Nonlinearity in the Mechanical Response of Rubber as Investigated by High-Frequency DMA

Nonlinear material response is analysed with the Fourier transform (FT) of the raw signal measured by a high-frequency dynamic mechanical analyzer (HF DMA). It is known from rheological behaviour of elastomers that reinforcing fillers additionally induce nonlinearity in an already inherently nonlinear system. This behaviour is often described in terms of a mechanical response of strain sweeps, essentially the transition from the linear viscoelastic (LVE) to the nonlinear viscoelastic (NVE) region. In the current investigation, the NVE region could be observed with respect to frequency under low-amplitude deformation. A foldover effect was observed, whereby the material exhibited a nonlinear dependency in relation to the increment of the filler amount above the percolation threshold. In addition, an apparent superharmonic resonance was observed within higher orders of vibrational modes which is further indication of nonlinearity. In this paper, the analytical approach is presented as a novel method to characterise the behaviour of the polymer–filler interaction by HF DMA.

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Comparing Predictive Accuracy and Computational Costs for Viscoelastic Modeling of Spinal Cord Tissues

Journal of Biomechanical Engineering ◽

10.1115/1.4043033 ◽

2019 ◽

Vol 141 (5) ◽

Cited By ~ 1

Author(s):

Nicole L. Ramo ◽

Kevin L. Troyer ◽

Christian M. Puttlitz

Keyword(s):

Experimental Data ◽

Spinal Cord ◽

Mechanical Response ◽

Predictive Accuracy ◽

Material Model ◽

Loading Conditions ◽

Nonlinear Viscoelastic ◽

Arbitrary Loading ◽

Linear Viscoelastic ◽

Viscoelastic Modeling

Abstract The constitutive equation used to characterize and model spinal tissues can significantly influence the conclusions from experimental and computational studies. Therefore, researchers must make critical judgments regarding the balance of computational efficiency and predictive accuracy necessary for their purposes. The objective of this study is to quantitatively compare the fitting and prediction accuracy of linear viscoelastic (LV), quasi-linear viscoelastic (QLV), and (fully) nonlinear viscoelastic (NLV) modeling of spinal-cord-pia-arachnoid-construct (SCPC), isolated cord parenchyma, and isolated pia-arachnoid-complex (PAC) mechanics in order to better inform these judgements. Experimental data collected during dynamic cyclic testing of each tissue condition were used to fit each viscoelastic formulation. These fitted models were then used to predict independent experimental data from stress-relaxation testing. Relative fitting accuracy was found not to directly reflect relative predictive accuracy, emphasizing the need for material model validation through predictions of independent data. For the SCPC and isolated cord, the NLV formulation best predicted the mechanical response to arbitrary loading conditions, but required significantly greater computational run time. The mechanical response of the PAC under arbitrary loading conditions was best predicted by the QLV formulation.

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Rheology of rounded mammalian cells over continuous high-frequencies

Nature Communications ◽

10.1038/s41467-021-23158-0 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Gotthold Fläschner ◽

Cosmin I. Roman ◽

Nico Strohmeyer ◽

David Martinez-Martin ◽

Daniel J. Müller

Keyword(s):

High Frequency ◽

Mammalian Cells ◽

Mechanical Response ◽

Cell Mass ◽

Low Frequency ◽

Mass Measurements ◽

High Frequencies ◽

Polymer Relaxation ◽

Continuous Frequency ◽

Rheological Experiments

AbstractUnderstanding the viscoelastic properties of living cells and their relation to cell state and morphology remains challenging. Low-frequency mechanical perturbations have contributed considerably to the understanding, yet higher frequencies promise to elucidate the link between cellular and molecular properties, such as polymer relaxation and monomer reaction kinetics. Here, we introduce an assay, that uses an actuated microcantilever to confine a single, rounded cell on a second microcantilever, which measures the cell mechanical response across a continuous frequency range ≈ 1–40 kHz. Cell mass measurements and optical microscopy are co-implemented. The fast, high-frequency measurements are applied to rheologically monitor cellular stiffening. We find that the rheology of rounded HeLa cells obeys a cytoskeleton-dependent power-law, similar to spread cells. Cell size and viscoelasticity are uncorrelated, which contrasts an assumption based on the Laplace law. Together with the presented theory of mechanical de-embedding, our assay is generally applicable to other rheological experiments.

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A Novel Method for Estimating the High Frequency Incremental DQ-axis and Cross-coupling Inductances in Interior Permanent Magnet Synchronous Machines

IEEE Transactions on Industry Applications ◽

10.1109/tia.2021.3089444 ◽

2021 ◽

pp. 1-1

Author(s):

Bo Shuang ◽

Z Q Zhu

Keyword(s):

Permanent Magnet ◽

High Frequency ◽

Cross Coupling ◽

Synchronous Machines ◽

Permanent Magnet Synchronous Machines ◽

Interior Permanent Magnet ◽

Novel Method

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Visco-Hyperelastic Characterization of the Equine Immature Zona Pellucida

Materials ◽

10.3390/ma14051223 ◽

2021 ◽

Vol 14 (5) ◽

pp. 1223

Author(s):

Elisa Ficarella ◽

Mohammad Minooei ◽

Lorenzo Santoro ◽

Elisabetta Toma ◽

Bartolomeo Trentadue ◽

...

Keyword(s):

Zona Pellucida ◽

Soft Matter ◽

Mechanical Response ◽

Mechanical Characterization ◽

Nonlinear Material ◽

Prony Series ◽

Critical Comparison ◽

Highly Nonlinear ◽

Good Agreement

This article presents a very detailed study on the mechanical characterization of a highly nonlinear material, the immature equine zona pellucida (ZP) membrane. The ZP is modeled as a visco-hyperelastic soft matter. The Arruda–Boyce constitutive equation and the two-term Prony series are identified as the most suitable models for describing the hyperelastic and viscous components, respectively, of the ZP’s mechanical response. Material properties are identified via inverse analysis based on nonlinear optimization which fits nanoindentation curves recorded at different rates. The suitability of the proposed approach is fully demonstrated by the very good agreement between AFM data and numerically reconstructed force–indentation curves. A critical comparison of mechanical behavior of two immature ZP membranes (i.e., equine and porcine ZPs) is also carried out considering the information on the structure of these materials available from electron microscopy investigations documented in the literature.

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