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A fully non-invasive hybrid IGA/FEM scheme for the analysis of localized non-linear phenomena

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Abstract

This work undertakes to combine the interests of IsoGeometric Analysis (IGA) and standard Finite Element Methods (FEM) for the global/local simulation of structures. The idea is to adopt a hybrid global-IGA/local-FEM modeling, thereby benefiting from: (i) the superior geometric description and per-Degree-Of-Freedom accuracy of IGA for capturing global, regular responses, and (ii) the ability of FEM to compute local, strongly non-linear or even singular behaviors. For the sake of minimizing the implementation effort, we develop a coupling scheme that is fully non-invasive in the sense that the initial global spline model to be enriched is never modified and the construction of the coupling operators can be performed using conventional FE packages. The key ingredient is to express the FEM-to-IGA bridge, based on Bézier extraction, to transform the initial global spline interface into a FE one on which the local FE mesh can be constructed. This allows to resort to classic FE trace operators to implement the coupling. It results in a strategy that offers the opportunity to simply couple an isogeometric code with any robust FE code suitable for the modelling of complex local behaviors. The method also easily extends in case the users only have at their disposal FE codes. This is the situation that is considered for the numerical illustrations. More precisely, we only make use of the FE industrial software Code_Aster to perform efficiently and accurately the hybrid global-IGA/local-FEM simulation of structures subjected locally to cracks, contact, friction and delamination.

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References

  1. Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput Methods Appl Mech Eng 194:4135–4195

    Article  MATH  Google Scholar 

  2. Cottrell JA, Hughes TJR, Bazilevs Y (2009) Isogeometric analysis: toward Integration of CAD and FEA, 1st edn. Wiley, London

    Book  MATH  Google Scholar 

  3. Cohen E, Lyche T, Riesenfeld R (1980) Discrete B-spline and subdivision techniques in computer aided geometric design and computer graphics. Comput Graphics Image Process 14:87–111

    Article  Google Scholar 

  4. Piegl L, Tiller W (1997) The NURBS book, 2Nd. Springer, New york

    Book  MATH  Google Scholar 

  5. Tirvaudey M, Bouclier R, Passieux JC, Chamoin L (2019) Non-invasive implementation of nonlinear Isogeometric Analysis in an industrial FE software. Eng Comput 37:237–261

    Article  Google Scholar 

  6. Xu G, Mourrain B, Duvigneau R, Galligo A (2013) Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications. Comput Aided Des 45:395–404

    Article  Google Scholar 

  7. Massarwi F, Antolin P, Elber G (2019) Volumetric untrimming: precise decomposition of trimmed trivariates into tensor products. Comput Aided Geom Des 71:1–15

    Article  MATH  Google Scholar 

  8. Ruess M, Schillinger D, Özcan AI, Rank E (2014) Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries. Comput Methods Appl Mech Eng 169:46–71

    Article  MATH  Google Scholar 

  9. Wei X, Marussig B, Antolin P, Buffa A (2021) Immersed boundary-conformal isogeometric method for linear elliptic problems. Comput Mech 68:1385–1405

    Article  MATH  Google Scholar 

  10. Wang J, Zhou G, Hillman M, Madra A, Bazilevs Y, Du J, Su K (2021) Consistent immersed volumetric Nitsche methods for composite analysis. Comput Methods Appl Mech Eng 385:114042

    Article  MATH  Google Scholar 

  11. De Luycker E, Benson DJ, Belytschko T, Bazilevs Y, Hsu MC (2011) X-FEM in isogeometric analysis for linear fracture mechanics. Int J Numer Meth Eng 87:541–565

    Article  MATH  Google Scholar 

  12. Yuan H, Yu T, Bui TQ (2021) Multi-patch local mesh refinement XIGA based on LR NURBS and Nitsche’s method for crack growth in complex cracked plates. Eng Fract Mech 250:107780

    Article  Google Scholar 

  13. Fathi F, de Borst R (2021) Geometrically nonlinear extended isogeometric analysis for cohesive fracture with applications to delamination in composites. Finite Elem Anal Des 191:103527

    Article  Google Scholar 

  14. Verhoosel CV, Scott MA, De Borst R, Hughes TJR (2011) An isogeometric approach to cohesive zone modeling. Int J Numer Meth Eng 87:336–360

    Article  MATH  Google Scholar 

  15. Dimitri R, De Lorenzis L, Wriggers P, Zavarise G (2014) NURBS-and T-spline-based isogeometric cohesive zone modeling of interface debonding. Comput Mech 54:369–388

    Article  MATH  Google Scholar 

  16. Borden MJ, Hughes TJR, Landis CM, Verhoosel CV (2014) A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework. Comput Methods Appl Mech Eng 273:100–118

    Article  MATH  Google Scholar 

  17. Proserpio D, Ambati M, De Lorenzis L, Kiendl J (2020) A framework for efficient isogeometric computations of phase-field brittle fracture in multipatch shell structures. Comput Methods Appl Mech Eng 372:113363

    Article  MATH  Google Scholar 

  18. Paul K, Zimmermann C, Mandadapu KK, Hughes TJR, Landis CM, Sauer RA (2020) An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS. Comput Mech 65:1039–1062

    Article  MATH  Google Scholar 

  19. Gendre L, Allix O, Gosselet P (2009) Non-intrusive and exact global/local techniques for structural problems with local plasticity. Comput Mech 44:233–245

    Article  MATH  Google Scholar 

  20. Passieux JC, Réthoré J, Gravouil A, Baietto MC (2013) Local/global non-intrusive crack propagation simulation using a multigrid X-FEM solver. Comput Mech 56:1381–1393

    Article  Google Scholar 

  21. Li H, O’Hara P, Duarte CA (2021) Non-intrusive coupling of a 3-D Generalized Finite Element Method and Abaqus for the multiscale analysis of localized defects and structural features. Finite Elem Anal Des 193:103554

    Article  Google Scholar 

  22. Fuenzalida-Henriquez I, Oumaziz P, Castillo-Ibarra E, Hinojosa J (2022) Global-Local non intrusive analysis with robin parameters: application to plastic hardening behavior and crack propagation in 2D and 3D structures. Comput Mech 69:965–978

    Article  MATH  Google Scholar 

  23. Meray F, Chaise T, Gravouil A, Depouhon P, Descharrieres B, Nélias D (2022) A novel SAM/X-FEM coupling approach for the simulation of 3D fatigue crack growth under rolling contact loading. Finite Elem Anal Des 206:103752

    Article  Google Scholar 

  24. Gerasimov T, Noii N, Allix O, De Lorenzis L (2018) A non-intrusive global/local approach applied to phase-field modeling of brittle fracture. Adv Model Simul Eng Sci 5(1):1–30

    Article  Google Scholar 

  25. Noii N, Aldakheel F, Wick T, Wriggers P (2020) An adaptive global-local approach for phase-field modeling of anisotropic brittle fracture. Comput Methods Appl Mech Eng 361:112744

    Article  MATH  Google Scholar 

  26. Aldakheel F, Noii N, Wick T, Wriggers P (2021) A global-local approach for hydraulic phase-field fracture in poroelastic media. Comput Math Appl 91:99–121

    Article  MATH  Google Scholar 

  27. Duval M, Passieux JC, Salaün M, Guinard S (2016) Non-intrusive coupling: recent advances and scalable nonlinear domain decomposition. Arch Comput Methods Eng 23:17–38

    Article  MATH  Google Scholar 

  28. Gosselet P, Blanchard M, Allix O, Guguin G (2018) Non-invasive global-local coupling as a Schwarz domain decomposition method: acceleration and generalization. Adv Model Simul Eng Sci 5:1–23

    Article  Google Scholar 

  29. Oumaziz P, Gosselet P, Boucard PA, Guinard S (2019) A parallel non-invasive mixed domain decomposition-Implementation and applications to mechanical assemblies. Finite Elem Anal Des 156:24–33

    Article  MATH  Google Scholar 

  30. Guinard S, Bouclier R, Toniolli M, Passieux JC (2018) Multiscale analysis of complex aeronautical structures using robust non-intrusive coupling. Adv Model Simul Eng Sci 5:1–27

    Article  Google Scholar 

  31. Wangermez M, Allix O, Guidault PA, Ciobanu O, Rey C (2020) Interface coupling method for the global-local analysis of heterogeneous models: A second-order homogenization-based strategy. Comput Methods Appl Mech Eng 365:113032

    Article  MATH  Google Scholar 

  32. Bouclier R, Passieux JC, Salaün M (2016) Local enrichment of NURBS patches using a non-intrusive coupling strategy: Geometric details, local refinement, inclusion, fracture. Comput Methods Appl Mech Eng 300:1–26

    Article  MATH  Google Scholar 

  33. Bouclier R, Passieux JC (2020) A Nitsche-based non-intrusive coupling strategy for global/local isogeometric structural analysis. Comput Methods Appl Mech Eng 340:253–277

    Article  MATH  Google Scholar 

  34. Bouclier R, Hirschler T (2022) IGA:non-conforming couplingand shape optimization of complex multipatchstructures. Wiley, londen. https://doi.org/10.1002/9781119988557

    Book  Google Scholar 

  35. Colantonio G, Chapelier M, Bouclier R, Passieux JC, Marenic E (2020) Noninvasive multilevel geometric regularization of mesh-based three-dimensional shape measurement. Int J Numer Meth Eng 121:1877–1897

    Article  Google Scholar 

  36. Borden M, Scott MA, Evans JA, Hughes TJR (2011) Isogeometric finite element data structures based on Bézier extraction of NURBS. Int J Numer Meth Eng 87:15–47

    Article  MATH  Google Scholar 

  37. Scott M, Borden M, Verhoosel C, Sederberg T, Hughes TJR (2011) Isogeometric finite element data structures based on bézier extraction of T-splines. Int J Numer Meth Eng 88:126–156

    Article  MATH  Google Scholar 

  38. Schillinger D, Ruthala PK, Nguyen LH (2016) Lagrange extraction and projection for NURBS basis functions: A direct link between isogeometric and standard nodal finite element formulations. Int J Numer Meth Eng 108:515–534

    Article  Google Scholar 

  39. Cottrell JA, Hughes TJR, Reali A (2007) Studies of refinement and continuity in isogeometric structural analysis. Comput Methods Appl Mech Eng 196:4160–4183

    Article  MATH  Google Scholar 

  40. Kamensky D, Bazilevs Y (2019) tIGAr: Automating isogeometric analysis with FEniCS. Comput Methods Appl Mech Eng 344:477–498

    Article  MATH  Google Scholar 

  41. Quarteroni A, Manzoni A, Negri F (2015) Reduced basis methods for partial differential equations: an introduction, vol 92. Springer, Berlin

    MATH  Google Scholar 

  42. Hesthaven JS, Rozza G, Stamm B (2016) Certified reduced basis methods for parametrized partial differential equations, vol 590. Springer, Berlin

    Book  MATH  Google Scholar 

  43. Benner P, Grivet-Talocia S, Quarteroni A, Rozza G, Schilders W, Silveira LM (2022) Model order reduction: snapshot-based methods and algorithms, De Gruyter

  44. Hennig P, Müller S, Kästner M (2016) Bézier extraction and adaptive refinement of truncated hierarchical NURBS. Comput Methods Appl Mech Eng 305:316–339

    Article  MATH  Google Scholar 

  45. D’Angella D, Reali A (2020) Efficient extraction of hierarchical B-Splines for local refinement and coarsening of Isogeometric Analysis. Comput Methods Appl Mech Eng 367:113131

    Article  MATH  Google Scholar 

  46. Evans E, Scott M, Li X, Thomas D (2015) Hierarchical T-splines: analysis-suitability, Bézier extraction, and application as an adaptive basis for isogeometric analysis. Comput Methods Appl Mech Eng 284:1–20

    Article  MATH  Google Scholar 

  47. Chen L, de Borst R (2018) Adaptive refinement of hierarchical T-splines. Comput Methods Appl Mech Eng 337:220–245

    Article  MATH  Google Scholar 

  48. Brivadis E, Buffa A, Wohlmuth B, Wunderlich L (2015) Isogeometric mortar methods. Comput Methods Appl Mech Eng 284:292–319

    Article  MATH  Google Scholar 

  49. Bouclier R, Passieux JC, Salaün M (2017) Development of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches. Comput Methods Appl Mech Eng 316:123–150

    Article  MATH  Google Scholar 

  50. Miao D, Zou Z, Scott MA, Borden M, Thomas DC (2020) Isogeometric Bézier dual mortaring: The enriched Bézier dual basis with application to second-and fourth-order problems. Comput Methods Appl Mech Eng 363:112900

    Article  MATH  Google Scholar 

  51. de Prenter F, Verhoosel CV, van Zwieten GJ, van Brummelen VH (2017) Condition number analysis and preconditioning of the finite cell method. Comput Methods Appl Mech Eng 316:297–327

    Article  MATH  Google Scholar 

  52. Allix O, Gosselet P (2020) Non intrusive global/local coupling techniques in solid mechanics: An introduction to different coupling strategies and acceleration techniques. Modeling in engineering using innovative numerical methods for solids and fluids. Springer, Cham, pp 203–220

    Chapter  MATH  Google Scholar 

  53. Chevreuil M, Nouy A, Safatly E (2013) A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties. Comput Methods Appl Mech Eng 255:255–274

    Article  MATH  Google Scholar 

  54. Geuzaine C, Remacle JF (2009) GMSH: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Meth Eng 79:1309–1331

    Article  MATH  Google Scholar 

  55. Ribes A, Caremoli C (2007) Salome platform component model for numerical simulation. In: 31st Annual International Computer Software and Applications Conference (COMPSAC 2007) 2:553-564

  56. de France Electricité. Finite element \(code\)_\({aster}\), Analysis of Structures and Thermomechanics for Studies and Research. Open source on www.code-aster.org, 1989–2017

  57. Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method: its basis and fundamentals. Elsevier, Amsterdam

    MATH  Google Scholar 

  58. Antolin P, Buffa A, Calabro F, Martinelli M, Sangalli G (2015) Efficient matrix computation for tensor-product isogeometric analysis: The use of sum factorization. Comput Methods Appl Mech Eng 285:817–828

    Article  MATH  Google Scholar 

  59. Mantzaflaris A, Jüttler B (2015) Integration by interpolation and look-up for galerkin-based isogeometric analysis. Comput Methods Appl Mech Eng 284:373–400

    Article  MATH  Google Scholar 

  60. Hirschler T, Antolin P, Buffa A (2022) Fast and multiscale formation of isogeometric matrices of microstructured geometric models. Comput Mech 69:439–466

    Article  MATH  Google Scholar 

  61. Hiemstra RR, Sangalli G, Tani M, Calabrò F, Hughes TJR (2019) Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity. Comput Methods Appl Mech Eng 355:234–260

    Article  MATH  Google Scholar 

  62. Hirschler T, Bouclier R, Dureisseix D, Duval A, Elguedj T, Morlier J (2019) A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff-Love shells. Comput Methods Appl Mech Eng 357:112578

  63. Bosy M, Montardini M, Sangalli G, Tani M (2020) A domain decomposition method for isogeometric multi-patch problems with inexact local solvers. Comput Math Appl 80(2020):2604–2621

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut Clement Ader (ICA), Université de Toulouse, CNRS-INSA-UPS-ISAE-Mines Albi, 5 rue Caroline Aigle, Toulouse, 31400, France

    Evgeniia Lapina, Paul Oumaziz, Robin Bouclier & Jean-Charles Passieux

  2. Institut de Mathématiques de Toulouse (IMT), Université de Toulouse, CNRS-INSA-UT1-UT2-UPS, 118, route de Narbonne, Toulouse, F-31062 Cedex 9, France

    Evgeniia Lapina & Robin Bouclier

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  1. Evgeniia Lapina
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  2. Paul Oumaziz
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  3. Robin Bouclier
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  4. Jean-Charles Passieux
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Correspondence to Robin Bouclier.

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Lapina, E., Oumaziz, P., Bouclier, R. et al. A fully non-invasive hybrid IGA/FEM scheme for the analysis of localized non-linear phenomena. Comput Mech 71, 213–235 (2023). https://doi.org/10.1007/s00466-022-02234-2

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