scholarly journals Numerical Simulation of Unstable Rock Failure Mechanisms Through Analysis of Energy Transformations

2021 ◽  
Author(s):  
Rennie Kaunda ◽  
Fei Wang
Keyword(s):  
Plastic Strain ◽  
Elastic Strain ◽  
Strain Energy ◽  
Failure Modes ◽  
Numerical Models ◽  
Elastic Strain Energy ◽  
Rock Failure ◽  
Loading System ◽  
Rock Brittleness ◽  
Unstable Rock

Abstract For rock specimen in uniaxial compression, the energy transformations from elastic strain energy in both the rock and the loading system to plastic strain work in the rock can be identified with the changes in these energy components, whose rates are also useful indicators for distinguishing stable and unstable rock failure. In this study, the influences of the loading system stiffness (LSS), the rock stiffness and the rock brittleness on rock failure modes are examined. The observed energy transformations during rock failure in numerical models are interpreted from an energy perspective. The results show that unstable rock failure tends to occur in rock with large brittleness and small stiffness under a soft loading system. A low LSS and rock stiffness will increase the magnitude of stored elastic strain energy before rock failure, while a brittle rock requires less elastic strain energy to be converted plastic strain work than a ductile rock during its failure. This energy-based approach is useful for investigating potential unstable rock failures that could ultimately be applied to analyze complex mine-scale rockburst cases.

Zur Formulierung der Hypothese von der elastischen Formänderungsenergiedichte mit einer Erweiterung auf den elastisch-plastischen Bereich / Formulation of the elastic strain energy theory with an enlargement to the elastic-plastic range

1973 ◽  
Vol 28 (1) ◽  
pp. 35-45 ◽  
Author(s):  
J. Betten
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Elastic Potential ◽  
Plastic Range ◽  
Elastic Case ◽  
Elastic Plastic ◽  
Energy Theory

Contrary to the MISES' theory, the effort of materials under load is discussed in this paper on the base of the elastic potential. This leads to the elastic strain energy theory due to BELTRAMI. This theory is only true for the elastic case. For υ = 1/2 we obtain the MISES' theory, and by changing υ to υep it is possible to enlarge the elastic strain energy theory to the elastic-plastic deformation. υep is the ratio between transverse and longitudinal elastic-plastic strain, and υ is the POISSON's ratio.

scholarly journals Strain energy-and stress-based approaches revisited in notch fatigue of ductile steels

2018 ◽  
Vol 165 ◽  
pp. 14009 ◽  
Author(s):  
Bruno Atzori ◽  
Mauro Ricotta ◽  
Giovanni Meneghetti
Keyword(s):  
Energy Density ◽  
Plastic Strain ◽  
Strain Energy Density ◽  
Elastic Strain ◽  
Strain Energy ◽  
Elastic Strain Energy ◽  
Fatigue Behaviour ◽  
Strength Reduction Factor ◽  
Plastic Strain Energy ◽  
Elastic Strain Energy Density

The constant amplitude, zero-mean stress, axial-fatigue behaviour of plain and bluntly notched AISI 304 L stainless steel specimens is investigated in terms of strain energy density. Concerning plain material, it was found that at the fatigue knee the plastic strain energy density is 1.49 times higher than the elastic strain energy density. In the authors’ opinion, the presence of plasticity at the fatigue knee is responsible for the unsuitableness of classical stress - based approaches to synthesise the fatigue behaviour of this material. On the contrary, the elastic-plastic strain energy density was found an efficient parameter to rationalise in a single scatter band fatigue data of plain and bluntly notched specimens. Based on this result, the classic stress-and the point stress-based approaches were revisited taking into account the presence of plasticity at the fatigue knee, by introducing an equivalent fully elastic material having a linear elastic strain energy density at the fatigue knee equal to that of the actual material. Accordingly, a coefficient of plasticity Kp was successfully introduced to modify the classical definition of fatigue strength reduction factor, Kf.

scholarly journals An Energy Preservation Index for Evaluating the Rockburst Potential Based on Energy Evolution

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3636
Author(s):  
Lin Gao ◽  
Feng Gao ◽  
Yan Xing ◽  
Zhizhen Zhang
Keyword(s):  
Elastic Strain ◽  
Strain Energy ◽  
Failure Modes ◽  
Elastic Strain Energy ◽  
Rock Deformation ◽  
Energy Evolution ◽  
Deformation And Failure ◽  
Rock Materials ◽  
Energy Preservation ◽  
Evolution Characteristics

The estimation of rockburst potential has attracted great attention in the field of rock mechanics and engineering. In this study, an original energy preservation index is proposed to evaluate the rockburst potential in view of the energy evolution characteristics of rock materials. To investigate the energy evolution during rock deformation and failure, a number of cyclic uniaxial compression experiments on five kinds of rocks were carried out. The results showed that the curves of energy evolution exhibited obvious stages and there were significantly different weakening degrees for different rock materials embodied by the decreasing degrees of the ratios of elastic strain energy to dissipated strain energy at the weakening stage. Then, the energy preservation index was further formulated based on the decreasing ratio. Furthermore, by analyzing the acoustic emission activities at the failure stage and failure modes of the five rock materials, the rockburst potential was analyzed according to the energy preservation index.

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.

scholarly journals Ut vis sic tensio

2018 ◽  
Vol 45 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Elastic Strain ◽  
Strain Energy ◽  
Nonlinear Response ◽  
Solid Mechanics ◽  
Functional Form ◽  
Elastic Strain Energy ◽  
Strongly Nonlinear ◽  
Long Time

The mechanical properties of rubber-like materials have been offering an outstanding challenge to the solid mechanics community for a long time. The behaviour of such materials is quite difficult to predict because rubber self-organizes into mesoscopic physical structures that play a prominent role in determining their complex, history-dependent and strongly nonlinear response. In this framework one of the main problems is to find a functional form of the elastic strain-energy that best describes the experimental data in a mathematical feasible way. The aim of this paper is to give a survey of recent advances aimed at solving such a problem.

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