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12. V. Kushch, S. Shmegera, P. Brondsted, L. Mishnaevsky, Numerical simulation of progressive
debonding in fiber reinforced composite under transverse loading. Int. J. Eng. Sci. 49, 17–29
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13. S. Soghrati, A. Aragón, C. Duarte, P. Geubelle, An interface-enriched generalized finite
element method for problems with discontinuous gradient fields. Int. J. Numer. Methods Eng.
89(8), 991–1008 (2012)
14. S. Soghrati, P. Geubelle, A 3D interface-enriched generalized finite element method for weakly
discontinuous problems with complex internal geometries. Comput. Methods Appl. Mech.
Eng. 217–220, 46–57 (2012)
15. A. Najafi, M. Safdari, D. Tortorelli, P. Geubelle, A gradient-based shape optimization scheme
using an interface-enriched generalized FEM. Comput. Methods Appl. Mech. Eng. 296, 1–17
(2015)
16. A. Najafi, M. Safdari, D. Tortorelli, P. Geubelle, Material design using a NURBS-based shape
optimization scheme, in In 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and
Materials Conference (American Institute of Aeronautics and Astronautics Inc, AIAA, 2016)
17. T. Hobbiebrunken, M. Hojo, T. Adachi, C.D. Jong, B. Fiedler, Evaluation of interfacial strength
in CF/epoxies using FEM and in-situ experiments. Compos. A: Appl. Sci. Manuf. 37, 2248–
2256 (2006)
18. E. Gamstedt, B. Sjogren, Micromechanisms in tension-compression fatigue of composite
laminates containing transverse plies. Combust. Sci. Technol. 59, 167–178 (1999)
19. N. Otsu, A threshold selection method from gray-level histograms. IEEE IEEE Trans. Syst.
Man Cybern. 9, 62–66 (1979)
20. M. Chandrakala, P. Devi, Threshold based segmentation using block processing. Int. J. Innov.
Res. Comput. Commun. Eng. 4, 821–826 (2016)
21. D. Ballard, Generalizing the Hough transform to detect arbitrary shapes. Pattern Recogn. 13,
111–122 (1981)
22. T. Atherton, D. Kerbyson, Size invariant circle detection. Image Vis. Comput. 17, 795–803
(1999)
23. C. Przybyla, T. Godar, S. Bricker, J. Simmons, M. Jackson, L. Zawada, J. Pearce, Statistical
characterization of SiC/SiC ceramic matrix composites at the filament scale with bayesian segmentation, Hough transform feature extraction, and pair correlation statistics, in International
SAMPE Technical Conference (2013), pp. 859–878
24. I. Scheider, W. Brocks, The effect of the traction separation law on the results of cohesive zone
crack propagation analyses. Key Eng. Mater. 251, 313–318 (2003)
25. Y.F. Gao, A.F. Bower, A simple technique for avoiding convergence problems in finite element
simulations of crack nucleation and growth on cohesive interfaces. Model. Simul. Mater. Sci.
Eng. 12(3), 453 (2004)
26. A. Aragón, A. Simone, The discontinuity-enriched finite element method. Int. J. Numer.
Methods Eng. 112, 1589–1613 (2017)
27. S. Zacek, Exploring the link between microstructure statistics and transverse ply fracture in
carbon/epoxy composites. Master’s thesis, University of Illinois – Urbana-Champaign (2017)
28. S. Balay, S. Abhyankar, M.F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin,
V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, K. Rupp, B.F. Smith,
S. Zampini, H. Zhang, H. Zhang, PETSc Web page. http://www.mcs.anl.gov/petsc (2016)
29. S. Potukuchi, Fracture analysis of carbon fiber/epoxy matrix interface through microbond and
cruciform tests. Master’s thesis, University of Illinois – Urbana-Champaign (2016)
30. J. Halpin, J. Kardos, The Halpin-Tsai equations: a review. Polym. Eng. Sci. 16, 344–352 (1976)
347
12. V. Kushch, S. Shmegera, P. Brondsted, L. Mishnaevsky, Numerical simulation of progressive
debonding in fiber reinforced composite under transverse loading. Int. J. Eng. Sci. 49, 17–29
(2011)
13. S. Soghrati, A. Aragón, C. Duarte, P. Geubelle, An interface-enriched generalized finite
element method for problems with discontinuous gradient fields. Int. J. Numer. Methods Eng.
89(8), 991–1008 (2012)
14. S. Soghrati, P. Geubelle, A 3D interface-enriched generalized finite element method for weakly
discontinuous problems with complex internal geometries. Comput. Methods Appl. Mech.
Eng. 217–220, 46–57 (2012)
15. A. Najafi, M. Safdari, D. Tortorelli, P. Geubelle, A gradient-based shape optimization scheme
using an interface-enriched generalized FEM. Comput. Methods Appl. Mech. Eng. 296, 1–17
(2015)
16. A. Najafi, M. Safdari, D. Tortorelli, P. Geubelle, Material design using a NURBS-based shape
optimization scheme, in In 57th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and
Materials Conference (American Institute of Aeronautics and Astronautics Inc, AIAA, 2016)
17. T. Hobbiebrunken, M. Hojo, T. Adachi, C.D. Jong, B. Fiedler, Evaluation of interfacial strength
in CF/epoxies using FEM and in-situ experiments. Compos. A: Appl. Sci. Manuf. 37, 2248–
2256 (2006)
18. E. Gamstedt, B. Sjogren, Micromechanisms in tension-compression fatigue of composite
laminates containing transverse plies. Combust. Sci. Technol. 59, 167–178 (1999)
19. N. Otsu, A threshold selection method from gray-level histograms. IEEE IEEE Trans. Syst.
Man Cybern. 9, 62–66 (1979)
20. M. Chandrakala, P. Devi, Threshold based segmentation using block processing. Int. J. Innov.
Res. Comput. Commun. Eng. 4, 821–826 (2016)
21. D. Ballard, Generalizing the Hough transform to detect arbitrary shapes. Pattern Recogn. 13,
111–122 (1981)
22. T. Atherton, D. Kerbyson, Size invariant circle detection. Image Vis. Comput. 17, 795–803
(1999)
23. C. Przybyla, T. Godar, S. Bricker, J. Simmons, M. Jackson, L. Zawada, J. Pearce, Statistical
characterization of SiC/SiC ceramic matrix composites at the filament scale with bayesian segmentation, Hough transform feature extraction, and pair correlation statistics, in International
SAMPE Technical Conference (2013), pp. 859–878
24. I. Scheider, W. Brocks, The effect of the traction separation law on the results of cohesive zone
crack propagation analyses. Key Eng. Mater. 251, 313–318 (2003)
25. Y.F. Gao, A.F. Bower, A simple technique for avoiding convergence problems in finite element
simulations of crack nucleation and growth on cohesive interfaces. Model. Simul. Mater. Sci.
Eng. 12(3), 453 (2004)
26. A. Aragón, A. Simone, The discontinuity-enriched finite element method. Int. J. Numer.
Methods Eng. 112, 1589–1613 (2017)
27. S. Zacek, Exploring the link between microstructure statistics and transverse ply fracture in
carbon/epoxy composites. Master’s thesis, University of Illinois – Urbana-Champaign (2017)
28. S. Balay, S. Abhyankar, M.F. Adams, J. Brown, P. Brune, K. Buschelman, L. Dalcin,
V. Eijkhout, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, K. Rupp, B.F. Smith,
S. Zampini, H. Zhang, H. Zhang, PETSc Web page. http://www.mcs.anl.gov/petsc (2016)
29. S. Potukuchi, Fracture analysis of carbon fiber/epoxy matrix interface through microbond and
cruciform tests. Master’s thesis, University of Illinois – Urbana-Champaign (2016)
30. J. Halpin, J. Kardos, The Halpin-Tsai equations: a review. Polym. Eng. Sci. 16, 344–352 (1976)