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Intrusion rheology in grains and other flowable materials

Nature Materials volume 15, pages 1274–1279 (2016)Cite this article

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Abstract

The interaction of intruding objects with deformable materials arises in many contexts, including locomotion in fluids and loose media, impact and penetration problems, and geospace applications. Despite the complex constitutive behaviour of granular media, forces on arbitrarily shaped granular intruders are observed to obey surprisingly simple, yet empirical ‘resistive force hypotheses’. The physics of this macroscale reduction, and how it might play out in other media, has however remained elusive. Here, we show that all resistive force hypotheses in grains arise from local frictional yielding, revealing a novel invariance within a class of plasticity models. This mechanical foundation, supported by numerical and experimental validations, leads to a general analytical criterion to determine which rheologies can obey resistive force hypotheses. We use it to explain why viscous fluids are observed to perform worse than grains, and to predict a new family of resistive-force-obeying materials: cohesive media such as pastes, gels and muds.

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Figure 1: Theoretically predicted intrusion flow fields.
Figure 2: Theoretically predicted versus experimentally obtained resistive force plots.
Figure 3: Demonstration of the superposition principle arising from the continuum model.
Figure 4: Validity check for superposition in 3D.
Figure 5: Schematic of an RFT litmus test geometry.

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Change history

  • 11 October 2016

    In the version of this Article originally published, an equation for the resistive force in cohesive media, located in the text between equations (6) and (7), should not have included a dependence of the constant yield stress, τy, within the function. This has been corrected in all versions of the Article.

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Acknowledgements

K.K. and H.A. gratefully acknowledge support from Army Research Office Grants W911NF-14-1-0205 and W911NF-15-1-0196.

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Authors and Affiliations

  1. Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

    Hesam Askari & Ken Kamrin

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  1. Hesam Askari
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Contributions

K.K. conceived the study and supervised the project. H.A. developed the computational routines and conducted the numerical modelling. K.K. and H.A. jointly performed the analysis and wrote the paper.

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Correspondence to Ken Kamrin.

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The authors declare no competing financial interests.

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Askari, H., Kamrin, K. Intrusion rheology in grains and other flowable materials. Nature Mater 15, 1274–1279 (2016). https://doi.org/10.1038/nmat4727

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