What is it about?
Many scientists have believed for decades that materials compressed by shock waves always follow the same mathematical rule: the strain rate (a measure of how fast the material is compressed) increases as the fourth power of the stress. This “fourth-power law” has been treated as a kind of universal truth in the field. However, this paper revisits the evidence behind that assumption using modern statistical tools. By looking at decades of experimental data for two metals, aluminium and iron, and applying a rigorous Bayesian approach, it becomes clear that the relationship between stress and strain rate is not universal after all. The actual power varies between materials: for example, aluminium follows something closer to a cube (third power), while iron is even further off. These results suggest that the idea of a one-size-fits-all rule may be misleading, and more care is needed when interpreting experimental data, especially when it’s sparse or noisy.
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Why is it important?
This work challenges a widely accepted rule in materials science that had previously gone untested at a statistical level. By doing so, it not only shows that the fourth-power law is not as universal as once thought, but also introduces a more rigorous, reproducible way of analysing experimental shock data. The approach accounts for noisy measurements, inconsistent definitions, and varying experimental quality, all of which often distort our understanding of how materials behave under extreme conditions. By moving away from blind acceptance of old laws and embracing statistical transparency, this study opens the door to more accurate modelling of materials under shock, which matters for designing spacecraft, armour, or even interpreting meteorite impacts.
Perspectives
Writing this article offered a chance to re-examine a foundational assumption in shock physics with fresh eyes. It was both humbling and gratifying to see how modern statistical tools, particularly Bayesian methods, can help clarify longstanding uncertainties in the field. I approached this work not to disprove, but to better understand, and in doing so came to appreciate how much nuance there is in interpreting experimental data. The process deepened my respect for the challenges faced by earlier experimentalists and reinforced the importance of transparency and rigour in model validation. I hope this study will be a helpful resource for others revisiting complex or noisy datasets, and that it contributes to building a more robust and inclusive framework for interpreting material behaviour under extreme conditions.
Benat Gurrutxaga-Lerma
University of Birmingham
Read the Original
This page is a summary of: A Bayesian analysis of the experimental evidence underpinning the fourth-power law in shock loading, Journal of Applied Physics, June 2025, American Institute of Physics,
DOI: 10.1063/5.0277406.
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