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Strain-stiffening universality in composite hydrogels and soft tissues

Nature Physics volume 21, pages 1125–1133 (2025)Cite this article

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Abstract

Soft biological tissues exhibit mechanical properties that reflect their composite structure of cells embedded within a biopolymer matrix. However, the microscopic mechanisms underlying their unique nonlinear mechanical response—characterized by strain stiffening in compression, but strain softening in shear or tension—remain poorly understood. Here we show that strain softening in composite systems can arise due to plastic dissipation, which is mediated by filler–polymer interactions. We characterize the nonlinear elasticity of composite hydrogels and soft tissues in isolation from these plastic effects, and show that their nonlinear elastic strain stiffening is driven by the stretching of the underlying biopolymer matrix. We thus show that strain stiffening in composite hydrogels and tissues is mediated by strain amplification factors that are universal in compression and shear. In doing so, we demonstrate the importance of fundamental composite properties such as filler concentration and filler–polymer interaction strength in mediating strain stiffening in composite systems. These findings highlight key structure–property relationships that underlie the nonlinear mechanics of biologically relevant soft solids such as composite gels and tissues.

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Fig. 1: Compression-stiffening universality in composite hydrogels.
Fig. 2: Shear-stiffening universality in composite hydrogels.
Fig. 3: Compression- and shear-stiffening universalities in soft biological tissues.

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Additional data regarding the study are available from the corresponding authors upon request.

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Acknowledgements

J.S. acknowledges financial support from the MIT Lemelson-Vest award and the MIT MathWorks fellowship. J.S. and G.H.M. acknowledge helpful discussions with P. Janmey (U Penn), I. Dellatolas (MIT), I. Bischofberger (MIT), E. Del Gado (Georgetown) and J. Shivers (U Chicago).

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Jake Song & Elad Deiss-Yehiely

  2. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Jake Song, Serra Yesilata & Gareth H. McKinley

  3. Department of Mechanical Engineering, Stanford University, Stanford, CA, USA

    Jake Song

  4. Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, Cambridge, MA, USA

    Elad Deiss-Yehiely

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  1. Jake Song
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  2. Elad Deiss-Yehiely
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Contributions

J.S. conceived the project. J.S. and G.H.M. designed the study. J.S. and S.Y. performed the experiments. E.D.-Y. prepared the tissue specimens for the study. G.H.M. supervised the study. J.S. and G.H.M. analysed the data and wrote the manuscript with input from all authors.

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Correspondence to Jake Song or Gareth H. McKinley.

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Nature Physics thanks Jasper van der Gucht and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Song, J., Deiss-Yehiely, E., Yesilata, S. et al. Strain-stiffening universality in composite hydrogels and soft tissues. Nat. Phys. 21, 1125–1133 (2025). https://doi.org/10.1038/s41567-025-02869-x

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