Library Subscription: Guest
International Journal for Multiscale Computational Engineering

Published 6 issues per year

ISSN Print: 1543-1649

ISSN Online: 1940-4352

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.4 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.3 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 2.2 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.00034 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.46 SJR: 0.333 SNIP: 0.606 CiteScore™:: 3.1 H-Index: 31

Indexed in

AN OPEN-SOURCE FENICS IMPLEMENTATION OF A PHASE FIELD FRACTURE MODEL FOR MICROPOLAR CONTINUA

Volume 17, Issue 6, 2019, pp. 639-663
DOI: 10.1615/IntJMultCompEng.2020033422
Get accessGet access

ABSTRACT

A micropolar phase field fracture model is implemented in an open source library FEniCS. This implementation is based on the theoretical study in Suh, H.S., Sun, W., and O'Connor, D. (under review) in which the resultant phase field model exhibits the consistent micropolar size effect in both elastic and damage regions identifiable via inverse problems for micropolar continua. By leveraging the automatic code generation technique in FEniCS, we provide a documentation of the source code expressed in a language very close to the mathematical expressions without comprising significant efficiency. This combination of generality and interpretability therefore enables us to provide a detailed walk-through that connects the implementation with the regularized damage theory for micropolar materials. By making the source code open source, the paper will provide an efficient development and educational tool for third-party verification and validation, as well as for future development of other higher order continuum damage models.

REFERENCES
  1. Alnss, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M.E., and Wells, G.N., The FEniCS Project Version 1.5, Arch. Numer. Software, vol. 3, no. 100, pp. 9-23,2015.

  2. Alnss, M.S., Logg, A., 0lgaard, K.B., Rognes, M.E., and Wells, G.N., Unified Form Language: A Domain-Specific Language for Weak Formulations of Partial Differential Equations, ACM Trans. Math. Softw., vol. 40, no. 2, pp. 1-37,2014.

  3. Alnss, M.S., UFL: A Finite Element Form Language, in Automated Solution of Differential Equations by the Finite Element Method, A. Logg, K.A. Mardal, and G. Wells, Eds., Berlin: Springer, pp. 303-338,2012.

  4. Ambati, M., Gerasimov, T., and De Lorenzis, L., A Review on Phase-Field Models of Brittle Fracture and a New Fast Hybrid Formulation, Comput. Mech, vol. 55, no. 2, pp. 383-405,2015.

  5. Amor, H., Marigo, J.J., and Maurini, C., Regularized Formulation of the Variational Brittle Fracture with Unilateral Contact: Numerical Experiments, J. Mech. Phys. Solids, vol. 57, no. 8, pp. 1209-1229,2009.

  6. Anderson, T.L., Fracture Mechanics-Fundamentals and Applications, NASA STI/Recon Tech. Rep. A, 92,1991.

  7. Ariman, T., On the Stresses around a Circular Hole in Micropolar Elasticity, Acta Mech, vol. 4, no. 3, pp. 216-229,1967.

  8. Atroshchenko, E. and Bordas, S.P., Fundamental Solutions and Dual Boundary Element Methods for Fracture in Plane Cosserat Elasticity, Proc. R. Soc. A, vol. 471, no. 2179,2015.

  9. Babuska, I. and Narasimhan, R., The Babuska-Brezzi Condition and the Patch Test: An Example, Comput. Methods Appl. Mech. Eng., vol. 140, nos. 1-2, pp. 183-199,1997.

  10. Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., and Zhang, H., PETSc, Portable, Extensible Toolkit for Scientific Computation, from http://www.mcs.anl.gov/petsc, 2001.

  11. Balay, S., Abhyankar, S., Adams, M., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Dener, A., Eijkhout, V., Gropp, W., and Karpeyev, D., PETSc User's Manual, from http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf, 2019.

  12. Bathe, K.J., The Inf-Sup Condition and Its Evaluation for Mixed Finite Element Methods, Comput. Struct., vol. 79, no. 2, pp. 243-252,2001.

  13. Bazant, Z.P., Belytschko, T.B., and Chang, T.P., Continuum Theory for Strain-Softening, J. Eng. Mech., vol. 110, no. 12, pp. 1666-1692,1984.

  14. Belytschko, T., Liu, W.K., Moran, B., and Elkhodary, K., Nonlinear Finite Elements for Continua and Structures, Hoboken, NJ: Wiley, 2013.

  15. Bleyer, J. and Alessi, R., Phase-Field Modeling of Anisotropic Brittle Fracture Including Several Damage Mechanisms, Comput. Methods Appl. Mech. Eng., vol. 336, pp. 213-236,2018.

  16. Bocca, P., Carpinteri, A., and Valente, S., Mixed Mode Fracture of Concrete, Int. J. Solids Struct., vol. 27, no. 9, pp. 1139-1153, 1991.

  17. Borden, M.J., Verhoosel, C.V., Scott, M.A., Hughes, T.J., and Landis, C.M., A Phase-Field Description of Dynamic Brittle Fracture, Comput. Methods Appl. Mech. Eng., vol. 217, pp. 77-95,2012.

  18. Bourdin, B., Francfort, G.A., and Marigo, J.J., The Variational Approach to Fracture, J. Elasticity, vol. 91, nos. 1-3, pp. 5-148, 2008.

  19. Brezzi, F. and Fortin, M., Mixed and Hybrid Finite Element Methods, Springer, New York, vol. 15,2012.

  20. Bryant, E.C. and Sun, W., A Mixed-Mode Phase Field Fracture Model in Anisotropic Rocks with Consistent Kinematics, Comput. Methods Appl. Mech. Eng., vol. 342, pp. 561-584,2018.

  21. Bryant, E.C. and Sun, W., A Micromorphically Regularized Cam-Clay Model for Capturing Size-Dependent Anisotropy of Geomaterials, Comput. Methods Appl. Mech. Eng., vol. 354, pp. 56-95,2019.

  22. Cazes, F. and Moes, N., Comparison of a Phase-Field Model and of a Thick Level Set Model for Brittle and Quasi-Brittle Fracture, Int. J. Numer. Methods Eng., vol. 103,no.2,pp. 114-143,2015.

  23. Chapelle, D. and Bathe, K.J., The Inf-Sup Test, Comput. Struct., vol. 47, nos. 4-5, pp. 537-545,1993.

  24. Choo, J. and Sun, W., Coupled Phase-Field and Plasticity Modeling of Geological Materials: From Brittle Fracture to Ductile Flow, Comput. Methods Appl. Mech. Eng., vol. 330, pp. 1-32,2018.

  25. Clayton, J.D. and Knap, J., Phase Field Modeling of Twinning in Indentation of Transparent Crystals, Model. Simul. Mater. Sci. Eng., vol. 19, no. 8, p. 085005,2011.

  26. Cosserat, E. and Cosserat, F., Theorie des Corps Deformables, Scientific Library A. Hermann and Sons, Paris, 1909.

  27. Diebels, S. and Geringer, A., Micromechanical and Macromechanical Modelling of Foams: Identification of Cosserat Parameters, Z. Angew. Math. Mech, vol. 94, no. 5, pp. 414-420,2014.

  28. Diegele, E., ElsABer, R., and Tsakmakis, C., Linear Micropolar Elastic Crack-Tip Fields under Mixed Mode Loading Conditions, Int. J. Fract., vol. 129, no. 4, pp. 309-339,2004.

  29. Ehlers, W. and Volk, W., On Theoretical and Numerical Methods in the Theory of Porous Media based on Polar and Non-Polar Elasto-Plastic Solid Materials, Int. J. Solids Struct, vol. 35, nos. 34-35, pp. 4597-4617,1998.

  30. Eringen, A.C., Linear Theory of Micropolar Elasticity, J. Math. Mech, vol. 15, no. 6, pp. 909-923,1966.

  31. Eringen, A.C., Microcontinuum Field Theories: I. Foundations and Solids, New York: Springer Science & Business Media, 2012.

  32. Fleck, N.A., Muller, G.M., Ashby, M.F., and Hutchinson, J.W., Strain Gradient Plasticity: Theory and Experiment, Acta Metall. Mater, vol. 42, no. 2, pp. 475-487,1994.

  33. Geelen, R.J., Liu, Y., Hu, T., Tupek, M.R., and Dolbow, J.E., A Phase-Field Formulation for Dynamic Cohesive Fracture, Comput. Methods Appl. Mech. Eng., vol. 348, pp. 680-711,2019.

  34. Green, A.E., General Bi-Harmonic Analysis for a Plate Containing Circular Holes, Proc. R. Soc. London Ser. A, vol. 176, no. 964, pp. 121-139,1940.

  35. Hofacker, M. and Miehe, C., A Phase Field Model of Dynamic Fracture: Robust Field Updates for the Analysis of Complex Crack Patterns, Int. J. Numer. Methods Eng., vol. 93, no. 3, pp. 276-301,2013.

  36. Hu, R. and Oskay, C., Multiscale Nonlocal Effective Medium Model for In-Plane Elastic Wave Dispersion and Attenuation in Periodic Composites, J. Mech. Phys. Solids, vol. 124, pp. 220-243,2019.

  37. Kim, K.Y., Suh, H.S., Yun, T.S., Moon, S.W., and Seo, Y.S., Effect of Particle Shape on the Shear Strength of Fault Gouge, Geosci. J, vol. 20, no. 3, pp. 351-359,2016.

  38. Kuhn, C. and Muller, R., A Continuum Phase Field Model for Fracture, Eng. Fract. Mech., vol. 77, no. 18, pp. 3625-3634,2010.

  39. Lakes, R.S., Experimental Methods for Study of Cosserat Elastic Solids and Other Generalized Elastic Continua, in Continuum Models for Materials With Microstructure, H. Muhlhaus, Ed., Hoboken, NJ: Wiley, pp. 1-25,1995.

  40. Lakes, R.S., Size Effects and Micromechanics of a Porous Solid, J. Mater. Sci, vol. 18, no. 9, pp. 2572-2580,1983.

  41. Langtangen, H.P., Logg, A., and Tveito, A., Solving PDEs in Python: The FEniCS Tutorial I, Springer International Publishing, New York, 2016.

  42. Lee, C., Suh, H.S., Yoon, B., and Yun, T.S., Particle Shape Effect on Thermal Conductivity and Shear Wave Velocity in Sands, Acta Geotech., vol. 12, no. 3, pp. 615-625,2017.

  43. Li, Y.D. and Lee, K.Y., Fracture Analysis in Micropolar Elasticity: Mode-I Crack, Int. J. Fract, vol. 156, no. 2, pp. 179-184,2009.

  44. Lin, J., Wu, W., and Borja, R.I., Micropolar Hypoplasticity for Persistent Shear Band in Heterogeneous Granular Materials, Comput. Methods Appl. Mech. Eng., vol. 289, pp. 24-43,2015.

  45. Logg, A., Mardal, K.A., and Wells, G., Eds., Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, New York, Springer Science & Business Media, vol. 84,2012.

  46. Lorentz, E., Cuvilliez, S., and Kazymyrenko, K., Modelling Large Crack Propagation: From Gradient Damage to Cohesive Zone Models, Int. J. Fract, vol. 178, nos. 1-2, pp. 85-95,2012.

  47. McGregor, M. and Wheel, M.A., On the Coupling Number and Characteristic Length of Micropolar Media of Differing Topology, Proc. R. Soc. A, vol. 470, no. 2169, p. 20140150,2014.

  48. Mesgarnejad, A., Bourdin, B., and Khonsari, M., Validation Simulations for the Variational Approach to Fracture, Comput. Methods Appl. Mech. Eng., vol. 290, pp. 420-437,2015.

  49. Miehe, C., Hofacker, M., and Welschinger, F., A Phase Field Model for Rate-Independent Crack Propagation: Robust Algorithmic Implementation based on Operator Splits, Comput. Methods Appl. Mech. Eng., vol. 199, nos. 45-48, pp. 2765-2778,2010a.

  50. Miehe, C., Welschinger, F., and Hofacker, M., Thermodynamically Consistent Phase-Field Models of Fracture: Variational Principles and Multi-Field FE Implementations, Int. J. Numer. Methods Eng., vol. 83, no. 10, pp. 1273-1311,2010b.

  51. Miehe, C., Aldakheel, F., and Mauthe, S., Mixed Variational Principles and Robust Finite Element Implementations of Gradient Plasticity at Small Strains, Int. J. Numer. MethodsEng, vol. 94, no. 11, pp. 1037-1074,2013.

  52. Miehe, C., Mauthe, S., and Teichtmeister, S., Minimization Principles for the Coupled Problem of Darcy-Biot-Type Fluid Transport in Porous Media Linked to Phase Field Modeling of Fracture, J. Mech. Phys. Solids, vol. 82, pp. 186-217,2015.

  53. Mindlin, R.D., Influence of Couple-Stresses on Stress Concentrations, Columbia University, New York, Tech. Rep. No. CU-TR-49, 1962.

  54. Mindlin, R.D. and Tiersten, H.F., Effects of Couple-Stresses in Linear Elasticity, Columbia University, New York, Tech. Rep. No. CU-TR-48,1962.

  55. Moes, N., Stolz, C., Bernard, P.E., and Chevaugeon, N., A Level Set based Model for Damage Growth: The Thick Level Set Approach, Int. J. Numer. Methods Eng, vol. 86, no. 3, pp. 358-380,2011.

  56. Mota, A., Sun, W., Ostien, J.T., Foulk, J.W., and Long, K.N., Lie-Group Interpolation and Variational Recovery for Internal Variables, Comput. Mech, vol. 52, no. 6, pp. 1281-1299,2013.

  57. Na, S. and Sun, W., Wave Propagation and Strain Localization in a Fully Saturated Softening Porous Medium under the Non-Isothermal Conditions, Int. J. Numer. Anal. Methods Geomech., vol. 40, no. 10, pp. 1485-1510,2016.

  58. Na, S. and Sun, W., Computational Thermo-Hydro-Mechanics for Multiphase Freezing and Thawing Porous Media in the Finite Deformation Range, Comput. Methods Appl. Mech.Eng, vol. 318, pp. 667-700,2017.

  59. Na, S. and Sun, W., Computational Thermomechanics of Crystalline Rock, Part I: A Combined Multi-Phase-Field/Crystal Plasticity Approach for Single Crystal Simulations, Comput. Methods Appl. Mech. Eng, vol. 338, pp. 657-691,2018.

  60. Na, S., Bryant, E.C., and Sun, W., A Configurational Force for Adaptive Re-Meshing of Gradient-Enhanced Poromechanics Problems with History-Dependent Variables, Comput. Methods Appl. Mech. Engrg., vol. 357, p. 112572,2019.

  61. Neff, P., The Cosserat Couple Modulus for Continuous Solids is Zero viz the Linearized Cauchy-Stress Tensor is Symmetric, Z. Angew. Math. Mech, vol. 86, no. 11, pp. 892-912,2006.

  62. Qinami, A., Bryant, E.C., Sun, W., and Kaliske, M., Circumventing Mesh Bias by R- and H-Adaptive Techniques for Variational Eigenfracture, Int. J. Fract., pp. 1-14,2019.

  63. Schmidt, B., Fraternali, F., and Ortiz, M., Eigenfracture: An Eigendeformation Approach to Variational Fracture, Multiscale Model. Simul., vol. 7, no. 3, pp. 1237-1266,2009.

  64. Song, J.H., Wang, H., and Belytschko, T., A Comparative Study on Finite Element Methods for Dynamic Fracture, Comput. Mech., vol. 42, no. 2, pp. 239-250,2008.

  65. Suh, H.S., Kim, K.Y., Lee, J., and Yun, T.S., Quantification of Bulk Form and Angularity of Particle with Correlation of Shear Strength and Packing Density in Sands, Eng. Geol., vol. 220, pp. 256-265,2017.

  66. Suh, H.S., Sun, W., and O'Connor, D., A Phase Field Model for Cohesive Fracture in Micropolar Continua, Comput. Methods Appl. Mech. Eng. , under review.

  67. Sun, W., A Stabilized Finite Element Formulation for Monolithic Thermo-Hydro-Mechanical Simulations at Finite Strain, Int. J. Numer. Methods Eng, vol. 103,no. 11,pp. 798-839,2015.

  68. Sun, W. and Mota, A., A Multiscale Overlapped Coupling Formulation for Large-Deformation Strain Localization, Comput. Mech., vol. 54, no. 3, pp. 803-820,2014.

  69. Sun, W., Ostien, J.T., and Salinger, A.G., A Stabilized Assumed Deformation Gradient Finite Element Formulation for Strongly Coupled Poromechanical Simulations at Finite Strain, Int. J. Numer. Anal. Methods Geomech., vol. 37, no. 16, pp. 2755-2788, 2013.

  70. Sun, W., Cai, Z., and Choo, J., Mixed Arlequin Method for Multiscale Poromechanics Problems, Int. J. Numer. Methods Eng, vol. 111, no. 7, pp. 624-659,2017.

  71. Wang, K. and Sun, W., A Unified Variational Eigen-Erosion Framework for Interacting Brittle Fractures and Compaction Bands in Fluid-Infiltrating Porous Media, Comput. Methods Appl. Mech. Eng, vol. 318, pp. 1-32,2017.

  72. Wang, K. and Sun, W., An Updated Lagrangian LBM-DEM-FEM Coupling Model for Dual-Permeability Fissured Porous Media with Embedded Discontinuities, Comput. Methods Appl. Mech. Eng., vol. 344, pp. 276-305,2019.

  73. Wang, K., Sun, W., Salager, S., Na, S., and Khaddour, G., Identifying Material Parameters for a Micro-Polar Plasticity Model via X-Ray Micro-Computed Tomographic (CT) Images: Lessons Learned from the Curve-Fitting Exercises, Int. J. Multiscale Comput. Eng., vol. 14, no. 4, pp. 389-413,2016.

  74. Wu, J.Y. and Nguyen, V.P., A Length Scale Insensitive Phase-Field Damage Model for Brittle Fracture, J. Mech. Phys. Solids, vol. 119, pp. 20-42,2018.

  75. Wu, J.Y., Mandal, T.K., and Nguyen, V.P., A Phase-Field Regularized Cohesive Zone Model for Hydrogen Assisted Cracking, Comput. Methods Appl. Mech. Eng., vol. 358, p. 112614,2020.

  76. Yang, Z., Kim, C.B., Cho, C., and Beom, H.G., The Concentration of Stress and Strain in Finite Thickness Elastic Plate Containing a Circular Hole, Int. J. Solids Struct., vol. 45, nos. 3-4, pp. 713-731,2008.

  77. Yavari, A., Sarkani, S., and Moyer Jr, E.T., On Fractal Cracks in Micropolar Elastic Solids, J. Appl. Mech, vol. 69, no. 1, pp. 45-54,2001.

CITED BY
  1. Suh Hyoung Suk, Sun WaiChing, O’Connor Devin T., A phase field model for cohesive fracture in micropolar continua, Computer Methods in Applied Mechanics and Engineering, 369, 2020. Crossref

  2. Bryant Eric C., Sun WaiChing, Phase field modeling of frictional slip with slip weakening/strengthening under non-isothermal conditions, Computer Methods in Applied Mechanics and Engineering, 375, 2021. Crossref

  3. Suh Hyoung Suk, Sun WaiChing, Asynchronous phase field fracture model for porous media with thermally non-equilibrated constituents, Computer Methods in Applied Mechanics and Engineering, 387, 2021. Crossref

  4. Xiao Mian, Liu Chuanqi, Sun WaiChing, DP-MPM: Domain partitioning material point method for evolving multi-body thermal–mechanical contacts during dynamic fracture and fragmentation, Computer Methods in Applied Mechanics and Engineering, 385, 2021. Crossref

  5. Suh Hyoung Suk, Sun WaiChing, An immersed phase field fracture model for microporomechanics with Darcy–Stokes flow, Physics of Fluids, 33, 1, 2021. Crossref

  6. Bui Tinh Quoc, Hu Xiaofei, A review of phase-field models, fundamentals and their applications to composite laminates, Engineering Fracture Mechanics, 248, 2021. Crossref

  7. Suh Hyoung Suk, Sun WaiChing, Multi‐phase‐field microporomechanics model for simulating ice‐lens growth in frozen soil, International Journal for Numerical and Analytical Methods in Geomechanics, 46, 12, 2022. Crossref

Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections Prices and Subscription Policies Begell House Contact Us Language English 中文 Русский Português German French Spain