Skip to main content
SpringerLink
Log in

Level set-based generation of representative volume elements for the damage analysis of irregular masonry

  • New Trends in Mechanics of Masonry
  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

Computational homogenization has been used extensively over the past two decades for the analysis of masonry structures based on various averaging schemes (periodic homogenization, transformation field analysis,...), focusing on regular periodic masonry. Irregular masonry has subsequently also been scrutinized using multiscale approaches. In such efforts, an efficient strategy is required for the generation and meshing of realistic representative volume elements (RVEs) geometries. In complement to existing generation approaches, the present contribution deals with a level set-based methodology to generate irregular masonry RVE geometries. Starting from inclusion-based RVEs, combinations of distance fields are used to produce typical geometries of irregular masonry RVEs. The resulting geometries are described by implicit functions. Such implicit geometry descriptions are next exploited in an automated procedure for producing high quality conformal 2D finite element meshes on implicit geometries. This automated RVE generation and discretization procedure is then illustrated by producing failure envelopes for irregular masonry, using an implicit gradient damage formulation. The interest of recently developed gradient models with decreasing interaction length parameters is also illustrated on a specific example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Lourenço PB (1996) Computational strategies for masonry structures. Ph.D. Dissertation, Delft University of Technology, Delft, The Netherlands

  2. Lourenço PB, De Borst R, Rots JG (1997) A plane stress softening plasticity model for orthotropic materials. Int J Numer Meth Eng 40(21):4033–4057

    Article  MATH  Google Scholar 

  3. Berto L, Saetta A, Scotta R, Vitaliani R (2002) An orthotropic damage model for masonry structures. Int J Numer Meth Eng 55(2):127–157

    Article  MATH  Google Scholar 

  4. Lourenço PB, Rots JG (1997) Multisurface interface model for analysis of masonry structures. J Eng Mech 123(7):660–668

    Article  Google Scholar 

  5. Alfano G, Sacco E (2006) Combining interface damage and friction in a cohesive-zone model. Int J Numer Meth Eng 68(5):542–582

    Article  MathSciNet  MATH  Google Scholar 

  6. Pegon P, Anthoine A (1997) Numerical strategies for solving continuum damage problems with softening: application to the homogenization of masonry. Comput Struct 64(1–4):623–642

    Article  MATH  Google Scholar 

  7. Massart TJ, Peerlings RHJ, Geers MGD, Gottcheiner S (2005) Mesoscopic modeling of failure in brick masonry accounting for three-dimensional effects. Eng Fract Mech 72(8):1238–1253

    Article  Google Scholar 

  8. Lofti H, Shing P (1994) Interface model applied to fracture of masonry structures. J Struct Eng 120(1):63–80

    Article  Google Scholar 

  9. Cecchi A, Sab K (2002) A multi-parameter homogenization study for modelling elastic masonry. Eur J Mech A Solids 21:249–268

    Article  MathSciNet  MATH  Google Scholar 

  10. Cecchi A, Sab K (2002) Out of plane model for heterogeneous periodic materials: the case of masonry. Eur J Mech A Solids 21:715–746

    Article  MathSciNet  MATH  Google Scholar 

  11. Cecchi A, Sab K (2007) A homogenized Reissner–Mindlin model for orthotropic periodic plates. Application to brickwork panels. Int J Solids Struct 44:6055–6079

    Article  MATH  Google Scholar 

  12. Anthoine A (1995) Derivation of the in-plane elastic characteristics of masonry through homogenization theory. Int J Solids Struct 32(2):137–163

    Article  MATH  Google Scholar 

  13. Peerlings RHJ, de Borst R, Brekelmans WAM, de Vree JHP (1996) Gradient enhanced damage for quasi-brittle materials. Int J Numer Methods Eng 39:3391–3403

    Article  MATH  Google Scholar 

  14. Massart TJ, Peerlings RHJ, Geers MGD (2004) Mesoscopic modeling of failure and damage-induced anisotropy in brick masonry. Eur J Mech A Solids 23(5):719–735

    Article  MATH  Google Scholar 

  15. Addessi D, Sacco E (2014) A kinematic enriched plane state formulation for the analysis of masonry panels. Eur J Mech A Solids 44:188–200

    Article  Google Scholar 

  16. Addessi D, Sacco E (2016) Enriched plane state formulation for nonlinear homogenization of in-plane masonry wall. Meccanica 51(11):2891–2907

    Article  MathSciNet  Google Scholar 

  17. Dvorak GJ (1992) Transformation field analysis of inelastic composite materials. In: Proceedings of the Royal Society A, vol 437

  18. Sacco E (2009) A nonlinear homogenization procedure for periodic masonry. Eur J Mech A Solids 28:209–222

    Article  MATH  Google Scholar 

  19. Chettah A, Mercatoris BCN, Sacco E, Massart TJ (2013) Localisation analysis in masonry using transformation field analysis. Eng Fract Mech 110:168–188

    Article  Google Scholar 

  20. Marfia S, Sacco E (2012) Multiscale damage contact-friction model for periodic masonry walls. Comput Methods Appl Mech Eng 205–208:189–203

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Sepe V, Marfia S, Sacco E (2013) A nonuniform TFA homogenization technique based on piecewise interpolation functions of the inelastic field. Int J Solids Struct 50:725–742

    Article  Google Scholar 

  22. Luciano R, Sacco E (1997) Homogenization technique and damage model for old masonry material. Int J Solids Struct 34(24):3191–3208

    Article  MathSciNet  MATH  Google Scholar 

  23. De Bellis ML, Addessi D (2011) A Cosserat based multiscale model for masonry structures. Int J Multiscale Comput Eng 9(5):543–563

    Article  Google Scholar 

  24. Addessi D, Sacco E, Paolone A (2010) Cosserat model for periodic masonry deduced by nonlinear homogenization. Eur J Mech A Solids 29:724–737

    Article  Google Scholar 

  25. Massart TJ, Peerlings RHJ, Geers MGD (2007) An enhanced multi-scale approach for masonry wall computations with localization of damage. Int J Numer Methods Eng 69(5):1022–1059

    Article  MATH  Google Scholar 

  26. Mercatoris BCN, Massart TJ (2009) Assessment of periodic homogenization-based multiscale computational schemes for quasi-brittle structural failure. Int J Multiscale Comput Eng 7(2):153–170

    Article  Google Scholar 

  27. Mercatoris BCN, Bouillard P, Massart TJ (2009) Multi-scale detection of failure in planar masonry thin shells using computational homogenisation. Eng Fract Mech 76(4):479–499

    Article  Google Scholar 

  28. Mercatoris BCN, Massart TJ (2011) A coupled two-scale computational scheme for the failure of periodic quasi-brittle thin planar shells and its application to masonry. Int J Numer Methods Eng 85:1177–1206

    Article  MATH  Google Scholar 

  29. Berke PZ, Peerlings RHJ, Massart TJ, Geers MGD (2014) A homogenization-based quasi-discrete method for the fracture of heterogeneous materials. Comput Mech 53:909–923

    Article  MathSciNet  MATH  Google Scholar 

  30. Cecchi A, Sab K (2009) Discrete and continuous models for in plane loaded random elastic brickwork. Eur J Mech A Solids 28:610625

    Article  MATH  Google Scholar 

  31. Cecchi A, Sab K (2009) A homogenized Love–Kirchhoff model for out-of-plane loaded random 2D lattices: application to quasi-periodic brickwork panels. Int J Solids Struct 46:2907–2919

    Article  MathSciNet  MATH  Google Scholar 

  32. Cluni F, Gusella V (2004) Homogenization of non-periodic masonry structures. Int J Solids Struct 41:1911–1923

    Article  MathSciNet  MATH  Google Scholar 

  33. Milani G, Esquivel YW, Lourenco PB, Riveiro B, Oliveira DV (2013) Characterization of the response of quasi-periodic masonry: geometrical investigation, homogenization and application to the Guimares castle, Portugal. Eng Struct 56:621–641

    Article  Google Scholar 

  34. Sorour M, Elmenshawi A, Parsekian G, Mufti A, Jaeger LG, Duchesne DPJ, Paquette J, Shrive N (2011) An experimental programme for determining the characteristics of stone masonry walls. Can J Civ Eng 38:1204–1215

    Article  Google Scholar 

  35. Elmenshawi A, Sorour M, Mufti A, Jaeger LG, Shrive N (2010) In-plane seismic behaviour of historic stone masonry. Can J Civ Eng 37:465–476

    Article  Google Scholar 

  36. Milani G, Lourenço PB (2010) A simplified homogenized limit analysis model for randomly assembled blocks out-of-plane loaded. Comput Struct 88:690–717

    Article  MATH  Google Scholar 

  37. Feo L, Luciano R, Misseri G, Rovero L (2016) Irregular stone masonries: analysis and strengthening with glass fibre reinforced composites. Compos B 92:84–93

    Article  Google Scholar 

  38. Cundari GA, Milani G (2013) Homogenized and heterogeneous limit analysis model for pushover analysis of ancient masonry walls with irregular texture. Int J Archit Herit 7:303–338

    Article  Google Scholar 

  39. Milosevic J, Sousa Gago A, Lopes M, Bento R (2013) Experimental assessment of shear strength parameters on rubble stone masonry specimens. Constr Build Mater 47:1372–1380

    Article  Google Scholar 

  40. Milosevic J, Sousa Gago A, Lopes M, Bento R (2015) In-plane seismic response of rubble stone masonry specimens by means of static cyclic tests. Constr Build Mater 82:919

    Article  Google Scholar 

  41. Vasconcelos G, Lourenço PB (2009) In-plane experimental behavior of stone masonry walls under cyclic loading. J Struct Eng 135(10):1269–1277

    Article  Google Scholar 

  42. Senthivel R, Lourenço PB (2009) Finite element modelling of deformation characteristics of historical stone masonry shear walls. Eng Struct 31:1930–1943

    Article  Google Scholar 

  43. Zeman J, Šejnoha M (2007) From random microstructures to representative volume elements. Modell Simul Mater Sci Eng 15(4):S325–S335

    Article  ADS  Google Scholar 

  44. Cavalagli N, Cluni F, Gusella V (2013) Evaluation of a statistically equivalent periodic unit cell for a quasi-periodic masonry. Int J Solids Struct 50:4226–4240

    Article  Google Scholar 

  45. Falsone G, Lombardo M (2007) Stochastic representation of the mechanical properties of irregular masonry structures. Int J Solids Struct 44:8600–8612

    Article  MATH  Google Scholar 

  46. Gusella V, Cluni F (2006) Random field and homogeization for masonry with nonperiodic microstructure. J Mech Mater Struct 1(2):357–386

    Article  Google Scholar 

  47. Spence SMJ, Gioffre M, Grigoriu MD (2008) Probabilistic models and simulation of irregular masonry walls. J Eng Mech 134(9):750–762

    Article  Google Scholar 

  48. Sonon B, Francois B, Massart TJ (2012) A unified level set based methodology for fast generation of complex microstructural multi-phase RVEs. Comput Methods Appl Mech Eng 223–224:103–122

    Article  Google Scholar 

  49. Bernard O, Friboulet D, Thevenaz P, Unser M (2009) Variational B-spline level-set: a linear filtering approach for fast deformable model evolutions. IEEE Trans Image Process 18(6):1179–1191

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. Poh LH, Sun G (2016) Localizing gradient damage model with decreasing interactions. Int J Numer Methods Eng. doi:10.1002/nme.5364 (in press)

  51. Sonon B, Francois B, Massart TJ (2015) An advanced approach for the generation of complex cellular material representative volume elements using distance fields and level sets. Comput Mech 56(2):221–242

    Article  MathSciNet  MATH  Google Scholar 

  52. Persson PO, Strang G (2004) A simple mesh generator in MATLAB. SIAM Rev 46(2):329–345

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. Ehab Moustafa Kamel K, Sonon B, Massart TJ, An integrated approach for the generation and conformal discretization of complex inclusion-based microstructures (in preparation)

  54. Lo DSH (2015) Finite element mesh generation. CRC Press, Boca Raton

    Book  MATH  Google Scholar 

  55. Lorensen WE, Cline HE (1987) Marching cubes: a high resolution 3D surface construction algorithm. SIG, Newington

    Google Scholar 

  56. Schewchuk JR (1997) Constrained delaunay tetrahedralizations and provably good boundary recovery. In: IMR

  57. Peerlings RHJ, Geers MGD, de Borst R, Brekelmans WAM (2001) A critical comparision of nonlocal and gradient-enhanced softening continua. Int J Solids Struct 38:7723–7746

    Article  MATH  Google Scholar 

  58. Bazant ZP, Jirasek M (2002) Nonlocal integral formulations of plasticity and damage: survey of progress. J Eng Mech 128(11):1119–1149

    Article  Google Scholar 

  59. Peerlings RHJ, Massart TJ, Geers MGD (2004) A thermodynamically motivated implicit gradient damage framework and its application to brick masonry cracking. Comput Methods Appl Mech Eng 193:3403–3417

    Article  ADS  MATH  Google Scholar 

  60. Geers MGD, de Borst R, Brekelmans WAM, Peerlings RHJ (1998) Strain-based transient-gradient damage model for failure analyses. Comput Methods Appl Mech Eng 160:133–153

    Article  ADS  MATH  Google Scholar 

  61. Simone A, Askes H, Sluys LJ (2004) Incorrect initiation and propagation of failure in non-local and gradient-enhanced media. Int J Solids Struct 41:351–363

    Article  MATH  Google Scholar 

  62. Forest S (2009) Micromorphic approach for gradient elasticity, viscoplasticity and damage. J Eng Mech 135(3):117–131

    Article  Google Scholar 

  63. Sun G, Poh LH (2016) Homogenization of intergranular fracture towards a transient gradient damage model. J Mech Phys Solids 95:374–392

    Article  ADS  MathSciNet  Google Scholar 

  64. Massart TJ, Peerlings RHJ, Geers MGD (2007) Structural damage analysis of masonry walls using computational homogenization. Int J Damage Mech 16(2):199–226

    Article  Google Scholar 

  65. Geers MGD (1999) Enhanced solution control for physically and geometrically non-linear problems. Part I—the subplane control approach. Int J Numer Methods Eng 46:177–204

    Article  MATH  Google Scholar 

  66. Massart TJ, Peerlings RHJ, Geers MGD (2005) A dissipation-based control method for the multi-scale modelling of quasi-brittle materials. C R Mecanique 527:333–521

    Google Scholar 

  67. Borri A, Corradi M, Castori G, De Maria A (2015) A method for the analysis and classification of historic masonry. Bull Earthq Eng 13:2647–2665

    Article  Google Scholar 

Download references

Acknowledgements

The third author acknowledges the support of FRIA under Grant No. 29340757. The first and second authors acknowledge the support of FRS-FNRS under Grant PDR No. 19471061.

Funding

The third author was funded by FRIA (Grant No. 29340757). The first and second authors benefited from the support of FRS-FNRS (Grant PDR T.1002.14F—No. 19471061).

Author information

Authors and Affiliations

  1. Building, Architecture and Town Planning, Universite libre de Bruxelles, CP 194/2, Avenue F.D. Roosevelt 50, 1050, Brussels, Belgium

    Thierry J. Massart, Bernard Sonon & Karim Ehab Moustafa Kamel

  2. Department of Civil and Environmental Engineering, National University of Singapore, 1 Engineering Drive 2, E1A-07-03, 117576, Singapore, Singapore

    Leong Hien Poh & Gang Sun

Authors
  1. Thierry J. Massart
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bernard Sonon
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Karim Ehab Moustafa Kamel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Leong Hien Poh
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Gang Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thierry J. Massart.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Massart, T.J., Sonon, B., Ehab Moustafa Kamel, K. et al. Level set-based generation of representative volume elements for the damage analysis of irregular masonry. Meccanica 53, 1737–1755 (2018). https://doi.org/10.1007/s11012-017-0695-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-017-0695-0

Keywords

Search

Navigation