On the change of energy caused by crack propagation in 3-dimensional anisotropic solids

Martin Steigemann; Maria Specovius-Neugebauer

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 2, page 401-416
  • ISSN: 0862-7959

Abstract

top
Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a small crack extension.

How to cite

top

Steigemann, Martin, and Specovius-Neugebauer, Maria. "On the change of energy caused by crack propagation in 3-dimensional anisotropic solids." Mathematica Bohemica 139.2 (2014): 401-416. <http://eudml.org/doc/261892>.

@article{Steigemann2014,
abstract = {Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a small crack extension.},
author = {Steigemann, Martin, Specovius-Neugebauer, Maria},
journal = {Mathematica Bohemica},
keywords = {crack propagation; energy principle; stress intensity factor; crack propagation; energy principle; stress intensity factor},
language = {eng},
number = {2},
pages = {401-416},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the change of energy caused by crack propagation in 3-dimensional anisotropic solids},
url = {http://eudml.org/doc/261892},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Steigemann, Martin
AU - Specovius-Neugebauer, Maria
TI - On the change of energy caused by crack propagation in 3-dimensional anisotropic solids
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 2
SP - 401
EP - 416
AB - Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a small crack extension.
LA - eng
KW - crack propagation; energy principle; stress intensity factor; crack propagation; energy principle; stress intensity factor
UR - http://eudml.org/doc/261892
ER -

References

top
  1. Argatov, I. I., Nazarov, S. A., 10.1016/S0021-8928(02)00059-X, J. Appl. Math. Mech. 66 (2002), 491-503. (2002) MR1937462DOI10.1016/S0021-8928(02)00059-X
  2. Bach, M., Nazarov, S. A., Wendland, W. L., Stable propagation of a mode-1 planar crack in an isotropic elastic space. Comparison of the Irwin and the Griffth approaches, Problemi attuali dell'analisi e della fisica matematica P. E. Ricci Dipartimento di Matematica, Univ. di Roma (2000), 167-189. (2000) MR1809025
  3. Bourdin, B., Francfort, G. A., Marigo, J.-J., 10.1016/S0022-5096(99)00028-9, J. Mech. Phys. Solids 48 (2000), 797-826. (2000) Zbl0995.74057MR1745759DOI10.1016/S0022-5096(99)00028-9
  4. Ciarlet, P. G., An introduction to differential geometry with applications to elasticity, J. Elasticity 78-79 (2005), 1-215. (2005) Zbl1086.74001MR2196098
  5. Costabel, M., Dauge, M., 10.1017/S0308210500021272, Proc. R. Soc. Edinb., Sect. A 123 (1993), 109-155. (1993) Zbl0791.35032MR1204855DOI10.1017/S0308210500021272
  6. Costabel, M., Dauge, M., 10.1017/S0308210500021284, Proc. R. Soc. Edinb., Sect. A 123 (1993), 157-184. (1993) Zbl0791.35033MR1204855DOI10.1017/S0308210500021284
  7. Costabel, M., Dauge, M., 10.1002/1522-2616(200202)235:1<29::AID-MANA29>3.0.CO;2-6, Math. Nachr. 235 (2002), 29-49. (2002) Zbl1094.35038MR1889276DOI10.1002/1522-2616(200202)235:1<29::AID-MANA29>3.0.CO;2-6
  8. Costabel, M., Dauge, M., Yosibash, Z., 10.1137/S0036141002404863, SIAM J. Math. Anal. 35 (2004), 1177-1202. (2004) Zbl1141.35363MR2050197DOI10.1137/S0036141002404863
  9. Dauge, M., Elliptic Boundary Value Problems on Corner Domains, Lecture Notes in Mathematics 1341 Springer, Berlin (1988). (1988) Zbl0668.35001MR0961439
  10. Lorenzi, H. G. de, 10.1007/BF00017129, Int. J. Fract. 19 (1982), 183-193. (1982) DOI10.1007/BF00017129
  11. Favier, E., Lazarus, V., Leblond, J.-B., 10.1016/j.ijsolstr.2005.06.041, Int. J. Solids Struct. 43 (2006), 2091-2109. (2006) Zbl1121.74449DOI10.1016/j.ijsolstr.2005.06.041
  12. Griffith, A. A., 10.1098/rsta.1921.0006, Philos. Trans. Roy. Soc. London 221 (1921), 163-198. (1921) DOI10.1098/rsta.1921.0006
  13. Hartranft, R. J., Sih, G. C., 10.1016/0013-7944(77)90083-2, Engineering Fracture Mechanics 9 (1977), 705-718. (1977) DOI10.1016/0013-7944(77)90083-2
  14. Il'in, A. M., 10.1090/mmono/102, Translated from the Russian. Translations of Mathematical Monographs 102 American Mathematical Society, Providence (1992). (1992) Zbl0754.34002MR1182791DOI10.1090/mmono/102
  15. Irwin, G., Fracture, Handbuch der Physik. Bd. 6: Elastizität und Plastizität S. Flügge Springer, Berlin 551-590 (1958). (1958) MR0094946
  16. Kondrat'ev, V. A., Boundary value problems for elliptic equations in domains with conical or angular points, Trans. Mosc. Math. Soc. 16 (1967), 227-313. (1967) MR0226187
  17. Kozlov, V. A., Maz'ya, V. G., Rossmann, J., Elliptic Boundary Value Problems in Domains with Point Singularities, Mathematical Surveys and Monographs 52 American Mathematical Society, Providence (1997). (1997) Zbl0947.35004MR1469972
  18. Kühnel, W., Differential Geometry. Curves--Surfaces--Manifolds. Translated from the German, Student Mathematical Library 16 American Mathematical Society, Providence (2002). (2002) MR1882174
  19. Lazarus, V., 10.1023/B:FRAC.0000005373.73286.5d, Int. J. Fract. 122 (2003), 23-46. (2003) DOI10.1023/B:FRAC.0000005373.73286.5d
  20. Leblond, J.-B., Torlai, O., 10.1007/BF00044514, J. Elasticity 29 (1992), 97-131. (1992) Zbl0777.73054DOI10.1007/BF00044514
  21. Maz'ya, V. G., Plamenevsky, B. A., The coefficients in the asymptotic of the solutions of elliptic boundary-value problems in domains with conical points, Russian Math. Nachr. 76 (1977), 29-60. (1977) 
  22. Maz'ya, V. G., Rossmann, J., 10.1002/mana.19881380103, German Math. Nachr. 138 (1988), 27-53. (1988) Zbl0672.35020MR0975198DOI10.1002/mana.19881380103
  23. Nazarov, S. A., 10.1007/s10808-005-0088-3, J. Appl. Mech. Techn. Phys. 46 (2005), 386-394. (2005) Zbl1088.74025MR2144814DOI10.1007/s10808-005-0088-3
  24. Nazarov, S. A., Plamenevsky, B. A., Elliptic Problems in Domains with Piecewise Smooth Boundaries, De Gruyter Expositions in Mathematics 13 Walter de Gruyter, Berlin (1994). (1994) Zbl0806.35001MR1283387
  25. Nazarov, S. A., Polyakova, O. R., Rupture criteria, asymptotic conditions at crack tips, and selfadjoint extensions of the Lamé operator, Russian Tr. Mosk. Mat. Obs. 57 (1996), 16-74. (1996) MR1468975
  26. Parks, D. M., 10.1007/BF00155252, Int. J. Fract. 10 (1974), 487-502. (1974) DOI10.1007/BF00155252
  27. Sih, G. C., Paris, P. C., Irwin, G. R., On cracks in rectilinearly anisotropic bodies, Int. J. Fract. 1 (1965), 189-203. (1965) 
  28. Steigemann, M., Verallgemeinerte Eigenfunktionen und lokale Integralcharakteristiken bei quasi-statischer Rissausbreitung in anisotropen Materialien, German Berichte aus der Mathematik Shaker, Aachen (2009). (2009) Zbl1181.35286
  29. Williams, M. L., Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mech. 19 (1952), 526-528. (1952) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.