1 / 13

Calibration of an Elastic-Plastic Material Model for Tire Shreds

Calibration of an Elastic-Plastic Material Model for Tire Shreds. Kallol Sett. Tire Shreds Material. Automobile tires shredded into pieces of sizes varying from long thin pieces (~ 30 cm X 5 cm X 0.8 cm) to massive rubber (~ 10 cm X 5 cm X 5 cm) to tire chips (~3 cm X 2 cm X 0.8 cm).

Download Presentation

Calibration of an Elastic-Plastic Material Model for Tire Shreds

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Calibration of an Elastic-Plastic Material Model for Tire Shreds Kallol Sett

  2. Tire Shreds Material • Automobile tires shredded into pieces of sizes varying from long thin pieces (~ 30 cm X 5 cm X 0.8 cm) to massive rubber (~ 10 cm X 5 cm X 5 cm) to tire chips (~3 cm X 2 cm X 0.8 cm). • Civil engineering applications is a growing market for scrap tires because of low unit weight, high permeability and good insulating properties. • Scrap tires has been successfully used as lightweight fill, insulation beneath road, lightweight backfill for retaining walls and overlay of underground ramps or storage space.

  3. 3 1 2 (1-2 is the plane of isotropy) Elastic Constitutive Law • The placement and compaction of tire shreds leads to a layered material and hence its elastic behavior can be best described by cross-anisotropic constitutive law. • Cross anisotropic material can be characterized by 5 independent material constants, E11, E33, G12, G13 and G31 (Drescher 1999)

  4. Wave Propagation and Governing Moduli 3 Wave propagation in the 1/2-direction with vertical polarization (Governing modulus G13) Wave propagation in the 3-direction with horizontal polarization (Governing modulus G31) Wave propagation in the 1/2-direction with horizontal polarization (Governing modulus G12) 1 2 Wave propagation in the 3-direction with polarization in the 3-direction (Governing modulus E33) Wave propagation in the 1/2-direction with polarization in the 1/2-direction (Governing modulus E11)

  5. 3 1 2 Elastic Constants • E11 = rVci2 (i = 1,2) • E33 = rVc32 • G12 = r (VsiH)2 (i = 1,2) • G31 = r (Vs3)2 • G13 = r (VsiV)2 (i = 1,2) • Redundant Constants: • n12 = (E11/2G12) -1 • n31 = (E33/2G31) -1 • n13 = (E11/2G13) -1

  6. Elastic-Plastic Constitutive Law Using Hooke’s law and additive decomposition of strain tensors in elastic and plastic parts (Jeremic and Sture 1997): Where, K = Bulk modulus G = Shear modulus f = Yield function

  7. Yield Function Salient features: • Based on Drucker-Prager yield surface, having fixed friction angle. • Yield surface has a shape of distorted (to model the cross anisotropy) and rotated (to model the Bauschinger effect) cone. • The plastic flow is assumed to be perpendicular to the yield surface.

  8. Principal Stress Space depij q p P- Plane a where, J2 = Second invariant of the deviatoric stress tensor I1 = First invariant of the hydrostatic stress tensor a and k = Drucker-Prager material constant • a can be related to the friction angle (f) as (Chen 1988),

  9. Elastic-Plastic Material Model The general form of Drucker-Prager elastic-perfectly plastic model is, which can be simplified to any direction of interest e.g. in 3-1 direction it reduces to: where

  10. Elastic-Plastic Material Model • Knowing E11, E33, n12, n31 (From wave propagation tests) and f = 20o (Tweedie et al. 1998) the elastic-plastic model was solved incrementally to get the stress-strain relationship in 3-1 direction. • Another important benefit of this model is that it represents the variation of G/Gmax which is usually found in traditional analysis of dynamics of soils.

  11. 1 t31 g31 3 Elastic Elastic-Plastic Predicted Elastic and Elastic-Plastic Stress-Strain Relationship

  12. 1 t31 g31 3 Elastic Elastic-Plastic Predicted Variation of Shear Modulus with strain

  13. Conclusions • 3-D P- and Shear- wave propagation tests can be used to determine 5 elastic constants necessary for modeling the behavior of cross-anisotropic tire shreds. 2. The data obtained from 3-D P- and Shear- wave propagation tests can be used to calibrate an elastic-plastic material model for the tire shreds. This model also represented the variation of G/Gmax, that is usually found in traditional analysis of dynamics of frictional media.

More Related