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Research Papers

Determining Material Parameters for Critical State Plasticity Models Based on Multilevel Extended Digital Database

[+] Author and Article Information
Yang Liu, Jacob Fish

Department of Civil Engineering
and Engineering Mechanics,
Columbia University,
New York, NY 10027

WaiChing Sun

Assistant Professor
Department of Civil Engineering
and Engineering Mechanics,
Columbia University,
New York, NY 10027
e-mail: wsun@columbia.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 10, 2015; final manuscript received September 15, 2015; published online October 15, 2015. Assoc. Editor: A. Amine Benzerga.

J. Appl. Mech 83(1), 011003 (Oct 15, 2015) (16 pages) Paper No: JAM-15-1423; doi: 10.1115/1.4031619 History: Received August 10, 2015; Revised September 15, 2015

This work presents a new staggered multilevel material identification procedure for phenomenological critical state plasticity models. The emphasis is placed on cases in which available experimental data and constraints are insufficient for calibration. The key idea is to create a secondary virtual experimental database from high-fidelity models, such as discrete element simulations, then merge both the actual experimental data and secondary database as an extended digital database (EDD) to determine material parameters for the phenomenological macroscopic critical state plasticity model. The calibration procedure therefore consists of two steps. First, the material parameters of the discrete (distinct) element method (DEM) simulations are identified via the standard optimization procedure. Then, the calibrated DEM simulations are used to expand the experimental database with new simulated loading histories. This expansion of database provides additional constraints necessary for calibration of the phenomenological critical state plasticity models. The robustness of the proposed material identification framework is demonstrated in the context of the Dafalias–Manzari plasticity model.

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Figures

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Fig. 1

The flowchart of the proposed multilevel material identification procedure using EDD and optimization

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Fig. 2

Contours of contact asperities (a) general power-form surface contour z = Aαrα [44]; (b) surface contour with different asperities used in DEM simulations (Reproduced with permission from Kuhn et al. [71]. Copyright 2014 by Matthew R. Kuhn, Professor, Dept. of Civil Engineering, Donald P. Shiley School of Engineering, Univ. of Portland, Portland, OR).

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Fig. 7

Undrained TC and extension of DEM simulations at three densities, comparing with Nevada sand tests (black dashed lines) at relative density of 60% with initial confining pressure of 40 kPa, 80 kPa, and 160 kPa (stress paths)

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Fig. 8

Undrained TC and extension of DEM simulations at three densities, comparing with Nevada sand tests (black dashed lines) at relative density of 60% with initial confining pressure of 160 kPa (stress–strain curves)

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Fig. 9

Drained TC (constant p′) of DEM simulation at e0 = 0.674, comparing with Nevada sand tests at relative density of 60% with initial confining pressure of 40 kPa, 80 kPa, and 160 kPa: (a) stress paths and (b) volumetric curves

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Fig. 10

Drained TC (constant p′) of DEM simulations at e0 = 0.640, comparing with Nevada sand tests at relative density of 60% with initial confining pressure of 40 kPa, 80 kPa, and 160 kPa: (a)stress paths and (b)volumetric curves

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Fig. 6

Drained TC (constant p′) of DEM simulations at e = 0.707, comparing with Nevada sand tests at relative density of 40% with initial confining pressure of 40 kPa, 80 kPa, and 160 kPa: (a) stress paths and (b) volumetric curves

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Fig. 15

DaMa model calibration for CTC tests on samples with different initial confining pressures (e0 = 0.640). (a) q versus axial strain and (b) void ratio versus mean effective stress.

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Fig. 16

DaMa model calibration for CTC tests on samples with different initial confining pressures (e0 = 0.550). (a) q versus axial strain and (b) void ratio versus mean effective stress.

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Fig. 5

Drained TC (constant p′) of DEM simulations at e = 0.732, comparing with Nevada sand tests at relative density of 40% with initial confining pressure of 40 kPa, 80 kPa, and 160 kPa: (a) stress paths and (b) volumetric curves

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Fig. 4

Undrained TC and extension of DEM simulations at three densities, comparing with Nevada sand tests (black dashed lines) at relative density of 40% with initial confining pressure of 160 kPa (stress–strain curves)

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Fig. 3

Undrained TC and extension of DEM simulations at three densities, comparing with Nevada sand tests (black dashed lines) at relative density of 40% with initial confining pressure of 40 kPa, 80 kPa, and 160 kPa (stress paths)

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Fig. 11

Application of major, intermediate and minor principal stresses, σ1, σ2, and σ3, to DEM assemblies in true triaxial tests to achieve all directions in the stress ratio π-plane (s1, s2, and s3 denote the deviatoric principal stresses) [81]

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Fig. 12

Calibrated critical state surface for DaMa model, and the loading paths of monotonic triaxial tests for DEM simulations and lab experiments [62] in the stress ratio π-plane (s1, s2, and s3 denote the deviatoric principal stresses)

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Fig. 13

DaMa model calibration for CTC tests on samples with different initial confining pressures (e0 = 0.783). (a) q versus axial strain and (b) void ratio versus mean effective stress.

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Fig. 14

DaMa model calibration for CTC tests on samples with different initial confining pressures (e0 = 0.746). (a) q versus axial strain and (b) void ratio versus mean effective stress.

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Fig. 18

Comparison between verification data and DaMa model prediction for: (a) and (b) drained monotonic CTC tests, and (c) and (d) undrained TC tests (experimental data in (c) are from Ref. [82])

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Fig. 19

Undrained cyclic SS test for Nevada sand: Dr = 40% and p0′ = 80 kPa: (a) experimental data from Ref. [62]; (b) Dafalias–Manzari model predictions

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Fig. 17

DaMa model calibration of q−p′ responses for monotonic undrained TC tests on samples with different initial confining pressures and densities

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