Stanford breakthrough advances modeling of heterogeneous materials for sustainable design

Researchers at Stanford University have used a new mathematical approach to describe how heterogeneous materials such as soils, rocks, and composites are spatially structured. The team developed a solution to the Poisson model for heterogeneous materials, a problem that had remained unsolved for decades in statistical physics and materials science.

The new approach allows scientists and engineers to mathematically reconstruct the internal arrangement of mixed materials, like pores, voids, and solid grains,  based on measurable statistical data. By extending multi-point correlation functions, the solution can predict how different phases of material are distributed and interact under stress or flow conditions.

According to lead author Alec Shelley, the concept works similarly to solving the game Battleship, where knowing the outcomes of a few “shots” helps infer the shape of an unseen target. In engineering terms, this analogy illustrates how sampling certain microstructural correlations can reconstruct an entire material layout. Such predictive capability is essential for simulating processes in groundwater transport, soil permeability, and structural composite behavior.

The researchers note that this advancement could directly improve groundwater modeling in fractured aquifers, enabling better estimation of flow paths, storage capacity, and contaminant migration through complex geological matrices. The same modeling principles could optimize nuclear waste isolation design, where engineers must predict radionuclide transport through multi-layered rock and clay formations over centuries.

Beyond environmental applications, the framework may also refine materials engineering, allowing civil and structural engineers to optimize concrete microstructure, enhance durability of composite materials, and simulate stress propagation at fine scales. It connects microstructural properties, such as porosity, grain orientation, or heterogeneity, with bulk mechanical or hydraulic behavior, improving simulation accuracy for infrastructure materials and subsurface systems.