[1] Ronsin O., Perrin B., Dynamics of quasistatic directional crack
growth. Physical Review E, Vol. 58, No. 6, pp. 7878, 1998.
[2] Yang B., Ravi-Chandar K., Crack path instabilities in a quenched glass plate. Journal of the Mechanics and Physics of Solids, Vol. 49, No.1, pp. 91–130, 2001.
[3] Yazid A., Abdelkader N., Abdelmadjid H., A state-of-the-art
review of the X-FEM for computational fracture mechanics.
Applied Mathematical Modelling, Vol. 33, No. 12, pp. 4269–
4282, 2009.
[4] Belytschko T., Black T., Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, Vol. 45, No. 5, pp. 601–620, 1999.
[5] Dolbow J., Belytschko T., A finite element method for crack
growth without remeshing. International Journal for Numerical Methods in Engineering, Vol. 46, No. 1, pp.131–150, 1999.
[6] Stolarska M., Chopp D. L., Moës N., Belytschko T., Modelling
crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering, Vol. 51, No. 8, pp. 943–960, 2001.
[7] Bordas S., Extended finite element and level set methods with
applications to growth of cracks and biofilms, PhD Thesis,
Northwestern University, 2003.
[8] Osher S., Sethian J. A., Fronts propagating with curvature-
dependent speed: algorithms based on Hamilton-Jacobi
formulations. Journal of Computational Physics, Vol. 79, No.1, pp.12–49, 1988.
[9] Duflot M., A study of the representation of cracks with level sets. International Journal for Numerical Methods in Engineering, Vol. 70, No. 11, pp. 1261–1302, 2007.
[10] Sukumar N., Moës N., Moran B., Belytschko T., Extended finite element method for three‐dimensional crack modelling. International Journal for Numerical Methods in Engineering,
Vol. 48, No. 11, pp. 1549–1570, 2000.
[11] Duflot M., The extended finite element method in thermoelastic fracture mechanic. International Journal for Numerical Methods in Engineering, Vol. 74, No. 5, pp. 827–847, 2008.
[12] Zamani A., Eslami M. R., Implementation of the extended finite element method for dynamic thermoelastic fracture initiation. International Journal of Solids and Structures, Vol. 47, No. 10, pp. 1392– 1404, 2010.
[13] Yuse A., Sano M., Transition between crack patterns in quenched glass plates. Nature, Vol. 362, No. 6418, pp. 329–331, 1993.
[14] Bouchbinder E., Hentschel H. G. E., Procaccia I., Dynamical
instabilities of quasistatic crack propagation under thermal stress. Physical Review E, Vol. 68, No. 3, pp. 36601, 2003.
[15] Yoneyama S., Kikuta H., Moriwaki K., Simultaneous observation of phase-stepped photoelastic fringes using a pixelated
microretarder array. Optical Engineering, Vol. 45, No. 8, pp.
83604, 2006.
[16] Sakaue K., Yoneyama S., Kikuta H., Takashi M., Evaluating crack tip stress field in a thin glass plate under thermal load. Engineering Fracture Mechanics, Vol. 75, No. 5, pp. 1015–1026, 2008.
[17] Pais M., Kim N. H., Davis T., Reanalysis of the extended finite
element method for crack initiation and propagation. In Proceedings of AIAA Structures, Structural Dynamics, and Materials Conference, 2010.
[18] Yoneyama S., Sakaue K., Experimental–numerical hybrid stress analysis for a curving crack in a thin glass plate under thermal load. Engineering Fracture Mechanics, Vol. 131, pp. 514–524, 2014.
[19] Bansal N. P., Doremus R. H., Handbook of glass properties,
Elsevier, 2013.
[20] Westergaard H. M., Bearing pressures and cracks. Journal of
Applied Mechanics, Vol. 61, pp. A49–A53, 1939.
[21] Williams M. L., On the Stress Distribution at the Base of a
Stationary Crack, Journal of Applied Mechanics, Vol. 24, No. 1, pp. 109–114, 1957.
[22] Mohammadi S., XFEM fracture analysis of composites, John
Wiley & Sons, 2012.
[23] Fleming M., Chu Y. A., Moran B., Belytschko T., Lu Y.Y., Gu L., Enriched element-free Galerkin methods for crack tip fields,
International Journal for Numerical Methods in Engineering,
Vol. 40, No. 8, pp. 1483–1504, 1997.
[24] Babuška I., Melenk J. M., The partition of unity method,
International Journal for Numerical Methods in Engineering,
Vol. 40, No. 4, pp. 727–758, 1997.
[25] Belytschko T., Moës N., Usui S., Parimi C., Arbitrary
discontinuities in finite elements, International Journal for
Numerical Methods in Engineering, Vol. 50, No. 4, pp. 993–1013, 2001.
[26] Bower A. F., Applied mechanics of solids, CRC press, pp. 49-73, 2009.
[27] Hutton D. V., Wu J., Fundamentals of finite element analysis, pp. 131-285,McGraw-Hill, New York, 2004.
[28] Astley R. J., Finite elements in solids and structures, An
introduction, pp. 102-104, Chapman & Hall (Springer), 1992.
[29] Goli E., Bayesteh H., Mohammadi S., Mixed mode fracture
analysis of adiabatic cracks in homogeneous and non-
homogeneous materials in the framework of partition of unity and the path-independent interaction integral, Engineering Fracture Mechanics, Vol. 131, pp. 100–127, 2014.
[30] Hetnarski R. B., Encyclopedia of Thermal Stresses, pp. 1611-1612, Springer Reference, 2014.
[31] Moaveni S., Finite element analysis: theory and application with ANSYS, pp. 445-451, Pearson Education, India, 2003.
[32] Charney J. G., Fjörtoft R., Neumann J. V., Numerical integration of the barotropic vorticity equation, Tellus A, Vol. 2, No. 4, pp. 237-254, 1950.
)