Issue
Mechanics & Industry
Volume 21, Number 5, 2020
Scientific challenges and industrial applications in mechanical engineering
Article Number 508
Number of page(s) 9
DOI https://doi.org/10.1051/meca/2020010
Published online 10 August 2020
  1. J.P. Hirth, Effects of hydrogen on the properties of iron and steel, Metal. Trans. A 11, 861–890 (1980) [Google Scholar]
  2. B.E. Sar, S. Fréour, A. Célino, F. Jacquemin, Accounting for differential swelling in the multi-physics modeling of the diffusive behavior of a tubular polymer structure, J. Compos. Mater. 49, 2375–2387 (2014) [Google Scholar]
  3. K. Derrien, P. Gilormini, Interaction between stress and diffusion in polymers, Defect Diffus. Forum 258–260, 447–452 (2006) [Google Scholar]
  4. A. McNabb, P.K. Foster, A new analysis of the diffusion of hydrogen in iron and ferritic steels, Trans. Metall. Soc. AIME 227, 618–627 (1963) [Google Scholar]
  5. H.G. Carter, K.G. Kibler, Langmuir-type model for anomalous moisture diffusion in composite resins, J. Compos. Mater. 12, 118–131 (1978) [Google Scholar]
  6. P. Sofronis, R.M. McMeeking, Numerical analysis of hydrogen transport near a blunting crack tip, J. Mech. Phys. Solids 37, 317–350 (1989) [Google Scholar]
  7. I.M. Bernstein, The role of hydrogen in the embrittlement of iron and steel, Mater. Sci. Eng. A 6, 1–19 (1970) [Google Scholar]
  8. C.-H. Shen, G.S. Springer, Effects of moisture and temperature on the tensile strength of composite materials, J. Compos. Mater. 11, 2–16 (1977) [Google Scholar]
  9. A.H.M. Krom, R.W.J. Koers, A.D. Bakker, Hydrogen transport near a blunting crack tip, J. Mech. Phys. Solids 47, 971–992 (1999) [Google Scholar]
  10. C.-S. Oh, Y.J. Kim, K.B. Yoon, Coupled analysis of hydrogen transport using ABAQUS, J. Solid Mech. Mater. Eng. 4, 908–917 (2010) [Google Scholar]
  11. N. Yazdipour, A.J. Haq, K. Muzaka, E.V. Pereloma, 2D modelling of the effect of grain size on hydrogen diffusion in X70 steel, Comput. Mater. Sci. 56, 49–57 (2012) [Google Scholar]
  12. T. Peret, A. Clement, S. Fréour, F. Jacquemin, Numerical transient hygro-elastic analyses of reinforced Fickian and non-Fickian polymers, Compos. Struct. 116, 395–403 (2014) [Google Scholar]
  13. Y. Charles, T.H. Nguyen, M. Gaspérini, Comparison of hydrogen transport through pre-deformed synthetic polycrystals and homogeneous samples by finite element analysis, Int. J. Hydrogen Energy 42, 20336–20350 (2017) [Google Scholar]
  14. Y. Charles, T.H. Nguyen, M. Gaspérini, FE simulation of the influence of plastic strain on hydrogen distribution during an U-bend test, Int. J. Mech. Sci. 120, 214–224 (2017) [Google Scholar]
  15. S. Benannoune, Y. Charles, J. Mougenot, M. Gaspérini, Numerical simulation of the transient hydrogen trapping process using an analytical approximation of the McNabb and Foster equation, Int. J. Hydrogen Energy 43, 9083–9093 (2018) [Google Scholar]
  16. Y. Zhao, P. Stein, Y. Bai, M. Al-Siraj, Y. Yang, B.-X. Xu, A review on modeling of electro-chemo-mechanics in lithium-ion batteries, J. Power Sources 413, 259–283 (2019) [Google Scholar]
  17. D. Kuhl, F. Bangert, G. Meschke, Coupled chemo-mechanical deterioration of cementitious materials. Part II: Numerical methods and simulations, Int. J. Solids Struct. 41, 41–67 (2004) [Google Scholar]
  18. T. Poulet, A. Karrech, K. Regenauer-Lieb, L. Fisher, P. Schaubs, Thermal-hydraulic-mechanical-chemical coupling with damage mechanics using ESCRIPTRT and ABAQUS, Tectonophysics 526–529, 124–132 (2012) [Google Scholar]
  19. A. Karrech, Non-equilibrium thermodynamics for fully coupled thermal hydraulic mechanical chemical processes, J. Mech. Phys. Solids 61, 819–837 (2013) [Google Scholar]
  20. S. Benannoune, Y. Charles, J. Mougenot, M. Gaspérini, G. De Temmerman, Numerical simulation by finite element modelling of diffusion and transient hydrogen trapping processes in plasma facing components, Nucl. Mater. Energy 19, 42–46 (2019) [Google Scholar]
  21. P. Gray, S.K. Scott, Autocatalytic reactions in the isothermal, continuous stirred tank reactor: isolas and other forms of multistability, Chem. Eng. Sci. 38, 29–43 (1983) [Google Scholar]
  22. P. Gray, S.K. Scott, Autocatalytic reactions in the isothermal, continuous stirred tank reactor: oscillations and instabilities in the system A + 2B → 3B; B → C, Chem. Eng. Sci. 39, 1087–1097 (1984) [Google Scholar]
  23. G. Molnár, A. Gravouil, 2D and 3D Abaqus implementation of a robust staggered phase-field solution for modeling brittle fracture, Finite Elem. Anal. Des. 130, 27–38 (2017) [Google Scholar]
  24. E. Martínez-Pañeda, A. Golahmar, C.F. Niordson, A phase field formulation for hydrogen assisted cracking, Comput. Methods Appl. Mech. Eng. 342, 742–761 (2018) [Google Scholar]
  25. Simulia, Abaqus User subroutines reference guide, Dassault Système (2011) [Google Scholar]
  26. S.A. Chester, C.V. Di Leo, L. Anand, A finite element implementation of a coupled diffusion-deformation theory for elastomeric gels, Int. J. Solids Struct. 52, 1–18 (2015) [Google Scholar]
  27. J. Chen, H. Wang, P. Yu, S. Shen, A finite element implementation of a fully coupled mechanical-chemical theory, Int. J. Appl. Mech. 09, 1750040 (2017) [Google Scholar]
  28. Simulia, Abaqus Analysis User's Manual, Dassault System (2011) [Google Scholar]
  29. Y. Charles, A finite element formulation to model extrinsic interfacial behavior, Finite Elem. Anal. Des. 88, 55–66 (2014) [Google Scholar]
  30. R.A. Barrio, Turing systems: a general model for complex patterns in nature, in: I. Licata, A. Sakaji (Eds.), Physics of Emergence and Organization, World Scientific (2008) 267–296 [Google Scholar]
  31. H. Meinhardt, Wie Schnecken sich in Schale werfen, Springer Berlin Heidelberg, Berlin, Heidelberg, 1997 [Google Scholar]
  32. B. Rudovics, E. Barillot, P.W. Davies, E. Dulos, J. Boissonade, P. De Kepper, Experimental studies and quantitative modeling of turing patterns in the (chlorine dioxide, iodine, malonic acid) reaction, J. Phys. Chem. A 103, 1790–1800 (1999) [Google Scholar]
  33. I. Szalai, P. De Kepper, Pattern formation in the ferrocyanide-iodate-sulfite reaction: the control of space scale separation, Chaos 18, 026105 (2008) [Google Scholar]
  34. P.W. Davies, P. Blanchedeau, A.E. Dulos, P. De Kepper, Dividing blobs, chemical flowers, and patterned islands in a reaction−diffusion system, Am. Chem. Soc. (1998). https://doi.org/10.1021/jp982034n. [Google Scholar]
  35. A.S. Mikhailov, G. Ertl, The Belousov-Zhabotinsky Reaction, in: Chemical Complexity, Springer, Cham, Cham (2017) 89–103 [Google Scholar]
  36. J.E. Pearson, Complex Patterns in a Simple System, Science 261, 189–192 (1993) [Google Scholar]
  37. W. Mazin, K.E. Rasmussen, E. Mosekilde, P. Borckmans, G. Dewel, Pattern formation in the bistable Gray-Scott model, Math. Comput. Simul. 40, 371–396 (1996) [Google Scholar]
  38. F. Lesmes, D. Hochberg, F. Morán, J. Pérez-Mercader, Noise-controlled self-replicating patterns, Phys. Rev. Lett. 91, 238301 (2003) [CrossRef] [PubMed] [Google Scholar]
  39. H. Wang, Z. Fu, X. Xu, Q. Ouyang, Pattern formation induced by internal microscopic fluctuations, J. Phys. Chem. A 111, 1265–1270 (2007) [CrossRef] [PubMed] [Google Scholar]
  40. W. Wang, Y. Lin, F. Yang, L. Zhang, Y. Tan, Numerical study of pattern formation in an extended Gray-Scott model, Commun. Nonlinear Sci. Numer. Simul. 16, 2016–2026 (2011) [Google Scholar]
  41. R.P. Munafo, Stable localized moving patterns in the 2-D Gray-Scott model. https://arxiv.org/abs/1501.01990 (2014) [Google Scholar]
  42. A. Adamatzky, Generative complexity of Gray-Scott model, Commun. Nonlinear Sci. Numer. Simul. 56, 457–466 (2018) [Google Scholar]
  43. T. Hutton, R.P. Munafo, A. Trevorrow, T. Rokicki, D. Wills, Ready, a cross-platform implementation of various reaction-diffusion systems, (2011) GNU General Public License. https://github.com/GollyGang/ready/ [Google Scholar]
  44. D. Bennewies, Final Report, Waterloo, Ontario, Canada, 2012. https://github.com/derekrb/gray-scott [Google Scholar]
  45. F. Buric, Pattern formation and chemical evolution in extended Gray-Scott models, Chalmers University of Technology, Göteborg, Sweden, 2014. http://github.com/phil-b-mt/egs [Google Scholar]
  46. R.P. Munafo, Reaction-Diffusion by the Gray-Scott Model: Pearson's Parametrization. https://mrob.com/pub/comp/xmorphia/ (accessed April 2017) [Google Scholar]
  47. D. Gizaw, Finite element method applied to gray-scott reaction-diffusion problem. Using FEniCs Software, Adv. Phys. Theories Appl. 58, 5–8 (2016) [Google Scholar]
  48. T. Lun, Finite Element Simulation of Pattern Formation in Gray-Scott Model, Researchgate.Net. (2016). https://doi.org/10.13140/RG.2.1.2780.6329 [Google Scholar]
  49. C. Xie, X. Hu, Finite element simulations with adaptively moving mesh for the reaction diffusion system, Numer. Math. Theory Methods Appl. 9, 686–704 (2016) [Google Scholar]
  50. T. Lun, Gray-Scott Coupled Mechanical Model, Researchgate.Net. (2016). https://doi.org/10.13140/RG.2.1.3994.3928 [Google Scholar]
  51. S. Benannoune, Y. Charles, J. Mougenot, M. Gaspérini, G. De Temmerman, Multidimensional finite element simulations of the diffusion and trapping of hydrogen in plasma-facing components including thermal expansion, Phys. Scripta (2020) [Google Scholar]

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