scholarly journals Unexpected power-law stress relaxation of entangled ring polymers

2008 ◽  
Vol 7 (12) ◽  
pp. 997-1002 ◽  
Author(s):  
M. Kapnistos ◽  
M. Lang ◽  
D. Vlassopoulos ◽  
W. Pyckhout-Hintzen ◽  
D. Richter ◽  
...  
Keyword(s):  
Stress Relaxation ◽  
Power Law ◽  
Ring Polymers

A Mechanical Equation of State for Inelastic Deformation of Iron: An Analytic Description

1977 ◽  
Vol 99 (1) ◽  
pp. 59-64 ◽  
Author(s):  
R. W. Rohde ◽  
J. C. Swearengen
Keyword(s):  
Equation Of State ◽  
Stress Relaxation ◽  
Power Law ◽  
Reaction Rate ◽  
Equations Of State ◽  
Analytic Description ◽  
Rate Theory ◽  
Predictive Capability ◽  
Reaction Rate Theory ◽  
The Relationship

The applicability of two familiar analytic descriptions of micromechanical deformation as equations of state for polycrystalline iron is discussed. These equations are the power law and the relationship based on reaction rate theory. It is shown that the reaction rate description fails to describe adequately individual stress relaxation events without invoking undue complexity from use of adjustable parameters. Moreover, even in that case, this formulation lacks the predictive capability required in an equation of state. Conversely, the power law is found not only to describe stress relaxation data properly but also to provide the capability of predicting stress relaxation following initial deformation by different loading paths. It thus appears to represent an equation of state for the material.

Role of Cytoskeletal Components in Stress-Relaxation Behavior of Adherent Vascular Smooth Muscle Cells

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
Jason D. Hemmer ◽  
Jiro Nagatomi ◽  
Scott T. Wood ◽  
Alexey A. Vertegel ◽  
Delphine Dean ◽  
...  
Keyword(s):  
Smooth Muscle ◽  
Stress Relaxation ◽  
Power Law ◽  
Relaxation Function ◽  
Cytochalasin D ◽  
Relaxation Behavior ◽  
Power Law Model ◽  
Stress Relaxation Behavior ◽  
Relaxation Experiments

A number of recent studies have demonstrated the effectiveness of atomic force microscopy (AFM) for characterization of cellular stress-relaxation behavior. However, this technique’s recent development creates considerable need for exploration of appropriate mechanical models for analysis of the resultant data and of the roles of various cytoskeletal components responsible for governing stress-relaxation behavior. The viscoelastic properties of vascular smooth muscle cells (VSMCs) are of particular interest due to their role in the development of vascular diseases, including atherosclerosis and restenosis. Various cytoskeletal agents, including cytochalasin D, jasplakinolide, paclitaxel, and nocodazole, were used to alter the cytoskeletal architecture of the VSMCs. Stress-relaxation experiments were performed on the VSMCs using AFM. The quasilinear viscoelastic (QLV) reduced-relaxation function, as well as a simple power-law model, and the standard linear solid (SLS) model, were fitted to the resultant stress-relaxation data. Actin depolymerization via cytochalasin D resulted in significant increases in both rate of relaxation and percentage of relaxation; actin stabilization via jasplakinolide did not affect stress-relaxation behavior. Microtubule depolymerization via nocodazole resulted in nonsignificant increases in rate and percentage of relaxation, while microtubule stabilization via paclitaxel caused significant decreases in both rate and percentage of relaxation. Both the QLV reduced-relaxation function and the power-law model provided excellent fits to the data (R2=0.98), while the SLS model was less adequate (R2=0.91). Data from the current study indicate the important role of not only actin, but also microtubules, in governing VSMC viscoelastic behavior. Excellent fits to the data show potential for future use of both the QLV reduced-relaxation function and power-law models in conjunction with AFM stress-relaxation experiments.

scholarly journals Oscillatory Microrheology, Creep Compliance and Stress Relaxation of Biological Cells Reveal Strong Correlations as Probed by Atomic Force Microscopy

2021 ◽  
Vol 9 ◽  
Author(s):  
D.A.D. Flormann ◽  
C. Anton ◽  
M.O. Pohland ◽  
Y. Bautz ◽  
K. Kaub ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Atomic Force Microscopy ◽  
Stress Relaxation ◽  
Optical Tweezers ◽  
Power Law ◽  
Creep Compliance ◽  
Culture Dish ◽  
Experimental Conditions ◽  
Force Microscopy ◽  
Atomic Force

The mechanical properties of cells are important for many biological processes, including wound healing, cancers, and embryogenesis. Currently, our understanding of cell mechanical properties remains incomplete. Different techniques have been used to probe different aspects of the mechanical properties of cells, among them microplate rheology, optical tweezers, micropipette aspiration, and magnetic twisting cytometry. These techniques have given rise to different theoretical descriptions, reaching from simple Kelvin-Voigt or Maxwell models to fractional such as power law models, and their combinations. Atomic force microscopy (AFM) is a flexible technique that enables global and local probing of adherent cells. Here, using an AFM, we indented single retinal pigmented epithelium cells adhering to the bottom of a culture dish. The indentation was performed at two locations: above the nucleus, and towards the periphery of the cell. We applied creep compliance, stress relaxation, and oscillatory rheological tests to wild type and drug modified cells. Considering known fractional and semi-fractional descriptions, we found the extracted parameters to correlate. Moreover, the Young’s modulus as obtained from the initial indentation strongly correlated with all of the parameters from the applied power-law descriptions. Our study shows that the results from different rheological tests are directly comparable. This can be used in the future, for example, to reduce the number of measurements in planned experiments. Apparently, under these experimental conditions, the cells possess a limited number of degrees of freedom as their rheological properties change.

Creep Behaviour of Closed Cell Aluminium Foams from Stress Relaxation Tests

2009 ◽  
Vol 423 ◽  
pp. 131-136 ◽  
Author(s):  
B. Carcel ◽  
A.C. Carcel ◽  
P. Arrué
Keyword(s):  
Stress Relaxation ◽  
Power Law ◽  
Creep Behaviour ◽  
Solid Material ◽  
Constant Load ◽  
Creep Tests ◽  
Closed Cell ◽  
Power Law Exponent ◽  
Order Of Magnitude ◽  
Power Law Creep

Creep behaviour of closed cell aluminium foams and transitions from power law to power law breakdown (PLB) creep regimes are investigated from results of stress relaxation tests (SRT) carried out on Alporas foams with densities between 0.20 to 0.32 g/cm3. Tests were carried out at temperatures between 200°C and 300°C and stress relaxation was measured from the collapse stress under compression of the foams. Under similar foam density, temperature and stress conditions, the values of strain rate calculated from SRT tests were of the same order of magnitude than those previously reported in the literature from conventional constant load creep tests. Under stress values close to the collapse stress, the creep mechanism seems to follow a PLB regime, with values of the power law exponent n=10-17, much higher than those corresponding to the power law creep in the solid material (n=4.4-6.5) and with activation energy values close to Q = 150 KJ/mol. Having in mind the limitations of available creep models for closed cell foams and the need for additional experimental results, the use of SRT testing would offer advantages for the assessment of the high temperature behaviour of aluminium foams, due to its lower testing times and reduced experimental effort.

scholarly journals Co-Entangled Actin-Microtubule Composites Exhibit Tunable Stiffness and Power-Law Stress Relaxation

2018 ◽  
Vol 115 (6) ◽  
pp. 1055-1067 ◽  
Author(s):  
Shea N. Ricketts ◽  
Jennifer L. Ross ◽  
Rae M. Robertson-Anderson
Keyword(s):  
Stress Relaxation ◽  
Power Law ◽  
Tunable Stiffness

scholarly journals On the identification of power-law creep parameters from conical indentation

2021 ◽  
Vol 477 (2252) ◽  
pp. 20210233
Author(s):  
Yupeng Zhang ◽  
Alan Needleman
Keyword(s):  
Stress Relaxation ◽  
Stress Exponent ◽  
Power Law ◽  
Exponential Factor ◽  
Creep Stress ◽  
Uniaxial Creep ◽  
Creep Stress Exponent ◽  
Power Law Creep ◽  
Good Agreement ◽  
Conical Indentation

Load and hold conical indentation responses calculated for materials having creep stress exponents of 1.15, 3.59 and 6.60 are regarded as input ‘experimental’ responses. A Bayesian-type statistical approach (Zhang et al. 2019 J. Appl. Mech. 86 , 011002 ( doi:10.1115/1.4041352 )) is used to infer power-law creep parameters, the creep exponent and the associated pre-exponential factor, from noise-free as well as noise-contaminated indentation data. A database for the Bayesian-type analysis is created using finite-element calculations for a coarse set of parameter values with interpolation used to create the refined database used for parameter identification. Uniaxial creep and stress relaxation responses using the identified creep parameters provide a very good approximation to those of the ‘experimental’ materials with stress exponents of 1.15 and 3.59. The sensitivity to noise increases with increasing stress exponent. The uniaxial creep response is more sensitive to the accuracy of the predictions than the uniaxial stress relaxation response. Good agreement with the indentation response does not guarantee good agreement with the uniaxial response. If the noise level is sufficiently small, the model of Bower et al. (1993 Proc. R. Soc. Lond. A 441 , 97–124 ()) provides a good fit to the ‘experimental’ data for all values of creep stress exponent considered, while the model of Ginder et al. (2018 J. Mech. Phys. Solids 112 , 552–562 ()) provides a good fit for a creep stress exponent of 1.15.

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