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Functional mechanical properties of spherical packings made of soft and rigid spheres are studied using ultrasonic waves and X-rays. Credit: Matthias Ruf (University of Stuttgart), Kianoosh Taghizadeh (University of Stuttgart and University of Twente)

Porous media such as concrete represent spherical packing of different components. It is difficult to calculate the mechanical properties of such mixtures because they are specialized. A team led by Prof. Holger Steeb (University of Stuttgart) and Prof. Stefan Luding (University of Twente, Netherlands) has now managed to investigate an unexpected property of a mixture of granular media consisting of soft and rigid spherical particles.

They used a combination of ultrasound and X-ray imaging, which allowed for three-dimensional imaging and evaluation, as reported in PNAS. The discovery could contribute to safer construction in earthquake zones.

The analysis of the precise composition of porous materials, such as concrete or asphalt, and its effect on the resulting mechanical properties, plays an extremely important role in various technical applications. Only with knowledge of the exact mixing ratio and the resulting effective material behavior can such porous materials be adapted to specific “application requirements”.

For example, when a composite material consists of a soft polymer matrix with stiff reinforcing fibers, the effective elastic stiffness of the composite material can be increased by increasing the fiber content. The resulting effective stiffness can be determined by non-destructive testing from the wave travel time of a sound pulse through the granular spherical packing.

Augmenting predictive models with targeted experimental studies

In this context, the team of Professor Holger Steeb, Principal Investigator at the Collaborative Research Center 1313 as well as at the Center of Excellence SimTech (EXC 2075), and Professor Stefan Luding (University of Twente, Netherlands) investigated the results. elastic properties of spherical packings using ultrasound in the Porous Media Lab at the University of Stuttgart. Dr. Kianoosh Taghizadeh and Matthias Ruf from the Chair of Continuous Mechanics are part of the Stuttgart team.

In the experiment, the researchers first prepared spherical packaging from equal-sized rigid glass spheres and soft rubber spheres in different mixing ratios. These packages were mechanically investigated in an X-ray (PMMA) cylinder equipped with a piezoelectric ultrasonic sensor and actuator under defined axial loading conditions.

Interestingly, it was found that the addition of up to 20% (soft) rubber balls did not reduce the effective stiffness of the packing, but improved it. However, when the percentage of rubber spheres is greater than 30%, the stiffness begins to decrease as the overall network is no longer dominated by rigid particles.

“This behavior defies all classical mixing rules,” says Holger Steeb. “To gain a better understanding of the unexpected mechanical response, the complete network of particles (force network), including the glass and rubber sub-networks, has been analyzed.”

No more classic solid material

The researchers successfully evaluated the morphology using a combination of ultrasound and X-ray tomography (XRCT). X-rays have shown that the higher effective stiffness of the gaskets with up to 20% rubber fragments can be explained by the length of the force chains of glass particles.

“At the same time, the glass particle network is in a so-called jammed state with a correspondingly high coordination number. If the volume fraction of the rubber spheres exceeds 30%, the force chains consist of mixed contacts between glass and rubber spheres. , which are much softer.”

Furthermore, an evaluation of the spheroids showed that the coordination number, i.e. the number of contiguous spheres of the same type, is significantly reduced at these higher volume fractions.

“At this volume ratio, neither of the spherical phases is in a solid state, so the effective material behavior is not comparable to a classical solid,” says Holger Steeb. The researchers see great practical potential for the construction industry in the further development of this research.

For example, in earthquake-prone areas, the stiffness and damping properties of soil could be adjusted with special ballast-rubber composites. The amplitudes and velocities of seismic waves could be manipulated in a targeted manner. Buildings could be protected from these hazards in an efficient and cost-effective manner.

More information:
K. Taghizadeh et al., Three-dimensional X-ray imaging-based micro-understanding of granular composites: Stiffness enhancement by adding small fractions of soft particles, Proceedings of the Academy of Sciences (2023). DOI: 10.1073/pnas.2219999120

Diary information:
Proceedings of the Academy of Sciences

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