The heart of the problem is a mismatch of scales. The Discrete Element Method, or DEM, has become the workhorse of computational granular physics since its development by Peter Cundall in 1971 and its landmark extension with Otto Strack in 1979. DEM applies Newton’s second law of motion to the centre of every particle and a force-displacement law at every contact, computing the trajectory of each grain through time. Collisions are typically modelled as viscoelastic spring-dashpot systems, capturing both the repulsive force and the dissipated kinetic energy. Coupled with Computational Fluid Dynamics in the early 1990s, DEM-CFD can now simulate landslides, debris flows, pyroclastic currents, riverbed transport and industrial powder handling with remarkable fidelity. But what the simulations deliver is a torrent of particle-scale data: individual velocities, individual forces, individual contacts. Science and engineering, however, speak the language of continuum fields such as pressure, stress, strain rate and density.

Bridging that gap requires a mathematical procedure known as coarse-graining, a discrete-to-continuum transformation in which macroscopic fields emerge as spatially weighted averages of microscopic quantities. Each particle contributes to the field at a given point according to a weighting function that spreads its influence over a small volume, effectively smearing the point-like mass of the particle into a smooth density. Crucially, the method makes no assumption that particles are spherical or rigid, and it works across flow regimes from solid-like quasi-static behaviour to fluid-like rapid flow. The theoretical foundations trace back to Babic’s 1997 averaging framework for granular media, itself inspired by spatio-temporal weighted averaging in molecular dynamics, and have been refined over decades to handle boundaries, scale dependence and polydisperse mixtures.

Despite this maturity, the software ecosystem has lagged. Some DEM packages, such as LAMMPS and MercuryDPM, include built-in coarse-graining capabilities. Others, notably the open-source MFiX-DEM developed by the United States National Energy Technology Laboratory, do not, forcing users to write custom post-processing code or contort their simulation outputs to fit other tools. That fragmentation, the Edinburgh team argues, hampers reproducibility and invites error propagation. Pysammos, whose name nods to Archimedes’ The Sand Reckoner and his attempt to count the grains of sand that could fill the universe, was built to fill this void: a user-friendly, computationally efficient Python package that reads MFiX-DEM output directly and produces continuum fields ready for analysis and visualisation.

Technically, the package implements the full weighted-average machinery. It computes the mass density, momentum density and velocity fields, and it evaluates the stress tensor as the sum of a contact part and a kinetic part. Contact forces are distributed along the branch vector connecting two touching particles through a line integral of the weighting function, which Pysammos evaluates numerically with a trapezoidal rule that the authors show is already converged with just ten sampling points. Users can choose among three smoothing kernels: the Lucy polynomial, a cut-off Gaussian and a Heaviside step function. The authors recommend the Lucy function, because the Heaviside kernel weights all particles in the averaging volume equally and thereby amplifies edge effects, while the truncated Gaussian technically violates the differentiability required for the continuum balance equations to hold exactly.

The choice of smoothing width, the resolution at which the continuum fields are computed, turns out to be anything but trivial. The kinetic stress tensor is intrinsically dependent on the square of the averaging width, because it captures velocity gradients between a particle’s position and the evaluation point. Previous work has identified two length scales at which coarse-grained fields become nearly independent of the averaging width: one below the particle scale, which can resolve thin flow layers near boundaries, and one at the particle scale, which yields smooth fields. Pysammos adopts a default smoothing width of 0.75 times a representative particle diameter, but the team stresses that users should verify the stability of their results for their particular flow regime.

One of the package’s most distinctive features is its automated phase detection. In polydisperse mixtures, particles segregate by size and density through competing mechanisms known as kinetic sieving and buoyancy. Pysammos clusters the particle data by diameter and density using the k-means algorithm, selecting the optimal number of phases via silhouette analysis, and then computes partial continuum fields for each phase separately. Mixture theory then superposes these partial fields to recover the bulk behaviour. The team demonstrated this on a simulated granular pile confined between walls, revealing the classic stress-arching phenomenon: instead of the hydrostatic pressure maximum a fluid would show beneath the pile’s peak, the basal pressure exhibits a local minimum because force chains redirect the weight sideways toward the flanks.

The showcase applications span the geosciences. A bedload transport simulation of polydisperse, non-spherical grains under travelling water waves revealed bands of elevated shear rate and inertial number at the wave fronts, invisible in the raw contact network. A high-speed impact on a million-particle granular bed, relevant to cratering on asteroids and seismology alike, showed a downward-propagating shock wave and a friction coefficient exceeding the static value around the impact zone. A pseudo-2D simulation of crystals suspended in magma flowing through a conduit quantified how the effective shear viscosity varies with wall friction. And an erodible-bed experiment reproduced the classic Bagnold velocity profile, with granular temperature increasing toward the base where grains rattle against a rough floor.

Benchmarking against established coarse-graining software, including MercuryCG, EDEM’s continuum analysis, Granulysed and Iota-Suite, showed that Pysammos reproduces the expected fields, with results from its Gaussian and Lucy kernels coinciding closely with MercuryCG’s weighted averaging scheme. Performance tests on the ARCHER2 supercomputer showed that the cost per particle decreases sub-linearly with system size, meaning overheads are amortised and caches are used efficiently. Efficient execution does not demand massive parallel resources: at sub-particle resolution a couple of cores suffice, while large dense packings at coarser resolution benefit from four to sixteen cores. That makes the tool practical on ordinary desktop machines as well as high-performance clusters, lowering the barrier for research groups without dedicated computing infrastructure.

The team positions Pysammos as a contribution to a broader effort to standardise and streamline DEM post-processing across an inherently interdisciplinary community spanning geosciences, engineering and physics. Future versions are planned to read data from other DEM packages such as LAMMPS and YADE, to offer more flexible meshing beyond the current structured cuboid grid, and to account for the effect of hard boundaries on the contact stress tensor. Work is also under way with the MFiX developers to enable rigorous coarse-graining of glued-sphere particles, which approximate irregular shapes such as angular volcanic ash. For a field in which the second-most-handled material by weight in global industry, behind only water, still defies a unified description, a well-documented, open-source bridge from grain to continuum may prove a quietly transformative piece of infrastructure.

Subject of Research: A discrete-to-continuum coarse-graining software tool for analysing the rheology of granular materials from DEM simulations

Article Title: Pysammos 1.0.0: a discrete-to-continuum transformation Python tool to analyse the rheology of granular materials

Article References: Pysammos 1.0.0: a discrete-to-continuum transformation Python tool to analyse the rheology of granular materials. (n.d.). https://doi.org/10.5194/gmd-19-9519-2026

Image Credits: AI Generated

DOI: 10.5194/gmd-19-9519-2026

Keywords: granular flows, Pysammos, Discrete Element Method, coarse-graining, rheology, DEM-CFD, MFiX, geohazards, sediment transport, open-source software, computational physics, continuum mechanics

The research, led by Jeong-Hoon Park and Il-Jun Hwang of Jeonbuk National University, together with Tae-Yong Park of STEP Lab, Hyun-Ung Oh of Korea Aerospace University and STEP Lab, and Jae Hyuk Lim of Kyung Hee University, tackles a problem that has long frustrated aerospace structural analysts. Metallic meshes do not behave like ordinary solid sheets. Because the wires are woven rather than fused, the material’s stiffness and strength depend strongly on the direction of loading. Pull along the warp direction and the mesh responds one way; pull along the weft and the response can be markedly different. This pronounced anisotropy arises from the interplay of wire stretching, bending, contact at crossover points, frictional sliding between wires, and the gradual rearrangement of the weave as deformation accumulates. Any simulation that ignores these effects risks giving designers a misleading picture of how a deployable antenna reflector will hold its shape in orbit or how a mesh-reinforced structure will absorb an impact.

The team’s approach centers on the concept of a representative volume element, or RVE, a small but statistically meaningful snapshot of the mesh’s microstructure that captures the essential geometry and contact behavior of the weave. Rather than modeling every wire in an entire antenna or panel, the researchers built a detailed finite element model of a small RVE and subjected it to controlled tensile loading. From that microscopic simulation, they extracted equivalent stress-strain curves that describe how the mesh as a whole responds to tension. Crucially, they performed this calibration within a moderate strain range, keeping strains below 0.2, a regime in which the mesh’s deformation remains dominated by reversible elastic response and predictable plastic flow rather than by the chaotic wire sliding and separation that occur at larger deformations.

With those equivalent material parameters in hand, the researchers constructed what is known as a continuum model, a simplified representation of the mesh as if it were a solid sheet of material. But because the mesh is so directionally dependent, a conventional isotropic model would not suffice. Instead, the team turned to the Hill-48 yield criterion, a classical mathematical description of anisotropic plasticity originally developed for sheet metal forming. By fitting the Hill-48 parameters to the RVE-derived stress-strain curves for both the warp and weft directions, they created an anisotropic elastoplastic continuum model capable of reproducing the mesh’s nonlinear tensile response in any in-plane direction, while treating the material as a homogeneous continuum rather than an assembly of thousands of individual wires.

The real test of any homogenization scheme is whether the simplified model agrees with the detailed one. To find out, the researchers compared the mechanical responses of their full wire-mesh finite element model and their homogenized continuum model under identical tensile loading conditions, applied separately in the warp and weft directions. They imposed an explicit numerical-consistency criterion: the normalized reaction-force error between the two models had to remain within 10 percent. This kind of quantitative benchmark is what separates rigorous multiscale modeling from mere curve fitting, because it tells downstream users exactly how far they can trust the simplified model before its predictions drift beyond an acceptable tolerance.

The results were striking. The anisotropic elastoplastic homogenized model extended the displacement range over which the 10 percent error criterion was satisfied by approximately 6.1 times compared with a simpler equivalent-elastic homogenized model, which assumes the mesh remains purely elastic and therefore cannot capture the progressive yielding and plastic flow that dominates at larger stretches. At the same time, the new model cut the computation time by roughly a factor of 5.36. That combination, a much wider valid range and much faster execution, is exactly what design engineers need when they must iterate through dozens of candidate antenna geometries or optimize a mesh-reinforced structure under tight program schedules. A simulation that takes hours instead of days changes not just the analysis workflow but the entire pace of design exploration.

To demonstrate practical applicability beyond the calibration exercises, the team applied their identified equivalent material parameters to a specimen-level tensile analysis, showing that the homogenized model could be deployed directly on realistic component-scale problems. This step matters because a multiscale framework is only useful if the parameters extracted from a tiny RVE remain meaningful when embedded in a much larger structural simulation. The specimen-level example served as a bridge between the micromechanical calibration and the macroscopic engineering use case, illustrating how the workflow could be adopted by other groups working on mesh-based aerospace hardware.

The authors are careful to frame their contribution honestly. The homogenized formulation is a design-oriented model for the calibrated moderate tensile strain regime, not a replacement for detailed micromechanical contact modeling. Once severe inter-wire sliding, wire separation, contact rearrangement, or post-buckling behavior becomes dominant, the equivalent continuum representation loses its physical grounding, and analysts must return to full micromechanical simulations or experimental testing. That limitation is not a weakness of the method so much as a definition of its operating envelope, and by stating it explicitly alongside the 10 percent error criterion, the researchers have given the engineering community a clear contract: within the calibrated range, the model is fast, accurate, and trustworthy; outside it, users know they are on their own.

The broader implications reach across several industries. For space applications, metallic meshes are the defining component of large deployable reflector antennas, where surface accuracy, thermal stability, and mass all depend on the mesh’s mechanical behavior, and missions ranging from Earth science CubeSats to commercial Ku- and Ka-band communications satellites rely on such reflectors. Beyond orbit, wire meshes reinforce concrete structures, absorb energy under low-velocity impact, filter fluids in chemical processing, and serve as biomedical implants, each application constrained by the same directional, nonlinear mechanics that this framework now captures efficiently. As simulation-driven design becomes the norm across aerospace and materials engineering, tools that compress computation time while widening the range of reliable prediction will shape what engineers dare to build. This study’s blend of rigorous micromechanics, classical anisotropic plasticity theory, and transparent error quantification offers a template for how heterogeneous fabric-like materials can be brought into the fast lane of modern computational design, one representative volume element at a time.

Subject of Research: An RVE-based multiscale homogenization framework for predicting the anisotropic elastoplastic tensile response of metallic wire-mesh structures.

Article Title: An RVE-Based Homogenization Framework for the Global Anisotropic Elastoplastic Response of Metallic Wire-Mesh Structures

Article References: Park, J.-H., Hwang, I.-J., Park, T.-Y., Oh, H.-U., & Lim, J. H. (2026). An RVE-Based Homogenization Framework for the Global Anisotropic Elastoplastic Response of Metallic Wire-Mesh Structures. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01290-9

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01290-9

Keywords: metallic wire mesh, multiscale modeling, homogenization, representative volume element, anisotropic elastoplasticity, Hill-48 yield criterion, finite element method, deployable mesh antennas, computational solid mechanics, aerospace structures, wire contact and friction, continuum mechanics