Nonlinear viscoelastic behavior of sedimentary rocks, Part I: Effect of frequency and strain amplitude

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 184-194 ◽  
Author(s):  
Azra N. Tutuncu ◽  
Augusto L. Podio ◽  
Alvin R. Gregory ◽  
Mukul M. Sharma
Keyword(s):  
Strain Amplitude ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Viscoelastic Behavior ◽  
Uniaxial Stress ◽  
Companion Paper ◽  
Elastic Behavior ◽  
Amplitude Dependence ◽  
Frequency Measurements ◽  
Young’S Moduli

Sedimentary rocks display nonlinear elastic behavior. This nonlinearity is a strong function of frequency, strain amplitude, and the properties of the saturating fluid. Experimental observations and potential mechanisms that cause these nonlinearities are presented in this and a companion paper. Young’s moduli and Poisson’s ratios obtained from ultrasonic laboratory measurements (50 kHz, 100 kHz, 180kHz and 1 MHz), low‐frequency measurements (1–2000 Hz) and static measurements (0.001–0.05 Hz) show significant differences under identical stress conditions. A comparison of the laboratory‐measured quantities with log‐derived moduli measured at 20 kHz indicates that [Formula: see text]. This shows clearly that a wide variety of sandstones demonstrate frequency‐dependent elastic behavior (viscoelastic behavior) over a range of frequencies. Differences between static (low‐frequency, high‐strain amplitude) velocities and ultrasonic velocities can be explained partially by differences in frequency as predicted by grain contact models. Such models, however, do not explain the strain amplitude dependence observed in our data. A series of uniaxial stress cycling measurements were carried out to investigate the influence of strain amplitude on elastic moduli. These low‐frequency measurements (0.01 Hz) clearly show that the Young’s modulus decreases with strain amplitude for a wide variety of sandstones. Attenuation increases with strain amplitude. The strain amplitude dependence does not change when the rocks are saturated with brine although the rocks soften measureably.

Nonlinear viscoelastic behavior of sedimentary rocks, Part II: Hysteresis effects and influence of type of fluid on elastic moduli

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 195-203 ◽  
Author(s):  
Azra N. Tutuncu ◽  
Augusto L. Podio ◽  
Mukul M. Sharma
Keyword(s):  
Strain Amplitude ◽  
Elastic Moduli ◽  
Pore Space ◽  
Viscoelastic Behavior ◽  
Uniaxial Stress ◽  
Amplitude Dependence ◽  
Stress Strain ◽  
Stick Slip ◽  
Young’S Moduli ◽  
Tangent Moduli

Uniaxial stress cycling experiments were conducted on dry, brine saturated and hexadecane saturated Berea sandstone samples to observe in detail the hysteresis in stress‐strain diagrams and to understand the influence of different fluids on the strain amplitude dependence of elastic moduli and attenuation. Cycling experiments were also conducted with sandstone samples saturated with CTAB, a cationic surfactant that renders the mineral surfaces hydrophobic. Hexadecane and CTAB were selected so as to investigate the relative contributions of adhesion hysteresis and stick‐slip sliding on attenuation in sedimentary granular rocks. Young’s moduli and Poisson’s ratios obtained from the cycling tests show a significant dependence on strain amplitude on dry as well as water and hexadecane saturated samples. Bow‐tie‐shaped diagrams are obtained when loading and unloading tangent moduli are plotted against strain. The type of fluid in the pore space and at the grain contacts has a large influence on the hysteresis observed in the stress‐strain diagrams.

Binder/Filler Interaction and the Nonlinear Behavior of Highly-Filled Elastomers

1990 ◽  
Vol 63 (4) ◽  
pp. 488-502 ◽  
Author(s):  
R. G. Stacer ◽  
C. Hübner ◽  
D. M. Husband
Keyword(s):  
Surface Area ◽  
Strain Amplitude ◽  
Nonlinear Response ◽  
Volume Fraction ◽  
Viscoelastic Behavior ◽  
Interaction Model ◽  
Nonlinear Behavior ◽  
Small Deformation ◽  
Amplitude Dependence ◽  
Filled Rubbers

Abstract 1. The small-deformation-viscoelastic response of elastomers containing nonreinforcing filler has been investigated. Nonlinear viscoelastic behavior was observed as a pronounced strain-amplitude dependence. The degree of this dependence was quantified using a power-law representation as a single nonlinear parameter, m. 2. The magnitude of m was a function of formulation variables. It was found that m increased with the volume fraction and particle size of filler material, as well as the volume fraction of plasticizer. Reduced values of m were observed in the presence of bonding agent and with greater degrees of apparent crosslinking. The latter was controlled in this study through imbalanced urethane cures. 3. Nonlinear behavior of elastomers containing nonreinforcing filler has been compared and contrasted with the data base for carbon-black-reinforced elastomers. The major difference is in the effect of the surface area of filler particles. Nonlinear response in black-filled rubbers increases with surface area, while the opposite is reported in this study. Additionally, the relationship between viscoelastic dissipation and the magnitude of nonlinear response, well established for black-filled rubbers, was not observed. These results indicate that the response of elastomers containing nonreinforcing filler, although nearly identical in appearance to that seen with reinforcing filler, is not driven by the same mechanism. 4. A binder/filler interaction model is proposed for materials containing nonreinforcing filler. This model is based on the ideal adhesive strength of the binder/filler interface. In this model, greater attraction between polymer and particle surfaces reduces molecular slippage during deformation, leading to a decreased dependence of the modulus on strain amplitude, or decreased nonlinearity. It is shown that the model provides reasonable predictions for the observed phenomena.

Strain Amplitude Dependence of Damping Capacity in High Damping Mg-Based Alloys Continuously Extending to Microplastic Strain

2010 ◽  
Vol 97-101 ◽  
pp. 937-940
Author(s):  
Di Qing Wan ◽  
Bo Lin He ◽  
Jin Cheng Wang ◽  
Gen Cang Yang
Keyword(s):  
Strain Amplitude ◽  
Low Frequency ◽  
Microplastic Deformation ◽  
Damping Capacity ◽  
Amplitude Dependence ◽  
Two Stage ◽  
Microplastic Strain ◽  
Damping Behavior ◽  
Dependent Part ◽  
Weakly Dependent

An investigation on low frequency strain amplitude dependence damping characteristic of as-cast high damping Mg-based alloys continuously extending to microplastic strain was carried out. Two-stage damping behavior via strain amplitude was particularly reported. The first is the strain amplitude strongly dependent part due to breakaway loss and the second is the strain amplitude weakly dependent part due to microplastic deformation loss, which is also frequency dependent. The damping mechanism is discussed in detail.

Influence of the Creep Effect on the Low-Frequency Measurements of the Elastic Moduli of Sedimentary Rocks

2019 ◽  
Author(s):  
R. Chavez ◽  
V. Mikhaltsevitch ◽  
M. Lebedev ◽  
B. Gurevich ◽  
E. Vargas ◽  
...  
Keyword(s):  
Elastic Moduli ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Frequency Measurements ◽  
Creep Effect

scholarly journals Anisotropic and age-dependent elastic material behavior of the human costal cartilage

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matthias Weber ◽  
Markus Alexander Rothschild ◽  
Anja Niehoff
Keyword(s):  
Costal Cartilage ◽  
Indentation Test ◽  
Biomechanical Properties ◽  
Material Behavior ◽  
Cartilage Tissue ◽  
Elastic Behavior ◽  
Unconfined Compression ◽  
Unconfined Compression Test ◽  
Young’S Moduli ◽  
Age Related

AbstractCompared to articular cartilage, the biomechanical properties of costal cartilage have not yet been extensively explored. The research presented addresses this problem by studying for the first time the anisotropic elastic behavior of human costal cartilage. Samples were taken from 12 male and female cadavers and unconfined compression and indentation tests were performed in mediolateral and dorsoventral direction to determine Young’s Moduli EC for compression and Ei5%, Ei10% and Eimax at 5%, 10% and maximum strain for indentation. Furthermore, the crack direction of the unconfined compression samples was determined and histological samples of the cartilage tissue were examined with the picrosirius-polarization staining method. The tests revealed mean Young’s Moduli of EC = 32.9 ± 17.9 MPa (N = 10), Ei5% = 11.1 ± 5.6 MPa (N = 12), Ei10% = 13.3 ± 6.3 MPa (N = 12) and Eimax = 14.6 ± 6.6 MPa (N = 12). We found that the Young’s Moduli in the indentation test are clearly anisotropic with significant higher results in the mediolateral direction (all P = 0.002). In addition, a dependence of the crack direction of the compressed specimens on the load orientation was observed. Those findings were supported by the orientation of the structure of the collagen fibers determined in the histological examination. Also, a significant age-related elastic behavior of human costal cartilage could be shown with the unconfined compression test (P = 0.009) and the indentation test (P = 0.004), but no sex effect could be detected. Those results are helpful in the field of autologous grafts for rhinoplastic surgery and for the refinement of material parameters in Finite Element models e.g., for accident analyses with traumatic impact on the thorax.

Mechanical monolithic tiltmeter for low frequency measurements

2012 ◽  
Author(s):  
F. Acernese ◽  
R. Canonico ◽  
R. De Rosa ◽  
G. Giordano ◽  
R. Romano ◽  
...  
Keyword(s):  
Low Frequency ◽  
Frequency Measurements

scholarly journals Kinetic extraordinary-mode eigenvalue equation for relativistic nonneutral electron flow in planar geometry

1989 ◽  
Vol 7 (1) ◽  
pp. 55-84 ◽  
Author(s):  
Ronald C. Davidson ◽  
Han S. Uhm
Keyword(s):  
Electron Flow ◽  
Low Frequency ◽  
Companion Paper ◽  
Field Configuration ◽  
Outer Edge ◽  
Eigenvalue Equation ◽  
Planar Geometry ◽  
Canonical Momentum ◽  
Stability Properties ◽  
Long Wavelength

Use is made of the Vlasov–Maxwell equations to derive an eigenvalue equation describing the extraordinary–mode stability properties of relativistic, non-neutral electron flow in high-voltage diodes. The analysis is based on well-established theoretical techniques developed in basic studies of the kinetic equilibrium and stability properties of nonneutral plasmas characterized by intense self fields. The formal eigenvalue equation is derived for extraordinary-mode flute perturbations in a planar diode. As a specific example, perturbations are considered about the choice of self-consistent Vlasov equilibrium , where . is the electron density at the cathode (x = 0), H is the energy, and Py is the canonical momentum in the Y-direction (the direction of the equilibrium electron flow). As a limiting case, the planar eigenvalue equation is further simplified for low-frequency long-wavelength perturbations with |ω − kvd, ≪ ωυ where and and ⋯c = eB0/mc, and B0ệz is the applied magnetic field in the vacuum region xb < x ≤ d. Here, the outer edge of the electron layer is located at x = xb; ω is complex oscillation frequency; k is the wavenumber in the y-direction; ωυ is the characteristic betatron frequency for oscillations in the x′-orbit about the equilibrium value x′ = x0 = xb/2; and Vd is the average electron flow velocity in the y-direction at x = x0. In simplifying the orbit integrals, a model is adopted in which the eigenfunction approximated by , where x′(t′) is the x′-orbit in the equilibrium field configuration. A detailed analysis of the resulting eigenvalue equation for , derived for low-frequency long-wavelength perturbations, is the subject of a companion paper.

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