Granular materials, ubiquitous in both natural and engineered systems, have long challenged scientists due to their inherently heterogeneous and discrete nature. Unlike traditional solids or fluids, their mechanical responses are governed by the collective interaction of countless individual particles, whose shapes, sizes, and arrangements dictate the overall behavior. The new research addresses this complexity by establishing a microstructure-informed constitutive model, which integrates detailed particle-scale attributes into predictive continuum mechanics frameworks. This marks a substantial leap towards accurately replicating real-world behaviors of granular media under complex loading scenarios.

At the heart of this study lies an intricate analysis of how granular materials respond to stresses applied from multiple directions. Traditional modeling approaches often rely on simplifying assumptions, treating granular media merely as homogeneous continua, thereby overlooking critical microstructural factors like force chain anisotropy and particle rearrangement phenomena. By employing advanced computational techniques combined with rigorous experimental validation, the research team has identified key microstructural parameters that govern the material’s global response, including contact network evolution and fabric tensor dynamics.

One of the most significant breakthroughs of this work is the quantitative linkage established between particle-scale mechanics and macroscopic constitutive laws. Through meticulous particle-resolved simulations, the researchers captured the intricate rearrangements of grains and force transmissions during multidirectional strain paths. These detailed observations enabled the derivation of constitutive formulations that inherently account for evolving microstructures, a feat that enhances the fidelity of continuum models under varying deformation histories and loading complexities.

This research also embraces the multidirectional nature of real-world loading conditions, moving beyond simpler uni-axial or bi-axial experimental setups. Granular media in natural settings, such as soils beneath infrastructure or sand layers in geological formations, often experience complex stress states involving shear, compression, and tension simultaneously. The proposed framework uniquely incorporates these multifaceted conditions, making it highly relevant for engineering applications ranging from foundation design to earthquake resilience and material handling processes.

Advanced imaging and particle tracking techniques played a pivotal role in validating the microstructural assumptions and observing particle kinematics in situ. By coupling micro-scale imaging data with numerical models, the research team substantiated the predictive capabilities of their constitutive equations. Such fused methodologies provide a more coherent understanding of how micro-scale interactions translate into macro-scale responses, effectively uniting experimental and theoretical realms within granular mechanics.

The constitutive model developed is robust in its adaptability, allowing for parameter calibration based directly on measurable microstructural features rather than relying solely on phenomenological fitting parameters. This innovation not only improves predictive accuracy but also enhances the interpretability of the model, granting engineers and scientists greater confidence when applying these formulations in critical design and analysis tasks.

Furthermore, the team’s approach sheds light on the mechanisms behind strain localization and failure modes in granular assemblies. By closely examining the evolution of force chains and contact anisotropy, the model captures the development of shear bands and anisotropic deformation patterns—phenomena that are crucial to understanding failure initiation and propagation in soils and granular materials.

Importantly, the study’s outcomes extend beyond purely theoretical contributions, offering practical recommendations for the deployment of this microstructure-informed constitutive model in computational geomechanics software. This ensures that practitioners can readily implement the new formulation within existing simulation platforms, paving the way for more reliable predictions in engineering projects involving granular media.

In addition to its engineering significance, this research provides fundamental insights that could influence diverse fields such as pharmaceuticals, where powder compaction behavior dictates tablet stability; agriculture, where soil mechanics impact crop growth; and planetary science, where regolith properties affect landing site safety for spacecraft. The universal challenge of predicting granular material behavior makes this work a keystone for multifaceted scientific and industrial advancements.

Moreover, the study embraces the inherent complexities of real granular systems by considering particle shape irregularities and size distributions within its modeling framework. Such inclusions reflect the natural diversity present in granular materials and underscore the model’s capacity to handle heterogeneity without sacrificing computational tractability.

To summarize, this microstructure-informed constitutive modeling advances the science of granular media by tightly coupling particle-scale observations with continuum-scale descriptions, especially under challenging multidirectional loading conditions. By transcending traditional empirical approaches and rooting constitutive laws in fundamental microstructural mechanics, the research charts a pathway towards more predictive and versatile models.

The team’s methodology, combining computational particle analysis, in situ experimental imaging, and continuum mechanics theory, establishes a new paradigm where microstructural evolution dictates constitutive responses dynamically. This approach not only refines theoretical frameworks but also enhances engineering assessment accuracy, offering tangible benefits across environmental and industrial domains.

As granular materials continue to underpin critical infrastructure and technological processes worldwide, this research equips the scientific community with a powerful tool to decode and harness their complex behavior. The ability to predict how granular assemblies deform and fail under various multidirectional stresses promises safer, more efficient, and innovative solutions in geotechnical engineering, manufacturing, and beyond.

By revealing the microstructural origins of granular behavior and translating them into actionable constitutive equations, this study anchors future research directions aimed at exploring more complex particulate systems, including cohesive powders and wet granular media. This lays the groundwork for even more comprehensive models that can tackle emerging challenges in materials science and engineering mechanics.

In essence, this pioneering work opens a new chapter in granular media research by inventively synthesizing microstructural insights with continuum constitutive modeling. Its ramifications resonate across scientific disciplines, technological applications, and practical engineering solutions, marking a transformative leap toward mastering the mechanics of one of nature’s most fascinating and ubiquitous materials.

Subject of Research: Constitutive modeling and microstructural behavior of granular media under multidirectional loading.

Article Title: Microstructure-informed constitutive modeling of granular media under multidirectional loading: From particle-scale to continuum.

Article References:
Irani, N., Golestaneh, P., Salimi, M. et al. Microstructure-informed constitutive modeling of granular media under multidirectional loading: From particle-scale to continuum. Commun Eng 5, 80 (2026). https://doi.org/10.1038/s44172-026-00652-1

DOI: https://doi.org/10.1038/s44172-026-00652-1

Image Credits: AI Generated

Rocks, often perceived as the epitome of solid and unyielding materials, harbor a complex internal world that belies their seemingly immutable nature. Despite their apparent stiffness and permanence, these natural materials exhibit dynamic mechanical properties that evolve under stress. Even minor loads can impair their structural integrity by reducing stiffness, an effect with profound implications for geophysics, engineering, and understanding natural hazards. This phenomenon is crucial in deciphering how material failure occurs in geological contexts, including landslides and earthquakes, where a reduction in rock strength can trigger catastrophic events.

The mechanical behavior of rocks, characterized by a loss of stiffness upon deformation, has the capacity to influence the stability of both natural and human-made structures. These time-dependent changes are especially prominent in heterogeneous, granular materials composed of stiff mineral grains interconnected by much softer contact planes. Such materials include not only rocks but also concrete and sediments, all of which showcase variable elastic properties when subjected to stress. The nuanced interplay among grains and their contact interfaces reveals a rich field of study that intersects geotechnical engineering, seismology, and materials science.

Until recently, the direct observation of these mechanical changes under realistic stress conditions was largely confined to laboratory settings, primarily utilizing acoustic techniques to detect variations in wave velocities through rock samples. The advent of seismic interferometry revolutionized this paradigm, enabling researchers to detect similar effects in situ by analyzing ambient seismic noise. Notably, a sudden drop in seismic wave velocity often follows significant seismic events, indicative of subsurface damage. This velocity drop is not a permanent feature; it slowly recovers over months or even years, revealing intricate healing mechanisms in the subsurface.

Despite decades of research and a plethora of observational data, the fundamental physical processes dictating these post-seismic variations have remained elusive. Prevailing theories suggest that the stark contrast in stiffness between rigid mineral grains and their comparatively compliant contact zones creates localized stress concentrations. These stress concentrations presumably drive changes in the elastic properties of the granular assembly. However, the precise micromechanical interactions underlying these phenomena had not been fully elucidated, leaving a gap in predictive models for seismic damage and recovery.

An innovative breakthrough has been achieved through meticulous laboratory experiments conducted by Manuel Asnar and colleagues at the GFZ Helmholtz Centre for Geosciences, alongside partners from the University of Edinburgh and the Université de Lorraine. Utilizing GFZ’s High-Pressure Labs, the team executed experiments involving a 10-centimeter cylinder of Bentheim sandstone, a rock known for its relatively uniform grain size and sedimentary origin. This sample was meticulously enclosed within a protective neoprene jacket to maintain surface integrity, with numerous sensors affixed to record wave velocity with unprecedented precision across multiple propagation directions.

The experimental design involved subjecting the sandstone sample to variable levels of axial stress, replicating conditions akin to those experienced in the Earth’s crust during tectonic loading. By measuring wave velocities along the cylinder’s main axis and perpendicular to it, the team observed a stark dichotomy in how static and time-dependent effects influenced wave propagation. As anticipated, static load application predominantly altered wave speeds parallel to the direction of compression, while waves traversing the diameter remained relatively stable under these immediate conditions. Intriguingly, the time-dependent phenomena—characterized by a rapid velocity decrease following stress alterations and a protracted velocity restoration—manifested uniformly across all measured directions.

This anisotropic pattern provokes a fundamental reevaluation of the causative mechanisms behind post-seismic wave velocity changes. The findings robustly suggest that these time-dependent signatures are not driven by mere variations in grain contact compression, as previously believed. Instead, the data affirm that sliding along grain contact planes—micro-scale frictional movement—plays a decisive role. These contact interfaces can slip relative to one another during both the application and release of stress, inducing transient damage and subsequent healing within the rock matrix.

Frictional sliding at grain contacts introduces a dynamic element to the mechanical response of rocks, extending beyond simple elastic deformation. This mechanism aligns with longstanding hypotheses but had lacked direct experimental corroboration in the context of anisotropic velocity changes. The novel approach adopted in this study, focusing on directional dependence and precise wave velocity measurements, provides compelling evidence substantiating frictional micro-slip as the dominant driver. This insight advances the fundamental understanding of how microstructural interactions propagate to macroscopic geophysical observables.

The implications of these findings extend far beyond academic interest. Improved physical models incorporating anisotropic frictional sliding can significantly enhance our capacity to forecast seismic hazard evolution and interpret post-earthquake subsurface behavior. Geotechnical applications stand to benefit by enabling better predictions of material failure in critical infrastructure, especially in regions prone to seismic activity. Furthermore, these refined models may inform engineering practices within the construction industry, particularly when dealing with concrete and sedimentary materials exhibiting similar granular structures.

In addition to their geophysical repercussions, the results encourage a shift in experimental methodologies. Future research can leverage the demonstrated importance of anisotropic data collection to unravel other micro-mechanical processes influencing rock behavior. High-fidelity, multi-directional wave velocity assessments promise to yield nuanced characterizations of aging, fatigue, and recovery in complex materials—pivotal parameters for both natural hazard assessment and materials engineering.

Overall, the collaborative experiment spearheaded by Asnar and his team harnesses advanced laboratory techniques to bridge gaps between microscopic frictional phenomena and their macroscopic seismic manifestations. By systematically quantifying velocity anisotropy and linking it to contact plane dynamics, their work illuminates a fundamental aspect of rock physics long conjectured but never experimentally delineated with such clarity. This lays the groundwork for subsequent theoretical developments and practical applications aimed at mitigating seismic risks.

As we deepen our grasp of Earth’s inner workings through such experiments, we unlock pathways to more resilient infrastructure and better-informed seismic risk management strategies. The careful dissection of how rocks respond to stress, not as inert masses but as dynamic assemblies of interacting grains, enriches both our scientific understanding and societal preparedness in the face of natural disasters.

Subject of Research: Mechanical behavior and time-dependent changes in wave velocities within sandstone due to post-seismic contact sliding and aging.

Article Title: Anisotropy reveals contact sliding and aging as a cause of post-seismic velocity changes

News Publication Date: 15-Aug-2025

Web References: http://dx.doi.org/10.1038/s41467-025-62667-0

References: Asnar, M., Sens-Schönfelder, C., Bonnelye, A. et al. Anisotropy reveals contact sliding and aging as a cause of post-seismic velocity changes. Nat Commun 16, 7587 (2025).

Image Credits: Manuel Asnar/GFZ

Keywords: Geophysics, Seismology, Material properties