The role of microstructure in the incremental behavior of granular materials V. Magnanimo, N. Kumar and S. Luding MSM - University of Twente (NL)

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Presentation transcript:

The role of microstructure in the incremental behavior of granular materials V. Magnanimo, N. Kumar and S. Luding MSM - University of Twente (NL)

We observe the (often disastrous) MACROSCOPIC behavior and we want to model it …. ….how is this related with the MICROSCOPIC structure?

Evolution of microstructure [Behringer (Duke)] Evolution of the microstructure

Inhomogeneity & anisotropy, instabilities & structures, rotations [Luding (UT)] Evolution of microstructure

Material idealization

Experimental background

Yang, Li and Yang (2008) Geotechnique 58(4) Triaxial compression samples prepared with: dry deposition moist tamping

ISOTROPIC SYSTEM

Numerical protocol

Coordination number: HISTORY of the sample Magnanimo et al. (2008) EPL

Elastic moduli We apply (  = inf) an incremental strain  ij and measure the variation in stress  ij after relaxation Calvetti et al. (2003) Rivista Italiana di Geotecnica 3 Magnanimo et al. (2008) EPL Sibille et al. (2009) EJECE 13(2)

Amplitude of the increment

Elastic moduli dependence on microstructure G/B Magnanimo et al. (2008) EPL

Theoretical model with anisotropy

Luding and Perdahcioglu CIT (2011), Magnanimo and Luding, Granular Matter (2011) Simple constitutive model

ANISOTROPIC SYSTEM undrained biaxial test

O.I. Imole et al. KONA (2013), Kumar et al. Acta Mechanica (under review) Shear Stress Evolution of stress and fabric Deviatoric fabric  dev =√3 J 2  F dev =√3 J 2 Fc definition of fabric

We apply purely deviatoric perturbations along the path Elastic moduli

Incremental elastic behavior

Small enough before any local rearrangement happens How small is small?

Bulk modulus

Anisotropy modulus

Shear modulus

Theoretical prediction undrained cyclic biaxial test

Incremental elastic behavior

F dev =√3 J 2 Fc

Luding and Perdahcioglu CIT (2011), Magnanimo and Luding, Granular Matter (2011) Simple constitutive model

Initial state: isotropic volume fraction Shear Stress Deviatoric Fabric Undrained biaxial test: calibration

Undrained CYCLIC biaxial test: prediction Initial state: isotropic volume fraction Shear Stress Deviatoric Fabric

Isobaric compression

Conclusions We analyzed the incremental behavior of isotropic granular samples and we linked is with the coordination number We analyzed the incremental behavior of anisotropic granular samples and we linked is with volumetric and deviatoric fabric When a simple constitutive model with evolution equation for fabric is introduced and calibrated with the moduli cyclic shear can be predicted

Thank you