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Automatic generation of statistical volume elements using multibody dynamics and an erosion-based homogenization method

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Abstract

Modeling particle based heterogeneous materials using statistical volume elements (SVE) for predicting its mechanical behavior can be tedious when the particles are densely packed or elongated. Positioning particles without creating overlaps and avoiding meshing problems are two obstacles frequently mentioned. To counter these obstacles, a new modeling methodology based on multibody dynamics (MBD) and on an erosion-based homogenization method is proposed. The CAD model of a SVE is first generated and particles causing meshing problems are excluded. Meshing and finite element analysis are automatically carried out and a subsequent erosion-based homogenization method is used to retrieve the macroscopic behavior of the SVE. To illustrate the potential of this new method, results obtained with a random sequential adsorption algorithm on non-eroded SVEs are compared with results obtained from the same SVEs submitted to our erosion method. These results are then compared with results obtained using the new MBD based approach.

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References

  1. Böhm HJ, Eckschlager A, Han W (2002) Multi-inclusion unit cell models for metal matrix composites with randomly oriented discontinuous reinforcements. Comput Mater Sci 25(1):42–53

    Article  Google Scholar 

  2. Rasool A, Böhm HJ (2012) Effects of particle shape on the macroscopic and microscopic linear behaviors of particle reinforced composites. Int J Eng Sci 58:21–34

    Article  Google Scholar 

  3. El Moumen A et al (2015) Effect of reinforcement shape on physical properties and representative volume element of particles-reinforced composites: statistical and numerical approaches. Mech Mater 83:1–16

    Article  Google Scholar 

  4. Tian W et al (2015) Representative volume element for composites reinforced by spatially randomly distributed discontinuous fibers and its applications. Compos Struct 131:366–373

    Article  Google Scholar 

  5. Pierard O et al (2007) Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions. Int J Solids Struct 44(21):6945–6962

    Article  MATH  Google Scholar 

  6. Segurado J, Llorca J (2002) A numerical approximation to the elastic properties of sphere-reinforced composites. J Mech Phys Solids 50(10):2107–2121

    Article  MATH  Google Scholar 

  7. Kari S, Berger H, Gabbert U (2007) Numerical evaluation of effective material properties of randomly distributed short cylindrical fibre composites. Comput Mater Sci 39(1):198–204

    Article  Google Scholar 

  8. Kari S et al (2007) Computational evaluation of effective material properties of composites reinforced by randomly distributed spherical particles. Compos Struct 77(2):223–231

    Article  Google Scholar 

  9. Gusev AA (1997) Representative volume element size for elastic composites: a numerical study. J Mech Phys Solids 45(9):1449–1459

    Article  MATH  Google Scholar 

  10. Kanit T et al (2003) Determination of the size of the representative volume element for random composites: statistical and numerical approach. Int J Solids Struct 40(13):3647–3679

    Article  MATH  Google Scholar 

  11. Khisaeva ZF, Ostoja-Starzewski M (2006) On the size of RVE in finite elasticity of random composites. J Elast 85(2):153

    Article  MathSciNet  MATH  Google Scholar 

  12. Gitman IM, Askes H, Sluys LJ (2007) Representative volume: existence and size determination. Eng Fract Mech 74(16):2518–2534

    Article  Google Scholar 

  13. Harper LT et al (2012) Representative volume elements for discontinuous carbon fibre composites—part 1: boundary conditions. Compos Sci Technol 72(2):225–234

    Article  Google Scholar 

  14. Dirrenberger J, Forest S, Jeulin D (2014) Towards gigantic RVE sizes for 3D stochastic fibrous networks. Int J Solids Struct 51(2):359–376

    Article  Google Scholar 

  15. Böhm HJ, Rasool A (2016) Effects of particle shape on the thermoelastoplastic behavior of particle reinforced composites. Int J Solids Struct 87:90–101

    Article  Google Scholar 

  16. Ferrié E et al (2006) Fatigue crack propagation: in situ visualization using X-ray microtomography and 3D simulation using the extended finite element method. Acta Mater 54(4):1111–1122

    Article  Google Scholar 

  17. Coleri E et al (2012) Development of a micromechanical finite element model from computed tomography images for shear modulus simulation of asphalt mixtures. Constr Build Mater 30:783–793

    Article  Google Scholar 

  18. Huang M, Li Y-M (2013) X-ray tomography image-based reconstruction of microstructural finite element mesh models for heterogeneous materials. Comput Mater Sci 67:63–72

    Article  Google Scholar 

  19. Suuronen J-P et al (2013) Analysis of short fibres orientation in steel fibre-reinforced concrete (SFRC) by X-ray tomography. J Mater Sci 48(3):1358–1367

    Article  Google Scholar 

  20. Ganesh VV, Chawla N (2005) Effect of particle orientation anisotropy on the tensile behavior of metal matrix composites: experiments and microstructure-based simulation. Mater Sci Eng A 391(1):342–353

    Article  Google Scholar 

  21. Hua Y, Gu L (2013) Prediction of the thermomechanical behavior of particle-reinforced metal matrix composites. Compos B Eng 45(1):1464–1470

    Article  Google Scholar 

  22. Segurado J, Llorca J (2006) Computational micromechanics of composites: The effect of particle spatial distribution. Mech Mater 38(8):873–883

    Article  Google Scholar 

  23. Segurado J, González C, Llorca J (2003) A numerical investigation of the effect of particle clustering on the mechanical properties of composites. Acta Mater 51(8):2355–2369

    Article  Google Scholar 

  24. Di Paola F (2010) Multi-scale modeling of the thermo-mechanical behavior of particle-based composites, France, p 160

  25. Brassart L, Doghri I, Delannay L (2010) Homogenization of elasto-plastic composites coupled with a nonlinear finite element analysis of the equivalent inclusion problem. Int J Solids Struct 47(5):716–729

    Article  MATH  Google Scholar 

  26. Bailakanavar M et al (2012) Automated modeling of random inclusion composites. Eng Comput 30:609–625

    Article  Google Scholar 

  27. Schneider K, Klusemann B, Bargmann S (2016) Automatic three-dimensional geometry and mesh generation of periodic representative volume elements for matrix-inclusion composites. Adv Eng Softw 99:177–188

    Article  Google Scholar 

  28. Wang X, Zhang M, Jivkov AP (2016) Computational technology for analysis of 3D meso-structure effects on damage and failure of concrete. Int J Solids Struct 80:310–333

    Article  Google Scholar 

  29. Ogierman W, Kokot G (2018) Generation of the representative volume elements of composite materials with misaligned inclusions. Compos Struct 201:636–646

    Article  Google Scholar 

  30. Pan Y, Iorga L, Pelegri AA (2008) Analysis of 3D random chopped fiber reinforced composites using FEM and random sequential adsorption. Comput Mater Sci 43(3):450–461

    Article  Google Scholar 

  31. Pan Y, Iorga L, Pelegri AA (2008) Numerical generation of a random chopped fiber composite RVE and its elastic properties. Compos Sci Technol 68(13):2792–2798

    Article  Google Scholar 

  32. Lu Z, Yuan Z, Liu Q (2014) 3D numerical simulation for the elastic properties of random fiber composites with a wide range of fiber aspect ratios. Comput Mater Sci 90:123–129

    Article  Google Scholar 

  33. Hales T et al (2017) A formal proof of the Kepler conjecture. In: Forum of mathematics, Pi, vol 5, p e2

  34. Cooper DW (1988) Random-sequential-packing simulations in three dimensions for spheres. Phys Rev A 38(1):522–524

    Article  Google Scholar 

  35. Sherwood JD (1997) Packing of spheroids in three-dimensional space by random sequential addition. J Phys A Math Gen 30(24):L839–L843

    Article  Google Scholar 

  36. Lubachevsky BD (1991) How to simulate billiards and similar systems. J Comput Phys 94(2):255–283

    Article  MathSciNet  MATH  Google Scholar 

  37. Lubachevsky BD, Stillinger FH, Pinson EN (1991) Disks vs. spheres: contrasting properties of random packings. J Stat Phys 64(3):501–524

    Article  MathSciNet  MATH  Google Scholar 

  38. Donev A, Torquato S, Stillinger FH (2005) Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles: I. Algorithmic details. J Comput Phys 202(2):737–764

    Article  MathSciNet  MATH  Google Scholar 

  39. Donev A, Torquato S, Stillinger FH (2005) Neighbor list collision-driven molecular dynamics simulation for nonspherical hard particles: II. Applications to ellipses and ellipsoids. J Comput Phys 202(2):765–793

    MathSciNet  MATH  Google Scholar 

  40. Mirtich BV (1996) Impulse-based dynamic simulation of rigid body systems. University of California

  41. Lloyd JE (2005) Fast implementation of Lemke's algorithm for rigid body contact simulation. In: Proceedings of the 2005 IEEE international conference on robotics and automation

  42. Acary V, Brogliato B (2008) Numerical methods for nonsmooth dynamical systems: applications in mechanics and electronics. Springer, Berlin

    Book  MATH  Google Scholar 

  43. Stewart DE, Trinkle JC (1996) An implicit time-step** scheme for rigid body dynamics with inelastic collisions and coulomb friction. Int J Numer Methods Eng 39(15):2673–2691

    Article  MathSciNet  MATH  Google Scholar 

  44. Frey PJ, George PL (2000) Mesh generation: application to finite elements. Hermes Science

  45. Couture A et al (2020) Automatic statistical volume element modeling based on the unified topology model. Int J Solids Struct 191–192:26–41

    Article  Google Scholar 

  46. Cuillière J-C, Francois V (2014) Integration of CAD, FEA and topology optimization through a unified topological model. Comput Aided Des Appl 11:493–508

    Article  Google Scholar 

  47. Chrono P. Chrono: An open source framework for the physics-based simulation of dynamic systems. https://projectchrono.org/

  48. Advani SG, Tucker CL III (1987) The use of tensors to describe and predict fiber orientation in short fiber composites. J Rheol 31(8):751–784

    Article  Google Scholar 

  49. EDF (2020) Code_Aster, Analysis of structures and thermomechanics for studies and research. www.code-aster.org

Download references

Funding

This study was carried out as part of a project supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Fondation de l’UQTR and the Ministère de l’Éducation et de la Recherche Français.

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Correspondence to Jean-Christophe Cuillière.

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Couture, A., François, V., Cuillière, JC. et al. Automatic generation of statistical volume elements using multibody dynamics and an erosion-based homogenization method. Comput Mech 69, 1041–1066 (2022). https://doi.org/10.1007/s00466-021-02130-1

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  • DOI: https://doi.org/10.1007/s00466-021-02130-1

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