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Short note: Discrete element method

Short answer

DEM, introduced by Cundall, models material as separate particles or blocks interacting through contacts. It computes contact forces from force-displacement laws and integrates Newton's second law explicitly, handling large displacements and discontinuities naturally. It is computationally expensive and contact parameters need calibration, but suits granular soils, jointed rock and rockfall.

Write a short note on the discrete element method.

The discrete element method (DEM), introduced by Cundall (1971), models a material as an assembly of separate rigid or deformable blocks or particles that interact at contacts. It is suited to discontinua where displacement and rotation are large and contacts open and close.

Working

  1. Define the particles/blocks and their initial positions.
  2. Detect contacts between neighbours.
  3. Compute contact forces from a force-displacement law, for example normal force Fn=kn δnF_n=k_n\,\delta_n and a friction-limited shear force.
  4. Sum forces on each particle and apply Newton's second law mx¨=∑Fm\ddot{x}=\sum F.
  5. Integrate in time with an explicit scheme, update positions and repeat (the time step must be small).

Advantages: handles fracture, sliding, rotation and large displacements naturally; no continuity assumption.

Disadvantages: computationally expensive; contact parameters (stiffness, friction, damping) need calibration.

Applications: granular soils and silo flow, jointed rock slopes, masonry and rockfill, landslides and rockfall.

✓ Answer checked by Claude Opus 5.5 (high effort)

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