On dissipated energy density in compression for concrete

2006 ◽  
Vol 73 (11) ◽  
pp. 1510-1530 ◽  
Author(s):  
Giuseppe Ferro
Keyword(s):  
Energy Density ◽  
Dissipated Energy

scholarly journals Explicit Q expressions for inhomogeneous P- and SV-waves in isotropic viscoelastic media

2019 ◽  
Vol 17 (2) ◽  
pp. 300-312 ◽  
Author(s):  
Xu Liu ◽  
Stewart Greenhalgh ◽  
Bing Zhou ◽  
Huijian Li
Keyword(s):  
Energy Density ◽  
Dissipation Factor ◽  
Energy Balance Equation ◽  
Dissipated Energy ◽  
P Waves ◽  
S Waves ◽  
Viscoelastic Media ◽  
Inhomogeneous Waves ◽  
Inhomogeneity Parameter ◽  
P And Sv Waves

Abstract We derive explicit expressions for the dissipation factors of inhomogeneous P and SV-waves in isotropic viscoelastic media. The Q−1 values are given as concise and simple functions of material parameters and the wave inhomogeneity parameter using two different definitions. Unlike homogenous waves, inhomogeneous waves may have significant differences in the values of dissipation factors because of different definitions. For example, under one of the three dissipation factor definitions that Q−1 is equal to the time-averaged dissipated-energy density divided by twice the time-averaged strain-energy density, it is found and proved that the dissipation factor of SV-waves is totally independent of the inhomogeneity parameter. For materials in which P-waves are normally more dissipative than S-waves (e.g. a porous reservoir), the dissipation factors of P-waves tend to decrease with increasing degree of inhomogeneity. Based on Buchan's classic real value energy balance equation, a parallel investigation is conducted for each step similar to that based on the Carcione equations, including derivation of explicit formulas (with inhomogeneity angle representing the degree of inhomogeneity of a plane wave), and dissipation curves calculations. We also obtain an inhomogeneity independent formula of $Q_{\, SV}^{ - 1}$, and exactly the same phase velocity and attenuation dispersion results for the example material.

On Energy Strength Theories for Geomaterials

2013 ◽  
Vol 353-356 ◽  
pp. 901-904
Author(s):  
Shou Yi Xue
Keyword(s):  
Energy Density ◽  
Shear Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Volumetric Strain ◽  
Dissipated Energy ◽  
Energy Theory ◽  
Shear Strain Energy ◽  
Shear Energy ◽  
Strain Energy Density Theory

The composition of the energy in the process of material deformation and failure and the relationship between energy and strength were summarized; the features, essences and main problems of the energy release rate theory, the three-shear energy theory and the net shear strain energy density theory were illustrated. It is pointed out that the roles of distortion strain energy, volumetric strain energy and dissipated energy are not identical, especially distortion strain energy and volumetric strain energy must be separately processed. The three-shear energy theory and the net shear strain energy density theory can properly deal with the problems, and also well reflect the intermediate principal stress effect. The above research results can provide references for further discussions.

scholarly journals Effect of Bedding Structure on the Energy Dissipation Characteristics of Dynamic Tensile Fracture for Water-Saturated Coal

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Shuang Gong ◽  
Lei Zhou ◽  
Zhen Wang ◽  
Wen Wang
Keyword(s):  
Particle Size ◽  
Energy Dissipation ◽  
Energy Density ◽  
Impact Velocity ◽  
Split Hopkinson Pressure Bar ◽  
Dissipated Energy ◽  
Tensile Fracture ◽  
Bedding Angle ◽  
Splitting Test ◽  
Water Saturated

The analysis of energy dissipation characteristics is a basic way to elucidate the mechanism of coal rock fragmentation. In order to study the energy dissipation patterns during dynamic tensile deformation damage of coal samples, the Brazilian disc (BD) splitting test under impact conditions was conducted on burst-prone coal samples using a split Hopkinson pressure bar (SHPB) loading system. The effects of impact velocity, bedding angle, and water saturated on the total absorbed energy density, total dissipated energy density, and damage variables of coal samples were investigated. In addition, the coal samples were collected after crushing to produce debris with particle sizes of 0-0.2 mm and 0.2-5 mm, and the distribution characteristics of different size debris were compared and analyzed. The results show that the damage variables of natural dry coal samples increase approximately linearly with the increase of impact velocity; however, the overall damage variables of saturated coal samples increase exponentially as a function of impact velocity. Compared with air-dry samples, the number of fragments with the particle size of 0-0.2 mm of saturated samples decreases by 14.1%-31.3%, and the number of fragments with the particle size of 0.2-5 mm decreases by 33.7%-53.0%. However, when the bedding angle is 45°, the percentage of fragment mass of saturated samples is larger than that of air-dry samples. The conclusions provide a theoretical basis for understanding the deterioration mechanism of coal after water saturation and the implementation of water injection dust prevention technology in coal mines.

Prediction of the Coating Durability Under Oscillating Sliding Contact: Introduction of a Local Energy Density Parameter

2005 ◽  
Author(s):  
S. Fouvry ◽  
V. Fridrici ◽  
T. Liskiewicz
Keyword(s):  
Energy Density ◽  
Industrial Applications ◽  
Sliding Contact ◽  
Hard Coatings ◽  
Dissipated Energy ◽  
Wear Volume ◽  
Density Parameter ◽  
Local Energy ◽  
Coating Durability ◽  
Local Energy Density

The knowledge of wear kinetics of thin soft lubricant or hard coatings under alternated sliding contact is of great interest for many industrial applications. Because the coating endurance is related to the substrate reaching condition, it has been shown that classical wear volume descriptions are not appropriated. A local damage description, based on a local friction dissipated energy density variable is then introduced. It consists to compare the coating endurance (i.e. number of sliding cycles) versus the maximum local energy density dissipated through the interface per sliding cycle. A “life time vs maximum dissipated energy density master curve” is obtained and rationalized through a parabolic evolution. The coating endurance is modelized through a simple ratio between an energy capacity variable, representative of the durability of the studied coating. Applied to hard coatings (TiN) the stability of this approach has been confirmed for solid lubricant coatings.

Inhomogeneous waves in isotropic anelastic media: explicit expressions for Q

2020 ◽  
Author(s):  
Xu Liu ◽  
Stewart Greenhalgh ◽  
Bing Zhou ◽  
Huijian Li
Keyword(s):  
Energy Balance ◽  
Energy Density ◽  
Phase Velocity ◽  
Plane Waves ◽  
Dissipation Factor ◽  
Dissipated Energy ◽  
Explicit Formulas ◽  
P Waves ◽  
S Waves ◽  
Inhomogeneous Waves

<p>Seismic waves propagating in attenuative materials are generally inhomogenous waves which, unlike homogeneous waves, have different directions of propagation and attenuation. The degree of wave inhomogeneity can be represented by the inhomogeneity parameter D which varies from 0 to infinity (Cerveny & Psencik, 2005). The dissipation (1/Q)  factors of   inhomogeneous waves vary according to the different definitions. Based on the complex energy balance equations (Carcione, 2001) and the mixed specification of the slowness vector (Cerveny & Psencik, 2005), explicit formulas for the dissipation factors of P- and SV-waves are developed under the two different definitions, (1) 1/Q<sub>V</sub>, the ratio of the time-averaged dissipated energy density to the time-averaged strain-energy density, and (2) 1/Q<sub>T</sub>, the time-averaged dissipated energy density to the time-averaged energy density. By setting the degree of wave inhomogeneity D as zero, these dissipation factor expressions are reduced to their special case versions as homogeneous waves, i.e., 1/Q<sub>VH</sub> = -Im(M)/Re(M) and 1/Q<sub>TH</sub> = 2α<em>v</em>/ω , where, M is the wave modulus, α the attenuation coefficient, <em>v</em> the phase velocity and ω the frequency. An example viscoelastic material is chosen to represent the dissipative features of a reservoir for which P-waves are normally more dissipative than S-waves. The calculated dissipation factors of P-waves under the two definitions (i.e. 1/Q<sub>PV</sub> and 1/Q<sub>PT</sub>) decrease with increasing degree of wave inhomogeneity. For the counterpart S waves, 1/Q<sub>SV</sub> is independent of the degree of wave inhomogeneity and 1/Q<sub>ST</sub> shows the trend of increasing with increasing degree of wave inhomogeneity. These findings can be explained by the limiting dissipation factors (defined at the infinite degree of inhomogeneity) which all depend only on the shear modulus.  To ensure the correctness of our results, we repeated each step of the investigation  in a parallel way based on Buchen’s (1971) classic real value energy balance equation, including derivation of explicit formulas for 1/Q<sub>PV</sub> and 1/Q<sub>PT</sub> , with inhomogeneity angle γ  ( -π/2 < γ < π/2) representing the degree of inhomogeneity of the plane wave. We also obtain the inhomogeneity-independent formula for 1/Q<sub>SV</sub>, and  exactly the same phase velocity and dissipation factor dispersion results for the example material.</p><p><strong>Acknowledgements</strong></p><p>We are grateful to the College of Petroleum Engineering & Geosciences, King Fahd University of Petroleum and Minerals, Kingdom of Saudi Arabia for supporting this research.</p><p><strong>References</strong></p><p>Buchen, P.W., 1971. Plane waves in linear viscoelastic media, Geophysical Journal of the Royal Astronomical Society, 23, 531-542.</p><p>Carcione, J. M., 2001. Wave fields in real media:Wave propagation in anisotropic, anelastic and porous media: Pergamon Press, Inc.</p><p>Cerveny, V. & Psencik, I., 2005. Plane waves in viscoelastic anisotropic media—I. Theory, Geophysical Journal International, 161, 197–212.</p>

Characterization of strain-induced damage in composites based on the dissipated energy density part I. Basic scheme and formulation

1995 ◽  
Vol 22 (2) ◽  
pp. 71-96 ◽  
Author(s):  
P.W. Mast ◽  
G.E. Nash ◽  
J.G. Michopoulos ◽  
R. Thomas ◽  
R. Badaliance ◽  
...  
Keyword(s):  
Energy Density ◽  
Dissipated Energy ◽  
Basic Scheme

Dissipated energy density as fatigue criterion for non-relaxing tensional loadings of non-crystallizing elastomers?

2019 ◽  
Vol 78 ◽  
pp. 105953 ◽  
Author(s):  
Oliver Gehrmann ◽  
Nils Hendrik Kröger ◽  
Maria Krause ◽  
Daniel Juhre
Keyword(s):  
Energy Density ◽  
Dissipated Energy ◽  
Fatigue Criterion

scholarly journals Study on Permeability of Deep-Buried Sandstone under Triaxial Cyclic Loads

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mingqiang Sheng ◽  
Awei Mabi ◽  
Xigen Lu
Keyword(s):  
Acoustic Emission ◽  
Cyclic Loading ◽  
Energy Density ◽  
Damage Variable ◽  
Dissipated Energy ◽  
Peak Strain ◽  
Rock Damage ◽  
Cyclic Loading And Unloading ◽  
Relative Strain ◽  
Loading And Unloading

The triaxial cyclic loading and unloading test was carried out on a TAW-2000 rock mechanics to study the permeability characteristics of deep-buried sandstone. This paper analyzed the evolution laws of permeability, elastic modulus, rock damage, dissipated energy, and acoustic emission events of sandstone under different confining pressures. It also introduced the concept of relative strain and further discussed the relationship between relative strain and permeability. The test results showed that the permeability of sandstone under cyclic loading and unloading obviously experienced three stages. At a low strain level, the damage degree of sandstone was low. As a result, both the number of acoustic emission events and the proportion of the dissipated energy density were small. In this stage, with increasing the stress, the permeability decreased. With the increase of the relative strain, the propagation of fissure increased through rock interior and the damage of rock was accumulated. Consequently, the number of acoustic emission events grew slowly, and the proportion of dissipated energy density and the damage variable (D) increased gradually. In this stage, the permeability increases. As the axial strain reached the peak strain, the fissures developed into cracks and the rock failure happened. The number of acoustic emission events increased rapidly; both the proportion of the dissipated energy density and the damage variable (D) obtain the maximum value. In this stage, the permeability increased greatly. In this study, the point of fissure propagation of rock specimens was used as the point of demarcation. Before the fissures propagated, the permeability increased slowly and it was in accordance with a linear function. After the fissures propagated, the degree of rock damage increased, and the permeability increased in the form of an exponential function. The larger the confining pressure was, the smaller the relative strain corresponding to the point of fissure propagation was.

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