Contact changes in shear-stabilized jammed packings
<p>Authors are listed in alphabetical order.</p> <p>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].</p> <p>These packings contain <span class="math-tex">\(N = 16 \ldots 4096\)</span> particles with harmonic interactions, under a confining pressure <span class="math-tex">\(p=10^{-7}\ldots10^{-2}\)</span>. Ensemble sizes range from 10 (N=4096) to 5000 (N=16). </p> <p>In addition, a data file summarizing properties of the first contact change for each packing is provided.</p> <p><strong>Particle interactions</strong></p> <p>The simulation code minimizes the enthalpy</p> <p><span class="math-tex">\(H = \sum_{} \frac{k}{2} \delta_{ij}^2 + pL^2\)</span></p> <p>where L² is the simulation box area, p the externally applied pressure, k=1 the spring constant and </p> <p><span class="math-tex">\(\delta_{ij} = \left\{ \begin{array}{ll} R_i + R_j - |\vec{r_{ij}}| & \textrm{if } |\vec{r_{ij}}| < R_i + R_j, \\ 0 & \textrm{otherwise.} \end{array}\right.\)</span></p> <p> </p> <p>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.</p> <p><strong>Data files</strong></p> <p>The packings are stored in HDF5 data files. For each ensemble, we provide two files: one with and one without particle positions:</p> <ul> <li>N1024~P3162e-3_shear_noparticles.h5 includes all simulation data, but omits particle positions (see below for which data is included).</li> <li>For small data sets, N1024~P3162e-3_shear.h5 contains all simulations and all particle positions</li> <li>For large data sets, N1024~P3162e-3_shear_partial.h5 contains <em>a subset</em> of all simulations, but with all particle positions.</li> <li>Full particle positions for all simulations are available upon request to the authors. Please contact Martin van Hecke .</li> </ul> <p>All files follow the same HDF5 layout:</p> <ul> <li>Example name: N1024~P3162e-3_shear.h5 and N1024~P3162e-3_shear_noparticles.h5 <ul> <li>Packings with <span class="math-tex">\(N=1024\)</span> particles</li> <li>Pressure <span class="math-tex">\(p = 3.162\cdot 10^{-3}\)</span></li> </ul> </li> <li>Packings are stored in a directory structure, e.g. /N1024/P3.1620e-03/0090/SR for the packing with id 0090. <ul> <li>This directory contains a table 'data' indicating system parameters for each simulation step: <ul> <li>boundary conditions L1 and L2 (also as L, alpha, delta)</li> <li>pressure P,</li> <li>strain gamma,</li> <li>stresses s_xy (simple shear), s_xx and s_yy, </li> <li>number of contacts Ncontacts, contact number Z and number of rattlers #rattler</li> <li>number of changed contacts for this contact change bisection Nchanges, N+ (created), N- (broken)</li> <li>contact number Z</li> <li>energy U, enthalpy H and their change in the last relaxation step (dU, dH)</li> <li>step runtime t_run (seconds), #CG, #FIRE (number of conjugate gradient and FIRE iterations)</li> <li>path to the packing corresponding to this state (does not always exist for each state for older simulations)</li> </ul> </li> <li>Each state is saved in /N1024/P3.1620e-03/0090/SR/0000 (initial), /N1024/P3.1620e-03/0090/SR/0001, ...etc. <ul> <li>States are not included in the _noparticles.h5 files</li> <li>Some files omit intermediate positions, and only store positions just before and just after a contact change.</li> <li>The format of these directories is the same as in https://dx.doi.org/10.5281/zenodo.59216.</li> </ul> </li> </ul> </li> </ul> <p>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:</p> <ul> <li>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).</li> </ul> <p> </p> <ul> <li>General/simulation properties <ul> <li>Number of particles 'N'</li> <li>Random seed ['num', 'PackingNumber_base']</li> <li>External pressure 'P0_base'</li> <li>Simulation step ['i_min', 'i_plus']</li> </ul> </li> <li>Relaxation statistics <ul> <li>Last change in enthalpy during relaxation ['dH_base', 'dH_plus', 'dH_min']</li> <li>Last change in energy during relaxation ['dU_base', 'dU_plus', 'dU_min']</li> <li>Maximum gradient ['maxGrad_base', 'gg_min', 'gg_plus']</li> <li>Initial simulation runtime ['runtime (s)_base']</li> </ul> </li> <li>State properties <ul> <li>Number of rattlers 'N - Ncorrected_base'</li> <li>Number of non-rattler particles ['Neff_min', 'Neff_plus']</li> <li>Number of contacts ['Ncontacts_plus', 'Ncontacts_min']</li> <li>Contact number z ['Z_base', 'Z_min', 'Z_plus']</li> <li>Internal pressure ['P', 'P_base', 'P_min', 'P_plus']</li> <li>Mean overlap δ ['mean_delta_base']</li> <li>Packing fraction ['phi_base', 'phi_min', 'phi_plus']</li> <li>Enthalpy ['H_base', 'H_plus', 'H_min']</li> <li>Energy ['Uhelper_base', 'U_min', 'U_plus']</li> <li>Simple shear parameter alpha ['alpha_base', 'alpha_min', 'alpha_plus']</li> <li>Pure shear parameter delta ['delta_base', 'delta_plus', 'delta_min']</li> <li>Square root of area ['L_base', 'L_min', 'L_plus']</li> <li>Stresses on boundaries: <ul> <li>xx ['sxx_base', 's_xx_min', 's_xx_plus',]</li> <li>yy [ 'syy_base', 's_yy_plus', 's_yy_min',]</li> <li>xy ['sxy_base', 's_xy_plus', 's_xy_min']</li> </ul> </li> <li>Elastic moduli: <ul> <li> ['c1_base', 'c1_min', 'c1_plus',</li> <li>'c2_base', 'c2_min', 'c2_plus',</li> <li>'c3_base', 'c3_min', 'c3_plus',</li> <li>'c4_base', 'c4_plus', 'c4_min',</li> <li>'c5_base', 'c5_plus', 'c5_min',</li> <li>'c6_base', 'c6_min', 'c6_plus',</li> <li>'Dac_base', 'Dac_plus', 'Dac_min',</li> </ul> </li> <li>AC component of G(θ) ['Gac_base', 'Gac_min', 'Gac_plus']</li> <li>DC component of G(θ) ['Gdc_base', 'Gdc_min', 'Gdc_plus',]</li> <li>AC component of U(θ) ['Uac_base', 'Uac_plus', 'Uac_min']</li> <li>DC component of U(θ) ['Udc_base', 'Udc_plus', 'Udc_min']</li> <li>Simple shear ['Galpha_base', 'Galpha_plus', 'Galpha_min' ]</li> </ul> </li> <li>Contact change properties <ul> <li>Applied strain gamma ['gamma_plus', 'gamma_min'] <ul> <li><em>gamma_min is used as contact change strain</em></li> </ul> </li> <li>Number of created/broken contacts ['N+_plus', 'N+_min', 'N-_plus', 'N-_min']</li> <li>Number of changed contacts (=N<sup>+</sup> + N<sup>-</sup>) ['Nchanges_plus', 'Nchanges_min']</li> <li>Making & breaking strain from upar and uperp: <ul> <li>simple linear (SL) solution: ['gmk_SL_base', 'gbk_SL_base']</li> <li>full quadratic (FQ) solution: ['gmk_FQ_base' 'gbk_FQ_base']</li> </ul> </li> <li>G up to CC from fit σ=Gγ & error bar ['Glin', 'Glinerr']</li> <li>G up to CC from fit σ=Gγ + λγ² & error bar ['Gquad', 'Gquaderr']</li> <li>λ up to CC from fit σ=Gγ + λγ² & error bar ['lambdaquad', 'lambdaquaderr']</li> </ul> </li> </ul> <p>[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</p> <p>[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</p> <p>[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</p> <p>[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</p>
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