Thermodynamic restriction on the initial slope of the stress-relaxation function

Reinforcement compaction sometimes referred as consolidation process and is one of the key steps in various composite manufacturing processes such as autoclave and out-of-autoclave processing. The prepregs consist of semi-cured thermoset resin system impregnating the fibers. hence, the prepreg shows strong viscoelastic compaction response, which strongly depends on compaction speed and stress relaxation. modeling of time-dependent response is of utmost importance to understand the behavior of prepregs during different stages of composites manufacturing processes. The quasilinear viscoelastic (QLV) theory has been extensively used for the modeling of viscoelastic response of soft tissues in biomedical applications. In QLV approach, the stress relaxation can be expressed in terms of the nonlinear elastic function and the reduced relaxation function. The constitutive equation can be represented by a convolution integral of the nonlinear strain history, and reduced relaxation function. This study adopted a quasilinear viscoelastic modeling approach to describe the time dependent behavior of uncured-prepregs under compression. The model was modified to account for the compaction behavior of the prepreg under a compressive load. The deformation behavior of the prepreg is usually characterized by the fiber volume fraction, V . In this study, the material used was a 2/2 Twill weave glass prepreg (M26T) supplied by Hexcel® Industries USA. We performed a compaction experiment of the uncured prepreg at room temperature at different displacement rate and subsequent relaxation to describe the viscoelastic behavior of the prepreg. The model parameter calibration was performed using the trust-region-reflective algorithm in matlab to a selected number of test data. The calibrated model was then used to predict the rate dependent compaction and relaxation response of prepregs for different fiber volume fractions and strain rates.

Stress relaxation function of bone and bone collagen

Journal of Biomechanics ◽

10.1016/0021-9290(93)90088-v ◽

1993 ◽

Vol 26 (12) ◽

pp. 1369-1376 ◽

Cited By ~ 98

Author(s):

Naoki Sasaki ◽

Yoshinori Nakayama ◽

Makoto Yoshikawa ◽

Atsushi Enyo

Keyword(s):

Stress Relaxation ◽

Relaxation Function ◽

Bone Collagen

Master stress relaxation function of silica glasses

Journal of Non-Crystalline Solids ◽

10.1016/0022-3093(95)00588-9 ◽

1996 ◽

Vol 196 ◽

pp. 210-215 ◽

Cited By ~ 10

Author(s):

Jan P. van den Brink

Keyword(s):

Stress Relaxation ◽

Relaxation Function ◽

Silica Glasses

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

Journal of Biomechanical Engineering ◽

10.1115/1.3049860 ◽

2009 ◽

Vol 131 (4) ◽

Cited By ~ 15

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.

Dynamic Response of Immature Bovine Articular Cartilage in Tension and Compression, and Nonlinear Viscoelastic Modeling of the Tensile Response

Journal of Biomechanical Engineering ◽

10.1115/1.2206201 ◽

2006 ◽

Vol 128 (4) ◽

pp. 623-630 ◽

Cited By ~ 46

Author(s):

Seonghun Park ◽

Gerard A. Ateshian

Keyword(s):

Articular Cartilage ◽

Stress Relaxation ◽

Tensile Stress ◽

Dynamic Modulus ◽

Relaxation Function ◽

Tensile Modulus ◽

Relaxation Response ◽

Unconfined Compression ◽

Tensile Response ◽

Cyclical Loading

Very limited information is currently available on the constitutive modeling of the tensile response of articular cartilage and its dynamic modulus at various loading frequencies. The objectives of this study were to (1) formulate and experimentally validate a constitutive model for the intrinsic viscoelasticity of cartilage in tension, (2) confirm the hypothesis that energy dissipation in tension is less than in compression at various loading frequencies, and (3) test the hypothesis that the dynamic modulus of cartilage in unconfined compression is dependent upon the dynamic tensile modulus. Experiment 1: Immature bovine articular cartilage samples were tested in tensile stress relaxation and cyclical loading. A proposed reduced relaxation function was fitted to the stress-relaxation response and the resulting material coefficients were used to predict the response to cyclical loading. Adjoining tissue samples were tested in unconfined compression stress relaxation and cyclical loading. Experiment 2: Tensile stress relaxation experiments were performed at varying strains to explore the strain-dependence of the viscoelastic response. The proposed relaxation function successfully fit the experimental tensile stress-relaxation response, with R2=0.970±0.019 at 1% strain and R2=0.992±0.007 at 2% strain. The predicted cyclical response agreed well with experimental measurements, particularly for the dynamic modulus at various frequencies. The relaxation function, measured from 2% to 10% strain, was found to be strain dependent, indicating that cartilage is nonlinearly viscoelastic in tension. Under dynamic loading, the tensile modulus at 10Hz was ∼2.3 times the value of the equilibrium modulus. In contrast, the dynamic stiffening ratio in unconfined compression was ∼24. The energy dissipation in tension was found to be significantly smaller than in compression (dynamic phase angle of 16.7±7.4deg versus 53.5±12.8deg at 10−3Hz). A very strong linear correlation was observed between the dynamic tensile and dynamic compressive moduli at various frequencies (R2=0.908±0.100). The tensile response of cartilage is nonlinearly viscoelastic, with the relaxation response varying with strain. A proposed constitutive relation for the tensile response was successfully validated. The frequency response of the tensile modulus of cartilage was reported for the first time. Results emphasize that fluid-flow dependent viscoelasticity dominates the compressive response of cartilage, whereas intrinsic solid matrix viscoelasticity dominates the tensile response. Yet the dynamic compressive modulus of cartilage is critically dependent upon elevated values of the dynamic tensile modulus.

A Nonlinear Viscoelastic Model for the Relaxation Behavior of Tendon

ASME 2012 Summer Bioengineering Conference, Parts A and B ◽

10.1115/sbc2012-80050 ◽

2012 ◽

Author(s):

Frances M. Davis ◽

Raffaella De Vita

Keyword(s):

Stress Relaxation ◽

Relaxation Function ◽

Viscoelastic Model ◽

Viscoelastic Behavior ◽

Relaxation Behavior ◽

Successful Model ◽

Viscoelastic Models ◽

Nonlinear Viscoelastic ◽

Linear Viscoelastic ◽

Nonlinear Viscoelastic Model

Tendons are viscoelastic materials which undergo stress relaxation when held at a constant strain. The most successful model used to describe the viscoelastic behavior of tendons is the quasi-linear viscoelastic (QLV) model [1]. In the QLV model, the relaxation function is assumed to be a separable function of time and strain. Recently, this assumption has been shown to be invalid for tendons [2] thus suggesting the need for new nonlinear viscoelastic models.

Density dependence of the stress relaxation function of a simple fluid

Physical Review E ◽

10.1103/physreve.87.032155 ◽

2013 ◽

Vol 87 (3) ◽

Cited By ~ 19

Author(s):

Remco Hartkamp ◽

Peter J. Daivis ◽

B. D. Todd

Keyword(s):

Stress Relaxation ◽

Density Dependence ◽

Relaxation Function ◽

Simple Fluid

An expansion formula for fractional derivatives of variable order

Open Physics ◽

10.2478/s11534-013-0243-z ◽

2013 ◽

Vol 11 (10) ◽

Cited By ~ 7

Author(s):

Teodor Atanackovic ◽

Marko Janev ◽

Stevan Pilipovic ◽

Dusan Zorica

Keyword(s):

Stress Relaxation ◽

Constitutive Equation ◽

Relaxation Function ◽

Fractional Derivatives ◽

Variable Order ◽

Elementary Functions ◽

Expansion Formula ◽

Derivatives Of

AbstractIn this work we extend our previous results and derive an expansion formula for fractional derivatives of variable order. The formula is used to determine fractional derivatives of variable order of two elementary functions. Also we propose a constitutive equation describing a solidifying material and determine the corresponding stress relaxation function.

Development of a reduced relaxation function and comparison of stress relaxation for anatomically paired tendons

Journal of Mechanical Science and Technology ◽

10.1007/s12206-009-0504-3 ◽

2009 ◽

Vol 23 (7) ◽

pp. 1893-1898 ◽

Cited By ~ 1

Author(s):

Keyoung Jin Chun ◽

Robert P. Hubbard

Keyword(s):

Stress Relaxation ◽

Relaxation Function ◽

Anatomically Paired