July 31, 2016 Dataset Open Access

Contact changes in shear-stabilized jammed packings

Simon Dagois-Bohy; Silke Henkes; Johannes Simon; Brian P. Tighe; Merlijn S. van Deen; Martin van Hecke; Zorana Zeravcic

Authors are listed in alphabetical order.

This data set contains the result of small simple shear deformations applied to approximately 140,000 shear-stabilized jammed packings (see [...]), focusing on contact changes, as described in [1,2,3,4].

These packings contain \(N = 16 \ldots 4096\) particles with harmonic interactions, under a confining pressure  \(p=10^{-7}\ldots10^{-2}\). Ensemble sizes range from 10 (N=4096) to 5000 (N=16). 

In addition, a data file summarizing properties of the first contact change for each packing is provided.

Particle interactions

The simulation code minimizes the enthalpy

\(H = \sum_{} \frac{k}{2} \delta_{ij}^2 + pL^2\)

where L² is the simulation box area, p the externally applied pressure, k=1 the spring constant and 

\(\delta_{ij} = \left\{ \begin{array}{ll} R_i + R_j - |\vec{r_{ij}}| & \textrm{if } |\vec{r_{ij}}| < R_i + R_j, \\ 0 & \textrm{otherwise.} \end{array}\right.\)

During shear, the boundary conditions are changed, and the system is relaxed to the new state. The simulation uses a bisection algorithm to efficiently step towards each subsequent contact change; see [3,4] for details.

Data files

The packings are stored in HDF5 data files. For each ensemble, we provide two files: one with and one without particle positions:

• N1024~P3162e-3_shear_noparticles.h5 includes all simulation data, but omits particle positions (see below for which data is included).
• For small data sets, N1024~P3162e-3_shear.h5 contains all simulations and all particle positions
• For large data sets, N1024~P3162e-3_shear_partial.h5 contains a subset of all simulations, but with all particle positions.
• Full particle positions for all simulations are available upon request to the authors. Please contact Martin van Hecke .

All files follow the same HDF5 layout:

• Example name: N1024~P3162e-3_shear.h5 and N1024~P3162e-3_shear_noparticles.h5
  • Packings with \(N=1024\) particles
  • Pressure \(p = 3.162\cdot 10^{-3}\)
• Packings are stored in a directory structure, e.g. /N1024/P3.1620e-03/0090/SR for the packing with id 0090.
  • ​This directory contains a table 'data' indicating system parameters for each simulation step:
    • boundary conditions L1 and L2 (also as L, alpha, delta)
    • pressure P,
    • strain gamma,
    • stresses s_xy (simple shear), s_xx and s_yy, 
    • number of contacts Ncontacts, contact number Z and number of rattlers #rattler
    • number of changed contacts for this contact change bisection Nchanges, N+ (created), N- (broken)
    • contact number Z
    • energy U, enthalpy H and their change in the last relaxation step (dU, dH)
    • step runtime t_run (seconds), #CG, #FIRE (number of conjugate gradient and FIRE iterations)
    • path to the packing corresponding to this state (does not always exist for each state for older simulations)
  • Each state is saved in /N1024/P3.1620e-03/0090/SR/0000 (initial), /N1024/P3.1620e-03/0090/SR/0001, ...etc.
    • States are not included in the _noparticles.h5 files
    • Some files omit intermediate positions, and only store positions just before and just after a contact change.
    • The format of these directories is the same as in https://dx.doi.org/10.5281/zenodo.59216.

Finally, we provide a summary file (shear_summary_cache.h5) which contains one table ('data') with properties of the first contact change of all packings. We provide the following columns:

• The variable postfix determines whether the value was calculated in the initial state (_base), just before the first contact change (_min) or just after the first contact change (_plus).

• General/simulation properties
  • Number of particles 'N'
  • Random seed ['num', 'PackingNumber_base']
  • External pressure 'P0_base'
  • Simulation step ['i_min', 'i_plus']
• Relaxation statistics
  • Last change in enthalpy during relaxation ['dH_base', 'dH_plus', 'dH_min']
  • Last change in energy during relaxation ['dU_base', 'dU_plus', 'dU_min']
  • Maximum gradient ['maxGrad_base', 'gg_min', 'gg_plus']
  • Initial simulation runtime ['runtime (s)_base']
• State properties
  • Number of rattlers 'N - Ncorrected_base'
  • Number of non-rattler particles ['Neff_min', 'Neff_plus']
  • Number of contacts ['Ncontacts_plus', 'Ncontacts_min']
  • Contact number z ['Z_base', 'Z_min', 'Z_plus']
  • Internal pressure ['P', 'P_base', 'P_min', 'P_plus']
  • Mean overlap δ ['mean_delta_base']
  • Packing fraction ['phi_base', 'phi_min', 'phi_plus']
  • Enthalpy ['H_base', 'H_plus', 'H_min']
  • Energy ['Uhelper_base', 'U_min', 'U_plus']
  • Simple shear parameter alpha ['alpha_base', 'alpha_min', 'alpha_plus']
  • Pure shear parameter delta ['delta_base', 'delta_plus', 'delta_min']
  • Square root of area ['L_base', 'L_min', 'L_plus']
  • Stresses on boundaries:
    • xx  ['sxx_base', 's_xx_min', 's_xx_plus',]
    • yy  [ 'syy_base', 's_yy_plus', 's_yy_min',]
    • xy ['sxy_base', 's_xy_plus', 's_xy_min']
  • Elastic moduli:
    •  ['c1_base', 'c1_min', 'c1_plus',
    • 'c2_base', 'c2_min', 'c2_plus',
    • 'c3_base', 'c3_min', 'c3_plus',
    • 'c4_base', 'c4_plus', 'c4_min',
    • 'c5_base', 'c5_plus', 'c5_min',
    • 'c6_base', 'c6_min', 'c6_plus',
    • 'Dac_base', 'Dac_plus', 'Dac_min',
  • AC component of G(θ) ['Gac_base', 'Gac_min', 'Gac_plus']
  • DC component of G(θ) ['Gdc_base', 'Gdc_min', 'Gdc_plus',]
  • AC component of U(θ) ['Uac_base', 'Uac_plus', 'Uac_min']
  • DC component of U(θ) ['Udc_base', 'Udc_plus', 'Udc_min']
  • Simple shear ['Galpha_base', 'Galpha_plus', 'Galpha_min' ]
• Contact change properties
  • Applied strain gamma ['gamma_plus', 'gamma_min']
    • gamma_min is used as contact change strain
  • Number of created/broken contacts ['N+_plus', 'N+_min', 'N-_plus', 'N-_min']
  • Number of changed contacts (=N⁺ + N^-) ['Nchanges_plus', 'Nchanges_min']
  • Making & breaking strain from upar and uperp:
    • simple linear (SL) solution: ['gmk_SL_base', 'gbk_SL_base']
    • full quadratic (FQ) solution: ['gmk_FQ_base' 'gbk_FQ_base']
  • G up to CC from fit σ=Gγ & error bar ['Glin', 'Glinerr']
  • G up to CC from fit σ=Gγ + λγ² & error bar ['Gquad', 'Gquaderr']
  • λ up to CC from fit σ=Gγ + λγ² & error bar ['lambdaquad', 'lambdaquaderr']

[1] Simon Dagois-Bohy, Brian P. Tighe, Johannes Simon, Silke Henkes, and Martin van Hecke. Soft-Sphere Packings at Finite Pressure but Unstable to Shear. Phys. Rev. Lett. 109, 095703. http://dx.doi.org/10.1103/PhysRevLett.109.095703

[2] Merlijn S. van Deen, Johannes Simon, Zorana Zeravcic, Simon Dagois-Bohy, Brian P. Tighe, and Martin van Hecke. Contact changes near jamming. Phys. Rev. E 90 020202(R). http://dx.doi.org/10.1103/PhysRevE.90.020202

[3] Merlijn S. van Deen, Brian P. Tighe, and Martin van Hecke. Contact Changes of Sheared Systems: Scaling, Correlations, and Mechanisms. arXiv:1606.04799. https://arxiv.org/abs/1606.04799

[4] Merlijn S. van Deen. Mechanical Response of Foams: Elasticity, Plasticity, and Rearrangements. PhD Thesis, Leiden University, 2016. https://openaccess.leidenuniv.nl/handle/1887/40902