Irregular Deformable Cluster DEM

An irregular deformable particle can be represented as a cluster of interacting constituent particles. The cluster geometry captures a non-circular or otherwise irregular outline, while relative motion among its constituents allows the aggregate to deform. If internal bonds soften or fail, the particle can also fragment. This differs from a rigid clump, whose constituents retain fixed relative positions and whose overall shape cannot change.

OpenFDEM’s project description identifies realistic particles as rigid or deformable, notes overlapping-particle and Fourier-Voronoi-based shape generation, and states that particle breakage is possible. The bonded-cluster equations below are a general theoretical description; the exact internal representation, bond law, and breakage criterion depend on the selected model.

Cluster kinematics and force balance

For a cluster with constituent particles \(a=1,\ldots,N_c\), each constituent obeys its own translational and rotational balances,

\[m_a\dot{\mathbf{v}}_a =\sum_{b}\mathbf{F}_{ab}^{\mathrm{int}} +\sum_{c}\mathbf{F}_{ac}^{\mathrm{ext}} +m_a\mathbf{g},\]

\[\mathbf{I}_a\dot{\boldsymbol{\omega}}_a +\boldsymbol{\omega}_a\times (\mathbf{I}_a\boldsymbol{\omega}_a) =\sum_b\mathbf{M}_{ab}^{\mathrm{int}} +\sum_c\mathbf{M}_{ac}^{\mathrm{ext}},\]

where \(\mathbf{F}^{\mathrm{int}}\) and \(\mathbf{M}^{\mathrm{int}}\) are forces and moments transmitted by internal contacts or bonds, while the external terms arise from other particles, boundaries, and applied loads. If all internal bonds remain intact and infinitely stiff, relative constituent motion is suppressed and the cluster approaches rigid-clump behavior. Finite bond stiffness permits deformation; bond damage or failure permits irreversible shape change and fragmentation.

Internal bond response and breakage

A simple bonded-contact idealization relates the local normal and tangential relative displacements \(\delta_n\) and \(\boldsymbol{\delta}_t\) to trial bond forces through

\[F_n^{\mathrm{trial}}=k_n^b\delta_n, \qquad \mathbf{F}_t^{\mathrm{trial}}=k_t^b\boldsymbol{\delta}_t,\]

where \(k_n^b\) and \(k_t^b\) are bond stiffnesses. A chosen strength criterion may trigger damage when the normal or shear traction reaches its corresponding tensile or shear capacity. After damage, the transmitted force is reduced according to the selected softening law; after complete failure, the interface no longer carries cohesive tension or shear, although ordinary compressive contact and friction may remain. These equations illustrate the mechanism and are not a claim about one specific OpenFDEM bond implementation.

Macroscopic response and calibration

The response of an irregular cluster assembly emerges from both external particle contacts and internal deformation. Cluster geometry affects packing, contact orientation, and interlocking; constituent size and bond properties affect the effective stiffness, strength, and breakage pattern. Resolution should be adequate to represent the target particle shape and expected deformation modes. Calibration should consider bulk observables such as packing density, stress-strain response, peak strength, dilation, and fragment size distribution, rather than fitting only individual bond parameters.

This cluster approach provides a mesoscale compromise: it can represent particle-scale deformation and breakage without resolving a continuum mesh inside every grain. Predictions remain dependent on the chosen cluster discretization, contact law, bond law, and numerical time step.