Living cells are a complex soft material with fascinating mechanical properties. A striking feature is that, regardless of their types or states, cells exhibit a universal power-law rheological behavior which to this date still has not been captured by a single theoretical model. Here, we propose a cellular structural model that accounts for the essential mechanical responses of cell membrane, cytoplasm and cytoskeleton. We demonstrate that this model can naturally reproduce the universal power-law characteristics of cell rheology, as well as how its power-law exponent is related to cellular stiffness. More importantly, the power-law exponent can be quantitatively tuned in the range of 0.1 ~ 0.5, as found in most types of cells, by varying the stiffness or architecture of the cytoskeleton. Based on the structural characteristics, we further develop a self-similar hierarchical model that can spontaneously capture the power-law characteristics of creep compliance over time and complex modulus over frequency. The present model suggests that mechanical responses of cells may depend primarily on their generic architectural mechanism, rather than specific molecular properties.

Living cells are active viscoelastic materials exhibiting diverse mechanical behaviors at different time scales. However, dynamical rheological characteristics of cells in frequency range spanning many orders of magnitude, especially in high frequencies, remain poorly understood. Here, we show that a self-similar hierarchical model can capture cell’s power-law rheological characteristics in different frequency scales. In low-frequency scales, the storage and loss moduli exhibit a weak power-law dependence on frequency with same exponent. In high-frequency scales, the storage modulus becomes a constant, while the loss modulus shows a power-law dependence on frequency with an exponent of 1.0. The transition between low- and high-frequency scales is defined by a transition frequency based on cell’s mechanical parameters. The cytoskeletal differences of different cell types or states can be characterized by changes in mechanical parameters in the model. This study provides valuable insights into potentially using mechanics-based markers for cell classification and cancer diagnosis.

Titanium honeycomb sandwich structures are gradually used in newly developed aircrafts in China. In this study, low-velocity impact tests on the titanium honeycomb sandwich structures were carried out to obtain the impact dynamic response and investigate the typical impact damage modes and parameters including the depths and diameters of the facesheet indentation and the core crushing region. The test results showed that the maximum contact force, the diameter and depth of the indentation had strong positive correlations to the impact energy. Numerical analysis was also conducted to study the low-velocity impact behaviour of the titanium honeycomb sandwich structures by using parametric finite element models that contained all the geometric and the structural details of the titanium honeycomb cores. The numerical results successfully captured the typical low-velocity impact damage modes of the titanium sandwich structures, similar to those observed in the tests. The predicted impact dynamic response also agreed very well with the test data. By using the validated finite element models, a parameter sensitivity study on the effects of the structural parameters on the low-velocity impact damage behaviour of the titanium sandwich structures was conducted. The parametric analysis results showed that the impactor diameter, the facesheet thickness and the core cell wall thickness had positive effect on the maximum contact force, and negative effect on the indentation depth, while the height of the honeycomb core had positive effect on the contact force, but little influence on the indentation depth.

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