Are elastic moduli of biological cells depth dependent or not? Another explanation using a contact mechanics model with surface tension

Soft Matter ◽  
2018 ◽  
Vol 14 (36) ◽  
pp. 7534-7541 ◽  
Author(s):  
Yue Ding ◽  
Jian Wang ◽  
Guang-Kui Xu ◽  
Gang-Feng Wang
Keyword(s):  
Surface Tension ◽  
Elastic Modulus ◽  
Contact Mechanics ◽  
Elastic Moduli ◽  
Contact Model ◽  
Biological Cells ◽  
Mechanics Model ◽  
Afm Indentation ◽  
A Cell ◽  
Indent Depth

Contrary to the existing reports that the apparent elastic modulus of a cell depends strongly on the indent depth in many AFM indentation experiments, we present a contact model with surface effects, and show that the actual elastic modulus of cell materials could be independent of the indent depth if surface tension is taken into account.

An Atomistically Enriched Continuum Model for Nanoscale Contact Mechanics and Its Application to Contact Scaling

2008 ◽  
Vol 8 (7) ◽  
pp. 3757-3773
Author(s):  
Roger A. Sauer ◽  
Shaofan Li
Keyword(s):  
Contact Mechanics ◽  
Scaling Laws ◽  
Coarse Graining ◽  
Contact Model ◽  
Geometrically Nonlinear ◽  
Lattice Statics ◽  
Mechanics Model ◽  
Contact Formulation ◽  
Wide Range ◽  
Length Scaling

This work provides a comprehensive exposition and extension of an atomistically enriched contact mechanics model initially proposed by the present authors. The contact model is based on the coarse-graining of the interaction occurring between the molecules of the contacting bodies. As these bodies may be highly compliant, a geometrically nonlinear kinematical description is chosen. Thus a large deformation continuum contact formulation is obtained which reflects the attractive and repulsive character of intermolecular interactions. Further emphasis is placed on the efficiency of the proposed atomistic-continuum contact model in numerical simulations. Therefore three contact formulations are discussed and validated by lattice statics computations. Demonstrated by a simple benchmark problem the scaling of the proposed contact model is investigated and some of the important scaling laws are obtained. In particular, the length scaling, or size effect, of the contact model is studied. Due to its formal generality and its numerical efficiency over a wide range of length scales, the proposed contact formulation can be applied to a variety of multiscale contact phenomena. This is illustrated by several numerical examples.

scholarly journals The Effects of Creep on Elastic Modulus Measurement Using Nanoindentation

2000 ◽  
Vol 649 ◽  
Author(s):  
G. Feng ◽  
A.H.W. Ngan
Keyword(s):  
Elastic Modulus ◽  
Elastic Deformation ◽  
Elastic Moduli ◽  
Holding Time ◽  
Time Dependent ◽  
Nanoindentation Test ◽  
Modification Method ◽  
Unloading Rate ◽  
Modulus Measurement

ABSTRACTDuring the unloading segment of nanoindentation, time dependent displacement (TDD) accompanies elastic deformation. Consequently the modulus calculated by the Oliver-Pharr scheme can be overestimated. In this paper we present evidences for the influence of the measured modulus by TDD. A modification method is also presented to correct for the effects of TDD by extrapolating the TDD law in the holding process to the beginning of the unloading process. Using this method, the appropriate holding time and unloading rate can be estimated for nanoindentation test to minimise the effects of TDD. The elastic moduli of three materials computed by the modification method are compared with the results without considering the TDD effects.

scholarly journals A Simple Contact Mechanics Model for Highly Strained Aqueous Surface Gels

2021 ◽  
Author(s):  
A. L. Chau ◽  
M. K. Cavanaugh ◽  
Y.-T. Chen ◽  
A. A. Pitenis
Keyword(s):  
Simple Model ◽  
Contact Mechanics ◽  
Contact Lenses ◽  
Radius Of Curvature ◽  
Winkler Foundation ◽  
Surface Layers ◽  
Mechanics Model ◽  
Soft Surface ◽  
Simple Contact ◽  
Highly Strained

Abstract Background Soft, biological, and bio-inspired materials are often compositionally heterogeneous and structurally anisotropic, and they frequently feature graded or layered organizations. This design complexity enables exceptional ranges in properties and performance yet complicates a fundamental understanding of the contact mechanics. Recent studies of soft gel layers have relied on Hertzian or Winkler foundation (“bed-of-springs”) models to characterize the mechanics but have found neither satisfactory. Objective The contact mechanics of soft gel layers are not yet fully understood. The aim of this work is to develop a simple contact mechanics model tailored for compositionally-graded materials with soft surface layers under high strains and deformations. Methods Concepts from polymer physics, fluid draining, and Winkler foundation mechanics are combined to develop a simple contact mechanics model which relates the applied normal force to the probe radius of curvature, elastic modulus, and thickness of soft surface layers subjected to high strains. Results This simple model was evaluated with two examples of graded surface gel layers spanning multiple length-scales, including commercially available contact lenses and stratified hydrogels. The model captures the nonlinear contact mechanics of highly strained soft aqueous gel layers more closely than either Hertz or Winkler foundation theory while simultaneously enabling a prediction for the thickness of the surface gel layer. Conclusion These results indicate that this simple model can adequately characterize the contact mechanics of highly strained soft aqueous gel layers.

scholarly journals In silico stress fibre content affects peak strain in cytoplasm and nucleus but not in membrane for uniaxial substrate stretch

2019 ◽  
Author(s):  
Tamer Abdalrahman ◽  
Neil H. Davies ◽  
Thomas Franz
Keyword(s):  
Elastic Modulus ◽  
In Silico ◽  
Focal Adhesions ◽  
Element Model ◽  
Homogenization Method ◽  
Fibre Volume ◽  
Fibre Content ◽  
Peak Strain ◽  
Stress Fibre ◽  
A Cell

AbstractExisting in silico models for single cell mechanics feature limited representations of cytoskeletal structures that contribute substantially to the mechanics of a cell. We propose a micromechanical hierarchical approach to capture the mechanical contribution of actin stress fibres. For a cell-specific fibroblast geometry with membrane, cytoplasm and nucleus, the Mori-Tanaka homogenization method was employed to describe cytoplasmic inhomogeneities and constitutive contribution of actin stress fibres. The homogenization was implemented in a finite element model of the fibroblast attached to a substrate through focal adhesions. Strain in cell membrane, cytoplasm and nucleus due to uniaxial substrate stretch was assessed for different stress fibre volume fractions and different elastic modulus of the substrate. A considerable decrease of the peak strain with increasing stress fibre content was observed in cytoplasm and nucleus but not the membrane, whereas the peak strain in cytoplasm, nucleus and membrane increased for increasing elastic modulus of the substrate.

Consistent red luminescence in π-conjugated polymers with tuneable elastic moduli over five orders of magnitude

2020 ◽  
Vol 7 (5) ◽  
pp. 1421-1426 ◽  
Author(s):  
Zhenfeng Guo ◽  
Akira Shinohara ◽  
Chengjun Pan ◽  
Florian J. Stadler ◽  
Zhonghua Liu ◽  
...  
Keyword(s):  
Elastic Modulus ◽  
Conjugated Polymers ◽  
Elastic Moduli ◽  
Luminescent Properties ◽  
Side Chains ◽  
Wide Range ◽  
Alkyl Side Chains ◽  
Red Luminescence

Bulky but flexible alkyl side chains enable π-conjugated polymers to possess wide-range elastic modulus tuneability, yet consistent red luminescent properties.

Coarse Aggregate Effects on Elastic Moduli of Concrete

1996 ◽  
Vol 1547 (1) ◽  
pp. 29-34 ◽  
Author(s):  
Bouzid Choubane ◽  
Chung-Lung Wu ◽  
Mang Tia
Keyword(s):  
Elastic Modulus ◽  
Dynamic Modulus ◽  
Laboratory Testing ◽  
Elastic Moduli ◽  
Coarse Aggregate ◽  
Textured Surface ◽  
Test Program ◽  
Static Modulus ◽  
Aggregate Effects ◽  
Strength And Stiffness

The results of a laboratory testing program carried out to investigate the effect of coarse aggregate types on the elastic modulus of typical pavement concretes are presented. The elastic modulus was determined in both flexure and compression using static and dynamic means. Three different mixes, made using three different aggregates, were compared. The water-cement ratio was kept at 0.53 throughout the test program. The results showed that within the tested range, the aggregate type significantly affected the studied properties of concrete. Calera aggregate (a dense limestone) with its rough-textured surface and angular shape produced a concrete with higher strength and stiffness than those of concretes made with Brooksville aggregate (a porous limestone) and river gravel. In addition, the measured dynamic modulus in compression was significantly different from that in flexure. Also, in flexure, the dynamic modulus was higher than the static modulus by an average of 23 percent, whereas in compression, the dynamic modulus appeared to be in the same range as the static modulus. The change in frequency from 1 to 7 Hz did not have a significant influence on the dynamic modulus.

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