A team of German researchers has settled a scientific debate about how to measure and interpret the complex Poisson’s ratio in viscoelastic materials – substances that exhibit both fluid-like and solid-like behavior when deformed.
Published on March 12, 2025, in Proceedings of the Royal Society A, the research led by Dominik Fauser and colleagues from multiple German institutions makes an important contribution to understanding how materials like polymers and rocks respond to forces over time.
What’s the Scientific Achievement?
The researchers compared two different methods for measuring the complex Poisson’s ratio – a property that describes how a material expands or contracts perpendicular to an applied stretching force.
Unlike elastic materials that immediately return to their original shape when a force is removed, viscoelastic materials exhibit time-dependent behavior, making their properties more difficult to measure accurately. When a viscoelastic material is subjected to oscillating forces, the strains in different directions can lag behind the stress with different time delays.
“There has been considerable debate regarding the definition and measurability of the complex Poisson’s ratio,” the authors state in their paper, noting that scientists in different fields have held contradictory views about how it should be defined and whether certain values can be positive or negative.
The Experimental Approach
The team conducted experiments on two very different materials: polymethyl methacrylate (PMMA, commonly known as acrylic or plexiglass) and Berea sandstone. They used three different measurement methods:
- Direct measurement in tension – measuring both longitudinal and transverse strains simultaneously while stretching the material
- Direct measurement in compression – measuring both strains while compressing the material
- Indirect measurement – calculating the Poisson’s ratio from separately measured complex moduli
The researchers employed sensitive strain gauges to measure tiny deformations in the materials while applying oscillating forces at different frequencies and temperatures.
What Did They Discover?
The study found that both direct and indirect methods yielded consistent values for the absolute magnitude of the complex Poisson’s ratio. However, the direct method provided much more accurate results for what’s called the “loss factor” – a measure of how the material’s response in different directions lags in time.
Most significantly, they confirmed that this loss factor can be either positive or negative depending on the material type. This resolves a longstanding disagreement between polymer scientists (who generally assumed it was always negative) and rock physicists (who typically assumed it was always positive).
“Our analysis showed that both methods yielded consistent values for the absolute value of the complex Poisson’s ratio. However, the direct method provided a more accurate determination of its loss factor,” the researchers explain.
Why Does This Matter?
Understanding the complex Poisson’s ratio is crucial for accurately modeling and predicting the behavior of viscoelastic materials in applications ranging from polymer processing to rock mechanics and earthquake science.
The research provides clear guidance on which measurement techniques are appropriate depending on what aspects of material behavior need to be captured. It also establishes that the sign of the loss factor is material-dependent rather than being universally positive or negative as previously argued by different scientific communities.
This improved understanding will help engineers and scientists better predict how materials will respond to dynamic forces in applications like aerospace structures, automotive components, construction, and geological processes.
The study represents a significant step forward in the field of materials characterization and closes a chapter on a scientific controversy that has persisted for decades.
Research Study Source:
Fauser, D., Rodríguez Agudo, J. A., Madadi, H., Haeberle, J., Renner, J., & Steeb, H. (2025). Complex Poisson’s ratio for viscoelastic materials: direct and indirect measurement methods and their correlation. Proceedings of the Royal Society A, 481(2257), 20240543. https://doi.org/10.1098/rspa.2024.0543
Disclaimer
This article summarizes peer-reviewed research published in the Proceedings of the Royal Society A. While efforts have been made to accurately represent the findings, readers interested in the complete methodology and results should refer to the original publication. The interpretation presented here aims to make complex scientific concepts accessible to a general audience and does not constitute engineering or scientific advice.
