scholarly journals Study on Energy Evolution and Damage Constitutive Model of Siltstone

Crystals ◽  
2021 ◽  
Vol 11 (11) ◽  
pp. 1271
Author(s):  
Ruihe Zhou ◽  
Longhui Guo ◽  
Rongbao Hong
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Yield Criterion ◽  
Axial Strain ◽  
Elastic Strain Energy ◽  
Confining Pressure ◽  
Energy Yield ◽  
Input Energy ◽  
Test Results ◽  
Damage Constitutive Model

In order to study the energy evolution characteristics and damage constitutive relationship of siltstone, the conventional triaxial compression tests of siltstone under different confining pressures are performed, and the evolution laws of input energy, elastic strain energy and dissipative energy of siltstone with axial strain and confining pressure are analyzed. According to the test results, the judgment criterion of the rock damage threshold is improved, and an improved three-shear energy yield criterion is proposed., The damage constitutive equation of siltstone is established based on the damage mechanics theory through the principle of minimum energy consumption and by considering the residual strength of rock, and lastly, the rationality of the model is verified by experimental data. The results reveal that (1) both the input energy and dissipative energy gradually increase with the increase of axial strain, and the elastic strain energy first increases and then decreases with the increase of axial strain, and reaches its maximum at the peak. (2) The input energy and dissipation energy increase exponentially with the increase of the confining pressure, and the elastic strain energy increases linearly with the increase of confining pressure. (3) According to the linear relationship between the sum of shear strain energy and hydrostatic pressure, an improved three-shear energy yield criterion is established. (4) The model curve can better describe the strain softening stage and the residual strength characteristics of siltstone. The relative standard deviation between the model results and the test results is only 4.35%, which verifies the rationality and feasibility of the statistical damage constitutive model that is established in this paper.

scholarly journals Study on the Meso-Energy Damage Evolution Mechanism of Single-Joint Sandstone under Uniaxial and Biaxial Compression

2021 ◽  
Vol 2021 ◽  
pp. 1-27
Author(s):  
Gui-Lin Wang ◽  
Tian-Ci Cao ◽  
Fan Sun ◽  
Xing-Xiang Wen ◽  
Liang Zhang
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Confining Pressure ◽  
Biaxial Compression ◽  
Level Energy ◽  
Energy Evolution ◽  
Peak Point ◽  
Joint Inclination ◽  
Joint Length

Energy conversion and release occur through the entire deformation and failure process in jointed rock masses, and the accumulation and dissipation of rock mass energy in engineering can reveal the entire process of deformation and instability. This study uses PFC2D to carry out numerical simulation tests on single-joint sandstone under uniaxial compression and biaxial compression, respectively, and analyse the influence of joint inclination, length, and confining pressure on the meso-energy conversion process and phase evolution of jointed sandstone. Through analysis, it is found that the input meso total strain energy is transformed into meso dissipated energy and meso-elastic strain energy. Macroscopic and microscopic joint sandstone law is consistent with the overall energy evolution; and the difference is reflected in two aspects: (1) the microlevel energy evolution has no initial compaction energy consumption section and (2) the linear energy storage section before the macroenergy evolution peak can be subdivided into two sections in the meso-level energy evolution. Under uniaxial compression, the energy values at the characteristic points of the meso-level energy evolution phases first asymmetrically decrease and then increase with the increase of the joint inclination. The initiation point of jointed sandstone is significantly affected by the length of the joint, and the degradation effect of the meso-energy at the damage point and peak point weakens with the increase of the joint length. Comparing the data obtained from the PFC numerical simulation with the experimental data, it is found that the error is small, which shows the feasibility of the numerical model in this paper. Under biaxial compression, the accumulation rate of meso-elastic strain at the peak point of the jointed sandstone first decreases and then increases with the joint inclination angle. After the peak of jointed sandstone, the rate of sudden change of meso-energy change decreases with the increase of joint length. The conditions of high confining pressure will promote the meso-accumulated damage degree of the jointed sandstone before the peak, while inhibiting the meso-energy and the mutation degree of the damage after the peak. The higher the confining pressure, the more obvious the joint length and inclination effect characteristics of the elastic strain energy at the peak point of the jointed sandstone.

scholarly journals Experimental Investigation of Early-Warning Critical Energy for Strainbursts

2021 ◽  
Author(s):  
Wang Ling ◽  
Ruyu Yan ◽  
Zhang zhi ◽  
Xie Lei ◽  
Huang chuhui
Keyword(s):  
Acoustic Emission ◽  
Energy Dissipation ◽  
Early Warning ◽  
Elastic Strain ◽  
Strain Energy ◽  
Triaxial Compression ◽  
Elastic Strain Energy ◽  
Critical Energy ◽  
Input Energy ◽  
Energy Evolution

Abstract This research aimed to establish an early-warning critical energy for coal instability based on the energy theory and acoustic emission characteristics of coal under triaxial compression. To obtain an early-warning critical strain energy indicating the increase in the risk of coal instability, conventional triaxial compression and acoustic emission (AE) tests were carried out on coal specimens taken from a 980-m-deep mine with initial confining pressures of 10, 15, 20, 25, 30 and 35 MPa. Stress-strain relations, AE features, and energy evolution characteristics during triaxial compression were analyzed. It was found that the energy evolution and AE event count changes across different loading stages. With increasing axial stress, most of the input energy stored in the coal specimens was in the form of elastic strain energy and the AE event count was close to zero, indicating that the coal grains reach a state of balance. After the elastic deformation stage, a portion of the input energy was consumed by inelastic deformation. Once the stress level exceeded the volumetric compressibility–dilatancy transition stress, the AE event entered a period of relative quiet, and the rate of energy dissipation abruptly accelerated, indicating that the coal grains achieved another state of balance before THE instability or failure. The balance of the rock grains is broken again (AE event count and the rate of energy dissipation both increased dramatically), coal achieved the peak strength and instability soon. The point at which the dissipated energy ratio α increased rapidly or the starting point of a quiet period, indicates an increase in the risk of coal instability. The corresponding elastic strain energy accumulated within the coal can be regarded as a precursor to instability or strainburst. Accordingly, a fitting formula is presented to predict the early-warning critical energy for brittle coal subject to different minimum principal stress. The analysis results in this paper can be helpful in the assessment of coal instability risk.

scholarly journals Discussions on the Complete Strain Energy Characteristics of Deep Granite and Assessment of Rockburst Tendency

2020 ◽  
Vol 2020 ◽  
pp. 1-9 ◽  
Author(s):  
Lu Chen ◽  
Lijie Guo
Keyword(s):  
Time Delay ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Confining Pressure ◽  
Strain Effect ◽  
Peak Strain ◽  
Rockburst Hazard ◽  
Linear Elastic ◽  
Loading And Unloading

In deep mining, the rockburst hazard has become a prominent problem. Rockburst is difficult to be predicted, and it gives a severe threat to mining safety. In this paper, the triaxial compressive tests with an acoustic emission (AE) device and full cyclic loading and unloading tests were carried out, respectively, to present characteristics of linear elastic strain energy and peak strain energy. Also, to consider the time-delay strain characteristics of granite found in the abovementioned tests, a new stage loading and unloading test with dual monitoring systems was designed and performed. Through 20 days’ time-delay strain monitoring, the peak-strength strain energy was further modified. The results showed that the peak strain energy is approximate 1.2-1.3 times than linear elastic strain energy under the same confining pressure, and after considering the time-delay strain effect, the modified maximal strain energy value of the deep granite significantly increased. The peak strain energy values are further enhanced from 1.0 × 104 J/m3 to 1.8 × 104 J/m3, respectively. At last, by taking advantage of the strain energy index model of rockburst, the tendency and intensity of rockburst were assessed contrastively.

scholarly journals Experimental Investigation on Deformation and Strength Behavior of Marble with the Complex Loading-Unloading Stress Path

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Chen Chen ◽  
Lipeng Liu ◽  
Yu Cong
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
High Stress ◽  
Elastic Strain Energy ◽  
Complex Loading ◽  
Energy Criterion ◽  
Confining Pressure ◽  
Stress Path ◽  
Surrounding Rock ◽  
Strength Behavior

The excavation of deep tunnel in rock mass undergoes complex loading and unloading stress paths, resulting in rib spalling, flaking, and even severe rockburst disasters. Based on the variation law of the stress path of the surrounding rock, laboratory tests of rock mechanics are designed, and the deformation and strength behavior of marble with different initial confining pressure and unloading rates are systematically studied. By introducing strain increment, the characteristic stress, and the dilatancy index, the rock’s dilatancy and brittleness under different unloading conditions are quantitatively analyzed. During unloading, the energy transformation mechanism of rock is described, and the law of deformation and failure is discussed based on characteristic energy. The rock failure strength fitting formula is given by applying the Mogi–Coulomb criterion and elastic strain energy criterion. The advantages of the elastic strain energy criterion are theoretically explained. This study shows that comprehensive consideration of the complex stress paths, confining pressure levels, and the loading-unloading rates of surrounding rock is an effective way to accurately study unloading rock characteristics. The results can provide theoretical basis for stability analysis of high-stress underground engineering.

Do muscles function as adaptable locomotor springs?

2002 ◽  
Vol 205 (15) ◽  
pp. 2211-2216 ◽  
Author(s):  
Stan L. Lindstedt ◽  
Trude E. Reich ◽  
Paul Keim ◽  
Paul C. LaStayo
Keyword(s):  
Skeletal Muscle ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Normal Animal ◽  
Eccentric Contractions ◽  
Normal Muscle ◽  
Energetic Costs ◽  
Locomotor Muscles ◽  
Power Outputs

SUMMARYDuring normal animal movements, the forces produced by the locomotor muscles may be greater than, equal to or less than the forces acting on those muscles, the consequences of which significantly affect both the maximum force produced and the energy consumed by the muscles. Lengthening (eccentric)contractions result in the greatest muscle forces at the lowest relative energetic costs. Eccentric contractions play a key role in storing elastic strain energy which, when recovered in subsequent contractions, has been shown to result in enhanced force, work or power outputs. We present data that support the concept that this ability of muscle to store and recover elastic strain energy is an adaptable property of skeletal muscle. Further, we speculate that a crucial element in that muscle spring may be the protein titin. It too seems to adapt to muscle use, and its stiffness seems to be`tuned' to the frequency of normal muscle use.

The Elastostatic Axisymmetric Problem of a Cracked Sphere Embedded in a Dissimilar Matrix

1980 ◽  
Vol 47 (3) ◽  
pp. 545-550 ◽  
Author(s):  
R. Kant ◽  
D. B. Bogy
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Companion Paper ◽  
Infinite Medium ◽  
Applied Mechanics ◽  
Axisymmetric Solution ◽  
Material Parameters ◽  
The Difference ◽  
Elastostatic Problem

The axisymmetric elastostatic problem of a cracked sphere embedded in a dissimilar matrix is solved by using the solution for a spherical cavity in an infinite medium together with the axisymmetric solution for a cracked sphere given in the companion paper in this issue of the Journal of Applied Mechanics, Pages 538-544. Numerical results are presented for (a) interface stress for various composites (b) dependence of the stress-intensity factor on the material parameters and ratios of crack to sphere radii, (c) the difference in the elastic strain energy for a cracked and uncracked composite.

scholarly journals Effect of Joint Density on Rockburst Proneness of the Elastic-Brittle-Plastic Rock Mass

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jiliang Pan ◽  
Fenhua Ren ◽  
Meifeng Cai
Keyword(s):  
Rock Mass ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Jointed Rock ◽  
Jointed Rock Mass ◽  
Joint Density ◽  
Dissipated Energy ◽  
Uniaxial Compression Test ◽  
Plastic Rock

The prediction of rockburst proneness is the basis of preventing and controlling rockburst disasters in rock engineering. Based on energy theory and damage mechanics, the quantitative functional relationship between joint density and energy density was derived. Then, the theoretical results were verified by numerical simulation and uniaxial compression test, and the effect of joint density on rockburst proneness of the elastic-brittle-plastic rock mass was discussed. The results show that the relationship between the joint density and the dissipated energy index of the jointed rock mass is a logarithmic function. With the same total input energy, the higher the joint density, the more the damage dissipation energy. Even in the case of high joint density, the rock mass still has limited resistance to external failure. Under the same joint density, the strength of parallel jointed rock mass is better than that of the cross-jointed rock mass, and the parallel jointed rock mass can accumulate more elastic strain energy and has higher rockburst proneness. The joint density is closely related to the ability of the rock mass to store high strain energy. The higher the joint density is, the weaker the ability to accumulate the elastic strain energy of rock mass is and the lower the rockburst proneness is. It is helpful to predict rockburst proneness by investigating and studying the properties of geological discontinuities. The research results have some theoretical and engineering guiding significance for the prediction of rockburst proneness of the jointed rock mass.

scholarly journals Dynamic Stability Critical State of Pin-Ended Arches under Sudden Central Concentrated Load

Mechanika ◽  
2020 ◽  
Vol 26 (5) ◽  
Author(s):  
Kai QIN ◽  
Jingyuan LI ◽  
Mengsha LIU ◽  
Jinsan JU
Keyword(s):  
Finite Element ◽  
Critical Load ◽  
Critical State ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
The State ◽  
Energy Principle ◽  
Concentrated Load ◽  
Elastic Plastic

The dynamic in-plane instability process of extreme point type for pin-ended arches when a central radial load applied suddenly with infinite duration is analyzed with finite element method in this study. The state of arch can be determined by the crown’s vertical displacement varied with time and the critical load can be obtained by repeating trial-calculation. When the arch structure reaches the dynamically stable critical state, the kinetic energy of the structure is very small or even zero. The dynamic critical load of elastic arch calculated with the theoretical analysis method which is based on energy principle is proved accuracy enough by comparing with the finite element calculation results and the percentage of the differences between them are no more than 4.5 %. The maximal elastic strain energy is certain for the elastic-plastic arch in certain geometry under both a sudden load and static load. The maximal elastic strain energy in static calculation can be used in determining the state of the elastic-plastic arch under dynamic sudden loads applied and this method is more accurate which errors won’t exceed 3.5 %. The accuracy of dynamic critical load calculation method for elastic arch is verified by numerical calculation in this study, and based on the characteristic of elastic strain energy in critical state, a method for determining the stability of elastic-plastic arch is presented.

Sign in / Sign up

Export Citation Format

Share Document