Periodic Graph Metamaterials Atlas

Data access

The catalog is distributed as a single static file. To use it programmatically:

import json, urllib.request
url = 'atlas.json'  # or full URL once hosted publicly
with urllib.request.urlopen(url) as f:
    atlas = json.load(f)

print(f"{atlas['metadata']['n_grounds']} grounds in version "
      f"{atlas['metadata'].get('version', 'unknown')}")

# Each ground is a dict with mechanical + dynamical + humidity fields
for g in atlas['grounds']:
    nu_min = g['beam']['nu_min'][1]   # AR=10 default
    eta_pore = g['humidity']['eta_pore']
    if nu_min < -2 and eta_pore < -0.3:
        print(g['family'], g['name'], nu_min, eta_pore)

For users who prefer a flat tabular form, a companion atlas_features.csv with one row per ground is provided alongside the JSON.

See the data dictionary below for field meanings and units.

Data dictionary

Every field in atlas.json. All quantities are dimensionless except where noted.

Metadata (atlas['metadata'])

Per-ground top-level fields (atlas['grounds'][i])

Manufacturability (g['manufacturability'])

Per-ground boolean predicates classifying the lattice's physical realizability. Each property is one of: true, false, or null (= "not yet checked").

For grounds in Irvine's TesseLace catalog, all four properties are known to be true by construction. Grounds added by the enumerator have these properties computed individually.

Provenance (g['provenance'])

Where the ground came from.

Mechanics: spring model (g['spring'])

The spring model (also referred to as the pin-jointed truss model, or central-force lattice model) treats each strut as an axial Hookean spring with stiffness k = 1 per unit length and frictionless pin joints at every vertex. To this base model we add a small angular regularization term kang at each vertex that penalizes changes in the angle between rods meeting there:

Uangular = (kang / 2) Σ (θij − θij(0))2

The angular term lifts mechanism-mode eigenvalues away from zero so the stiffness matrix is invertible. Mechanism modes are kinematic deformations that change vertex positions without stretching any rod — they are central to auxetic behavior in this catalog. We sweep kang over spring_k_ang_grid (with axial stiffness fixed at 1) to characterize the sensitivity of the elastic response to this regularization. The default reported value is kang = 0.01, where angular stiffness is 1% of axial: mechanism modes remain soft but the calculation is well-conditioned.

The spring model is distinct from the beam model below: spring uses pin joints with adjustable angular regularization, beam uses rigid Euler-Bernoulli joints with bending stiffness set by the strut aspect ratio. Each field below is a list, one entry per value in spring_k_ang_grid.

Mechanics: beam model (g['beam'])

Same shape as the spring model but indexed by strut aspect ratio.

Phonon dispersion (g['phonon'])

Spring-model phonon dispersion (k_ang = 0.01) sampled on a Brillouin-zone path. 22 scalar descriptors summarize the dispersion.

Humidity / swelling response (g['humidity'])

Macroscopic strain ε per unit perpendicular swelling δ on each strut (fiber-grain model: water swells perpendicular to strut axis, not along it).