DOI: 10.5281/zenodo.59217
title: Contact Changes In Shear-Stabilized Jammed Packings

description: 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.

<strong>Particle interactions</strong>

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 

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

 

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.

<strong>Data files</strong>

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 <em>a subset</em> 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']
		
			<em>gamma_min is used as contact change strain</em>
		
		
		Number of created/broken contacts ['N+_plus', 'N+_min', 'N-_plus', 'N-_min']
		Number of changed contacts (=N<sup>+</sup> + N<sup>-</sup>) ['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. <em>Soft-Sphere Packings at Finite Pressure but Unstable to Shear. </em>Phys. Rev. Lett. <strong>109</strong>, 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. <em>Contact changes near jamming</em>. Phys. Rev. E <strong>90</strong> 020202(R). http://dx.doi.org/10.1103/PhysRevE.90.020202

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

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