Tune particles and contact laws for stable integration. Compare forces, damping, and time steps, then export summaries fast online. Ideal for granular powder studies.
| Scenario | Radius (m) | Density (kg/m³) | kn (N/m) | e | μ | dt (s) | Expected note |
|---|---|---|---|---|---|---|---|
| Dry sand, moderate stiffness | 0.005 | 2650 | 1.0e5 | 0.4 | 0.6 | 1.0e-5 | Stable dt; friction cap often activates. |
| Soft pellets, high damping | 0.010 | 1100 | 2.0e4 | 0.2 | 0.4 | 5.0e-5 | Large dt possible; forces are smaller. |
| Stiff grains, low damping | 0.003 | 7800 | 5.0e5 | 0.8 | 0.3 | 2.0e-6 | Small dt recommended; contact oscillations strong. |
Discrete element models evolve particle motion using Newton’s law:
m d²x/dt² = Σ(Fn + Ft) + m g
For a linear spring–dashpot normal contact (no cohesion):
Fn = kn δn − cn vn, Fn ≥ 0
Tangential force is trialed, then limited by Coulomb friction:
|Ft| = min(|kt δt − ct vt|, μ|Fn|)
Damping is linked to restitution e using a common linear mapping:
η = −ln(e) / √(π² + ln(e)²), cn = 2 η √(kn meff)
A pragmatic stable time step estimate uses the contact oscillation scale:
dtcrit ≈ π/ωd, dtrec = safety × dtcrit
Discrete Element Method represents bulk solids as many interacting particles. It is used for sand, powders, pellets, ballast, and ore. Engineers track motion, contacts, and energy dissipation to predict flow, segregation, and impact loads in equipment.
Density and radius control inertia and collision energy. For quartz sand, density is about 2600 kg/m³, while polymer pellets are often 900–1200 kg/m³. A radius change from 3 mm to 10 mm increases particle mass by almost 37×, strongly affecting stable time steps.
In linear contacts, the normal force follows Fn=knδn. Typical kn values span 10⁴–10⁶ N/m for “soft-sphere” studies. If δn=10 µm and kn=10⁵ N/m, the elastic term alone gives 1 N before damping.
Restitution e encodes impact losses. Common laboratory values are e≈0.2–0.6 for damped grains and e≈0.7–0.9 for harder, cleaner impacts. The calculator converts e to a damping ratio and computes cn so that higher e reduces damping.
Tangential stiffness is often set as kt/kn=0.2–0.8. Sliding is limited by |Ft|≤μ|Fn|. In chute flow, μ values of 0.3–0.7 are common; higher μ increases shear strength but can amplify numerical stiffness.
Explicit DEM needs dt well below the contact oscillation period. A conservative rule is dt≈0.1–0.3 of the estimated critical step. Increasing kn by 10× raises ω and can reduce dt by about √10, so stiffness “speedups” must be justified.
For many granular benchmarks, dt values fall between 1e-6 and 5e-5 s when radii are millimeters. Always verify by monitoring peak overlap and kinetic energy; both should remain bounded without artificial heating during steady operating conditions.
Packing fraction φ compares total particle volume to the box volume. Random loose packing for spheres is roughly 0.55–0.58, while random close packing is near 0.64. If φ exceeds 0.64 without compaction physics, your particle count or domain size is inconsistent.
Professional DEM work documents units, contact law, integrator, and dt. Exported CSV and PDF summaries support peer review and troubleshooting. Record calibration sources, such as drop tests for e and shear tests for μ, then validate against a measurable bulk response.
It estimates particle mass, contact damping from restitution, approximate normal and tangential forces, and conservative time-step guidance. It does not integrate trajectories, handle neighbor search, or model complex boundaries; use it to sanity-check parameters before running a solver.
Choose kₙ to keep overlaps small relative to radius, often below 0.1–1% for soft-sphere models. Start from expected load scales, compare δ≈F/kₙ, and tune with calibration tests or published benchmarks for similar particles.
Contact oscillation frequency scales roughly with √(kₙ/meff). Larger kₙ increases ω, shrinking the period that explicit integration must resolve. If you raise kₙ by 10×, a safe dt often drops by about √10, all else equal.
The tool uses a common linear spring–dashpot mapping: η = −ln(e)/√(π²+ln(e)²), then cn = 2η√(knmeff). Lower e yields higher damping and reduces rebound, which changes force histories and collision energy loss.
When the trial tangential force exceeds μ|Fn|, the model limits sliding to Coulomb friction. Higher μ raises the cap and can increase shear resistance. If Fn becomes small, the cap tightens and Ft quickly saturates.
Use the unit system that matches your source data. The calculator converts CGS (cm, g/cm³, dyn/cm) into SI internally for computation. Keep units consistent across radius, stiffness, velocity, and gravity to avoid misleading forces.
Monitor maximum overlap, contact force spikes, and total kinetic energy. With stable dt, overlaps remain bounded and energy does not drift upward without input. Run a short benchmark, then reduce dt by 2× to confirm results change minimally.
Calibrate wisely, validate often, and document every simulation decision.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.