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Micro-fracture instabilities in granular solids

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Abstract

We study the aspect of unstable behavior (like strain localization bands) in elastic solids as a consequence of micro-fracturing. A two-scale approach of computational homogenization is considered. The macroscopic behavior is investigated by finite element computations on a unit cell. At the micro-level, we consider a granular structure with elastic grains. The inter-granular boundaries are modeled with cohesive laws, friction and unilateral contact. We show that decohesion between grains gives rise to macro-instabilities, indicated by the loss of ellipticity, typical for deformation localization bands. The relation between the microscopic softening on inter-granular boundaries and the onset of macro-instabilities is studied through numerical examples. The influence of the cohesive law and friction parameters is analyzed. For periodic distributions of granular structures, we prove the loss of periodicity by failure and the corresponding size dependence effect in the homogenized response. We present numerical examples of bifurcation of solutions for granular cell structures and of particular solutions specific to elementary volumes with periodic cell distribution. Size dependence appears in the unstable regime and is strongly influenced by cohesion and friction parameters.

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References

  1. Caillerie D (2002) Modeling by homogeneization of the saturated porous medium consolidation under large transformations. In: Auriault JL et al (eds) Poromechanics II, second Biot conference on poromechanics. Org Balkema, Grenoble, pp 141–144

    Google Scholar 

  2. Dascalu C, Ionescu IR, Campillo M (2000) Fault finiteness and initiation of dynamic shear instability. Earth Planet Sci Lett 177:163–176

    Article  Google Scholar 

  3. Geers MGD, Kouznetsova VG, Brekelmans WAM (2003) Multi-scale first-order and second-order computational homogenization of microstructures towards continua. Int J Multiscale Comput Eng 1:371–386

    Article  Google Scholar 

  4. Knowles JK, Sternberg E (1977) On the failure of ellipticity of the equations for finite elastostatic plane strain. Arch Rat Mech Anal 63:321–336

    Article  MATH  MathSciNet  Google Scholar 

  5. Kouznetsova V, Geers MGD, Brekelmans WAM (2002) Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. Int J Numer Methods Eng 54:1235–1260

    Article  MATH  Google Scholar 

  6. Matlab users guide, The Mathworks, Inc (2004)

  7. Miehe C (2003) Computational micro-to-macro transition for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy. Comput Methods Appl Mech Eng 192:559–591

    Article  MATH  MathSciNet  Google Scholar 

  8. Miehe C, Schroder J, Becker M (2002) Computational homogenization analysis in finite elasticity: material and structural instabilities on micro- and macro-scale of periodic composites and their interaction. Comput Methods Appl Mech Eng 191:4971–5005

    Article  MATH  MathSciNet  Google Scholar 

  9. Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44:1267

    Article  MATH  Google Scholar 

  10. Pruchnicki E (1998) Hyperelastic homogenized law for reinforced elastomer at finite strain with edge effects. Acta Mechanica 129:139–162

    Article  MATH  MathSciNet  Google Scholar 

  11. Rice JR (1976) The localization of plastic deformation. In: Koiter WT (ed) Theoretical and applied mechanics. North-Holland, Amsterdam, pp 207–220

    Google Scholar 

  12. Tvergaard V (2003) Cohesive zone representations of failure between elastic or rigid solids and ductile solids. Eng Fract Mech 70:1859–1868

    Article  Google Scholar 

  13. Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42:1397–1434

    Article  MATH  Google Scholar 

  14. Yang B, Ravi-Chandar K (1998) A single-domain dual-boundary-element formulation incorporating a cohesive zone model for elastostatic cracks. Int J Fract 93:115–144

    Article  Google Scholar 

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Authors and Affiliations

  1. Laboratoire 3S-R, UJF, INPG, CNRS UMR 5521, BP 53, 38041, Grenoble cedex 9, France

    Gabriela Bilbie, Cristian Dascalu, Rene Chambon & Denis Caillerie

Authors
  1. Gabriela Bilbie
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  2. Cristian Dascalu
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  3. Rene Chambon
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  4. Denis Caillerie
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Correspondence to Cristian Dascalu.

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Bilbie, G., Dascalu, C., Chambon, R. et al. Micro-fracture instabilities in granular solids. Acta Geotech. 3, 25–35 (2008). https://doi.org/10.1007/s11440-007-0046-8

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  • DOI: https://doi.org/10.1007/s11440-007-0046-8

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