-596.
doi: 10.1016/j.matpur.2010.06.002. |
[12] |
G. Lazzaroni and R. Toader, Energy release rate and stress intensity factor in antiplane elasticity, J. Math. Pures Appl., 95 (2011), 565-584.
doi: 10.1016/j.matpur.2011.01.001. |
[13] |
N. G. Meyers, An $L^p$-estimate for the gradient of solutions of second order elliptic divergence equations, Ann. Scuola Norm. Sup. Pisa (3), 17 (1963), 189-206. |
[14] |
M. Negri, A comparative analysis on variational models for quasi-static brittle crack propagation, Adv. Calc. Var., 3 (2010), 149-212.
doi: 10.1515/acv.2010.008. |
[15] |
G. C. Sih and F. Erdogan, On the crack extension in plates under plane loading and transverse shear, J. Basic Engineering, 85 (1963), 519-527.
doi: 10.1115/1.3656897. |
[16] |
G. J. Williams and P. D. Ewing, Fracture under complex stress - the angled crack problem, Int. J. Fracture, 8 (1972), 441-446.
doi: 10.1007/BF00191106. |
[17] |
M. L. Williams, On the stress distribution at the base of a stationary crack, J. Appl. Mech., 24 (1957), 109-114. |
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