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Strength, dilatancy, energy and dissipation in quasi-static deformation of granular materials N.P. Kruyt Department of Mechanical Engineering University.

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Presentation on theme: "Strength, dilatancy, energy and dissipation in quasi-static deformation of granular materials N.P. Kruyt Department of Mechanical Engineering University."— Presentation transcript:

1 Strength, dilatancy, energy and dissipation in quasi-static deformation of granular materials N.P. Kruyt Department of Mechanical Engineering University of Twente, The Netherlands L. Rothenburg Department of Civil Engineering University of Waterloo, Canada

2 Objective Relation interparticle friction and macroscopic behaviour: shear strength dilatancy energy dissipation

3 DEM simulations two-dimensional biaxial tests various friction coefficients periodic boundary conditions 50,000 disks dense and loose initial assembly Invariants :

4 Contact constitutive relation Special cases: ktkt knkn

5 Shear strength and dilatancy Increasing Shear strengthDilatancy

6 Plastic strains: unloading paths

7 Dilatancy rate Formulated in plastic strains

8 Strength at peak & steady-state, dilatancy rate at peak strength

9 Strength-dilatancy relation

10 Energy

11 Dissipation Dissipation Work input Change in energy

12 Dissipation Dissipation Work input Change in energy

13 Dissipation function Work input dissipated: Strength-dilatancy: Resulting dissipation function:

14 Conclusions For all (including and macroscopic frictional behaviour Macroscopic dissipation even for and Strength-dilatancy relation Constant ratio of tangential over normal energy beyond initial range All work input is dissipated beyond initial range

15 Discussion Origin of macroscopic frictional behaviour: Interparticle friction: NO Contact disruption and creation: POSSIBLY Origin of dissipation if 0 or Dynamics & viscous dissipation Microscopic viscous dissipation macroscopic plastic dissipation [Puglisi & Truskinovsky, JMPS ]

16 Questions and comments Thank you for your attention! Questions and comments? Presentation can be downloaded from:


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