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Viscoelastic interpretation of AFM nanoindentation for predicting nanoscale stiffness in soft biomaterials.

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Title: Viscoelastic interpretation of AFM nanoindentation for predicting nanoscale stiffness in soft biomaterials.
Authors: Minopoli, Antonio1,2 (AUTHOR), Evangelista, Davide1,2 (AUTHOR), Marras, Matteo1,2 (AUTHOR), Perini, Giordano1,2 (AUTHOR), Palmieri, Valentina3 (AUTHOR), De Spirito, Marco1,2 (AUTHOR), Papi, Massimiliano1,2 (AUTHOR) massimiliano.papi@unicatt.it
Source: Polymer Testing. Dec2025, Vol. 153, pN.PAG-N.PAG. 1p.
Subjects: Viscoelasticity, Hydrogels, Stiffness (Mechanics), Nanoindentation, Tissue engineering, Mechanical behavior of materials, Biomaterials, Atomic force microscopy
Abstract: Precise characterization of biomechanical properties at the micro- and nanoscale is essential for developing biomaterials for tissue engineering, regenerative medicine, and drug delivery. Traditional bulk techniques fail to capture the local mechanical heterogeneities of soft materials such as hydrogels, polymers, and biological tissues. Atomic force microscopy (AFM) nanoindentation enables high-resolution stiffness mapping under near-physiological conditions; however, the standard Hertz model assumes purely elastic behavior, overlooking the viscoelastic nature of most biological systems. This study relies on established viscoelastic models to better interpret rate-dependent mechanical responses in AFM nanoindentation experiments. Force-displacement curves were analyzed to separate elastic and viscous contributions and account for the effect of indentation speed. Experiments on four hydrogels (alginate, Cellink-RGD, GelMA, GelMA A) revealed nonlinear stiffening trends with increasing indentation rate, associated with polymer network dynamics and crosslinking density. Additional analyses on erythrocytes and zona pellucida confirmed their complex viscoelastic responses, highlighting physiological and pathological differences in cells and species-specific behavior in reproductive structures. Our approach provides a simple and effective method to predict nanoscale stiffness as a function of indentation rate, improving accuracy in nanomechanical characterization and supporting the design of advanced bioengineered constructs. [Display omitted] • A new viscoelastic model was developed for nanoindentation testing. • Experiments reveal rate-dependent stiffness in hydrogels and cells. • Hydrogels exhibit nonlinear stiffening linked to network dynamics. • Diabetic erythrocytes asymptotically stiffened at 7.5 μm/s while healthy at 20 μm/s. • Porcine and equine zone pellucida stiffens linearly in the range 0–10 μm/s. [ABSTRACT FROM AUTHOR]
Copyright of Polymer Testing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Viscoelastic interpretation of AFM nanoindentation for predicting nanoscale stiffness in soft biomaterials.
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  Data: Precise characterization of biomechanical properties at the micro- and nanoscale is essential for developing biomaterials for tissue engineering, regenerative medicine, and drug delivery. Traditional bulk techniques fail to capture the local mechanical heterogeneities of soft materials such as hydrogels, polymers, and biological tissues. Atomic force microscopy (AFM) nanoindentation enables high-resolution stiffness mapping under near-physiological conditions; however, the standard Hertz model assumes purely elastic behavior, overlooking the viscoelastic nature of most biological systems. This study relies on established viscoelastic models to better interpret rate-dependent mechanical responses in AFM nanoindentation experiments. Force-displacement curves were analyzed to separate elastic and viscous contributions and account for the effect of indentation speed. Experiments on four hydrogels (alginate, Cellink-RGD, GelMA, GelMA A) revealed nonlinear stiffening trends with increasing indentation rate, associated with polymer network dynamics and crosslinking density. Additional analyses on erythrocytes and zona pellucida confirmed their complex viscoelastic responses, highlighting physiological and pathological differences in cells and species-specific behavior in reproductive structures. Our approach provides a simple and effective method to predict nanoscale stiffness as a function of indentation rate, improving accuracy in nanomechanical characterization and supporting the design of advanced bioengineered constructs. [Display omitted] • A new viscoelastic model was developed for nanoindentation testing. • Experiments reveal rate-dependent stiffness in hydrogels and cells. • Hydrogels exhibit nonlinear stiffening linked to network dynamics. • Diabetic erythrocytes asymptotically stiffened at 7.5 μm/s while healthy at 20 μm/s. • Porcine and equine zone pellucida stiffens linearly in the range 0–10 μm/s. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Polymer Testing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.polymertesting.2025.109026
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      – Code: eng
        Text: English
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        PageCount: 1
        StartPage: N.PAG
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      – SubjectFull: Viscoelasticity
        Type: general
      – SubjectFull: Hydrogels
        Type: general
      – SubjectFull: Stiffness (Mechanics)
        Type: general
      – SubjectFull: Nanoindentation
        Type: general
      – SubjectFull: Tissue engineering
        Type: general
      – SubjectFull: Mechanical behavior of materials
        Type: general
      – SubjectFull: Biomaterials
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      – SubjectFull: Atomic force microscopy
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      – TitleFull: Viscoelastic interpretation of AFM nanoindentation for predicting nanoscale stiffness in soft biomaterials.
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            – D: 01
              M: 12
              Text: Dec2025
              Type: published
              Y: 2025
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