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Journal articles on the topic 'Griffith's criterion'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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1

NEGRI, MATTEO, and CHRISTOPH ORTNER. "QUASI-STATIC CRACK PROPAGATION BY GRIFFITH'S CRITERION." Mathematical Models and Methods in Applied Sciences 18, no. 11 (2008): 1895–925. http://dx.doi.org/10.1142/s0218202508003236.

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We consider the propagation of a crack in a brittle material along a prescribed crack path and define a quasi-static evolution by means of stationary points of the free energy. We show that this evolution satisfies Griffith's criterion in a suitable form which takes into account both stable and unstable propagations, as well as an energy balance formula which accounts for dissipation in the unstable regime. If the load is monotonically increasing, this solution is explicit and almost everywhere unique. For more general loads we construct a solution via time discretization. Finally, we consider

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2

Zhao, Yishu. "Griffith's criterion for mixed mode crack propagation." Engineering Fracture Mechanics 26, no. 5 (1987): 683–89. http://dx.doi.org/10.1016/0013-7944(87)90133-0.

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3

Akash, Tanmay Sarkar, Rafsan A. S. I. Subad, Pritom Bose, and Md Mahbubul Islam. "Nanomechanics of antimonene allotropes under tensile loading." Physical Chemistry Chemical Physics 23, no. 10 (2021): 6241–51. http://dx.doi.org/10.1039/d0cp05563h.

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Mechanical properties of monolayer antimonene been investigated with molecular dynamics simulations. A crackline stress distribution based fracture toughness calculation is established as a method to compare with Griffith's criterion for highly brittle 2D materials.

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4

Sato, Tamao, and Hiroo Kanamori. "Beginning of earthquakes modeled with the Griffith's fracture criterion." Bulletin of the Seismological Society of America 89, no. 1 (1999): 80–93. http://dx.doi.org/10.1785/bssa0890010080.

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Abstract We present a source model for the beginning of earthquakes based on the Griffith's fracture criterion. The initial state is a critical state of pre-existing circular fault, which is on the verge of instability. After the onset of instability, the fault grows with a progressively increasing rupture speed, satisfying the condition of fracture energy balance at the crack tip. We investigate the difference in rupture growth patterns in two classes of models that are considered to represent end-member cases. In the first model (Spontaneous model), we assume that the surface energy varies s

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5

Popov, Valentin. "Energetic criterion for adhesion in viscoelastic contacts with non-entropic surface interaction." Reports in Mechanical Engineering 2, no. 1 (2021): 57–64. http://dx.doi.org/10.31181/rme200102057p.

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We suggest a detachment criterion for a viscoelastic elastomer contact based on Griffith's idea about the energy balance at an infinitesimal advancement of the boundary of an adhesive crack. At the moment of detachment of a surface element at the boundary of an adhesive contact, there is some quick (instant) relaxation of stored elastic energy which can be expressed in terms of the creep function of the material. We argue that it is only this "instant part" of stored energy which is available for doing work of adhesion and thus it is only this part of energy relaxation that must be used in Gri

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6

KNEES, DOROTHEE, ALEXANDER MIELKE, and CHIARA ZANINI. "ON THE INVISCID LIMIT OF A MODEL FOR CRACK PROPAGATION." Mathematical Models and Methods in Applied Sciences 18, no. 09 (2008): 1529–69. http://dx.doi.org/10.1142/s0218202508003121.

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We study the evolution of a single crack in an elastic body and assume that the crack path is known in advance. The motion of the crack tip is modeled as a rate-independent process on the basis of Griffith's local energy release rate criterion. According to this criterion, the system may stay in a local minimum before it performs a jump. The goal of this paper is to prove the existence of such an evolution and to shed light on the discrepancy between the local energy release rate criterion and models which are based on a global stability criterion (as for example the Francfort/Marigo model). W

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7

Einav, Itai. "Fracture propagation in brittle granular matter." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2087 (2007): 3021–35. http://dx.doi.org/10.1098/rspa.2007.1898.

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It is nearly a century since Alan Arnold Griffith developed his energy criterion for the fracture propagation of cracks in ‘near-continuous’ solids. Needless to say that his celebrated work has revolutionized the world of material science. In a very succinct way, Griffith connected between three important aspects of the fracture process: (i) the material, (ii) the stress level, and (iii) the geometry of the crack. Nothing similar was developed for brittle granular matter, although in these materials fracture propagates in the sense of comminution. Recently, I have developed an energy theory, c

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8

MORI, Takahisa, and Hisashi TOKUTOMI. "TRIAXIAL AND BIAXIAL COMPRESSIVE STRENGTHS OF CONCRETE BY "MENNODO" CONCEPT APPLYING THE GRIFFITH'S FRACTURE CRITERION." Journal of Structural and Construction Engineering (Transactions of AIJ) 68, no. 569 (2003): 9–13. http://dx.doi.org/10.3130/aijs.68.9_4.

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9

Kendall, Kevin. "Energizing ASTM lap joint fracture standards." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2203 (2021): 20200287. http://dx.doi.org/10.1098/rsta.2020.0287.

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Several ASTM standards on the fracture of glued and welded joints need attention because they do not consider the Griffith energy criterion of cracking which was proposed a century ago. It is almost as if Griffith never existed because the ASTM definition of failure is the stress criterion postulated by Galileo in 1638 in which stress at failure (i.e. strength = force/area) is defined as the determinant of fracture. Irene Martinez Villegas (Villegas, Rans 2021 Phil. Trans. R. Soc. A 376, 20200296. ( doi:10.1098/rsta.2020.0296 )) shows in this volume that attempts to use ASTM D5868 to standardi

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10

Hong-Lam, DANG. "A study of tensile strength of fractured rock mass by phase field method in DEAL.II with local refinement technique." Transport and Communications Science Journal 71, no. 7 (2020): 737–45. http://dx.doi.org/10.25073/tcsj.71.7.1.

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Cracking propagation in elastic and porous media is still challenge topics in mechanical, energy, and environmental engineering. In this paper, the phase field method will be used to model the cracking propagation at the small scale for elastic media. This method is doing well in DEAL.II with the help of local refinement technique which allows studying the tensile strength of fractured rock mass behavior without prior knowledge of cracking propagation path and reduction of computational consumption. This implementation is applied to model a fractured rock mass in which a plenty of explicit fra

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11

Hong Lam, Dang. "A study of tensile strength of fractured rock mass by phase field method in DEAL.II with local refinement technique." Transport and Communications Science Journal 71, no. 7 (2020): 737–45. http://dx.doi.org/10.47869/tcsj.71.7.1.

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Cracking propagation in elastic and porous media is still challenge topics in mechanical, energy, and environmental engineering. In this paper, the phase field method will be used to model the cracking propagation at the small scale for elastic media. This method is doing well in DEAL.II with the help of local refinement technique which allows studying the tensile strength of fractured rock mass behavior without prior knowledge of cracking propagation path and reduction of computational consumption. This implementation is applied to model a fractured rock mass in which a plenty of explicit fra

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12

DAL MASO, G., and R. TOADER. "A MODEL FOR THE QUASI-STATIC GROWTH OF BRITTLE FRACTURES BASED ON LOCAL MINIMIZATION." Mathematical Models and Methods in Applied Sciences 12, no. 12 (2002): 1773–99. http://dx.doi.org/10.1142/s0218202502002331.

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We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time ver

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13

Louchet, F., J. Faillettaz, D. Daudon, et al. "Possible deviations from Griffith’s criterion in shallow slabs, and consequences on slab avalanche release." Natural Hazards and Earth System Sciences 2, no. 3/4 (2002): 157–61. http://dx.doi.org/10.5194/nhess-2-157-2002.

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Abstract. Possible reasons for deviations from Griffith’s criterion in slab avalanche triggerings are examined. In the case of a major basal crack, we show (i) that the usual form of Griffith’s criterion is valid if elastic energy is stored in a shallow and hard slab only, and (ii) that rapid healing of broken ice bonds may lead to shear toughnesses larger than expected from tensile toughness experiments. In the case of avalanches resulting from failure of multi-cracked weak layers, where a simple Griffith’s criterion cannot be applied, frequency/size plots obtained from discrete elements and

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14

Li, S. "A multiscale Griffith criterion." Philosophical Magazine Letters 87, no. 12 (2007): 945–54. http://dx.doi.org/10.1080/09500830701647972.

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15

Li, Chun Guang, Xiu Run Ge, Hong Zheng, and Shui Lin Wang. "Two-Parameter Parabolic Mohr Strength Criterion and Its Damage Regularity." Key Engineering Materials 306-308 (March 2006): 327–32. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.327.

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A series of formulas about two-parameter parabolic Mohr strength criterion(2-PP Mohr criterion) are derived. Based on the results of uniaxial tension and uniaxial compression tests, the parameters involved in the criterion can be easily determined, then the criterion in terms of the major principal stress and the minor principal stress is derived, and the damage pattern is also discussed. At last, the formulas about the rupture angle and the friction angle are presented, and their relationship is also given. 2-PP Mohr criterion can describe not only shear but also tensile failure. In this crit

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16

Lee, Younggi, Jeehoon Park, Junyeong Park, and Jaehyun Yim. "An algorithm for a lifted Massey triple product of a smooth projective plane curve." International Journal of Algebra and Computation 30, no. 08 (2020): 1651–69. http://dx.doi.org/10.1142/s0218196720500587.

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We provide an explicit algorithm to compute a lifted Massey triple product relative to a defining system for a smooth projective plane curve [Formula: see text] defined by a homogeneous polynomial [Formula: see text] over a field. The main idea is to use the description (due to Carlson and Griffiths) of the cup product for [Formula: see text] in terms of the multiplications inside the Jacobian ring of [Formula: see text] and the Cech–deRham complex of [Formula: see text]. Our algorithm gives a criterion whether a lifted Massey triple product vanishes or not in [Formula: see text] under a parti

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17

Yin, Hanqing, H. Jerry Qi, Feifei Fan, Ting Zhu, Baolin Wang, and Yujie Wei. "Griffith Criterion for Brittle Fracture in Graphene." Nano Letters 15, no. 3 (2015): 1918–24. http://dx.doi.org/10.1021/nl5047686.

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18

Louat, N. P., and B. B. Rath. "Plastic flow and the Griffith fracture criterion." Acta Metallurgica 35, no. 12 (1987): 2921–27. http://dx.doi.org/10.1016/0001-6160(87)90291-4.

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19

Dégué, K. M., M. Soulié, and B. Ladanyi. "Extension of the Griffith's fracture criteria to saturated clays." International Journal for Numerical and Analytical Methods in Geomechanics 27, no. 4 (2003): 275–88. http://dx.doi.org/10.1002/nag.271.

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20

Knees, Dorothee, and Matteo Negri. "Convergence of alternate minimization schemes for phase-field fracture and damage." Mathematical Models and Methods in Applied Sciences 27, no. 09 (2017): 1743–94. http://dx.doi.org/10.1142/s0218202517500312.

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We consider time-discrete evolutions for a phase-field model (for fracture and damage) obtained by alternate minimization schemes. First, we characterize their time-continuous limit in terms of parametrized [Formula: see text]-evolutions, introducing a suitable family of “intrinsic energy norms”. Further, we show that the limit evolution satisfies Griffith’s criterion, for a phase-field energy release, and that the irreversibility constraint is thermodynamically consistent.

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21

Bartenev, G. M. "Thermofluctuation theory of strength and the Griffith criterion." Strength of Materials 21, no. 11 (1989): 1533–40. http://dx.doi.org/10.1007/bf01529408.

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22

Jarić, J. P., and E. S. Şuhubi. "Griffith criterion for brittle fracture in micropolar continuum." International Journal of Engineering Science 26, no. 5 (1988): 495–502. http://dx.doi.org/10.1016/0020-7225(88)90007-9.

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23

Hatzitrifon, N. K., and E. E. Gdoutos. "On the griffith criterion for three-dimensional cracks." International Journal of Engineering Science 26, no. 8 (1988): 833–36. http://dx.doi.org/10.1016/0020-7225(88)90033-x.

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24

Yuan, Mingqing, Haitao Zhao, Li Tian, et al. "Comparison of mixed mode fracture criteria in finite element analysis for matrix crack density estimation of laminated composites." Journal of Composite Materials 55, no. 2 (2020): 277–89. http://dx.doi.org/10.1177/0021998320948246.

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A mixed mode crack density estimation method based on the finite element analysis (FEA) for laminated composites is proposed and verified in this paper. The damaged properties of cracked ply are obtained using semi-analytical micro-mechanical method for the first time. The piecewise functions of the mode I and mode II energy release rates involving crack density are given based on Griffith’s energy principle and discrete damage mechanics (DDM). Any mixed mode fracture criteria could be simply applied to the FEA of the structure to calculate the initiation and evolution of the micro-cracks in t

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25

Sumigawa, Takashi, Takahiro Shimada, Shuuhei Tanaka, et al. "Griffith Criterion for Nanoscale Stress Singularity in Brittle Silicon." ACS Nano 11, no. 6 (2017): 6271–76. http://dx.doi.org/10.1021/acsnano.7b02493.

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26

Pirola, Gian Pietro, and Cecilia Rizzi. "Infinitesimal Invariant and vector bundles." Nagoya Mathematical Journal 186 (2007): 95–118. http://dx.doi.org/10.1017/s0027763000009375.

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AbstractWe study the Saito-Ikeda infinitesimal invariant of the cycle defined by curves in their Jacobians using rank k + 1 vector bundles. We give a criterion for which the higher cycle class map is not trivial. When k = 2, this turns out to be strictly linked to the Petri map for vector bundles. In this case we can improve a result of Ikeda: an explicit construction on a curve of genus g ≥ 10 shows the existence of a non trivial element in the higher Griffiths group.

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27

Yang, Q., L. G. Tham, and G. Swoboda. "Relationship between refined Griffith criterion and power laws for cracking." Mechanics Research Communications 31, no. 4 (2004): 429–34. http://dx.doi.org/10.1016/j.mechrescom.2004.02.002.

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28

Huang, Kai, Takahiro Shimada, Naoki Ozaki, et al. "A unified and universal Griffith-based criterion for brittle fracture." International Journal of Solids and Structures 128 (December 2017): 67–72. http://dx.doi.org/10.1016/j.ijsolstr.2017.08.018.

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29

Zhou, Fei, and Hao Wu. "A novel three-dimensional modified Griffith failure criterion for concrete." Engineering Fracture Mechanics 284 (May 2023): 109287. http://dx.doi.org/10.1016/j.engfracmech.2023.109287.

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30

Nazarov, S. A. "The Irwin’s and Griffith’s criteria for a set of cracks." Doklady Physics 45, no. 7 (2000): 333–35. http://dx.doi.org/10.1134/1.1307083.

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31

Gontarz, Jakub, and Jerzy Podgórski. "Comparison of Various Criteria Determining the Direction of Crack Propagation Using the UDMGINI User Procedure Implemented in Abaqus." Materials 14, no. 12 (2021): 3382. http://dx.doi.org/10.3390/ma14123382.

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This paper describes a method of predicting the direction of crack propagation implemented by user subroutines in the Simulia-Abaqus FEA system with the use of the extended finite element method (X-FEM). This method is based on displacements and stresses according to Westergaard’s solution of Griffith’s crack problem. During the calculations, in each crack increment, the algorithm reads the stresses and displacements in the model around the crack tip, calculates the criterion values at the read points, reduces them to a unit distance from the crack tip, fits a polynomial to these points, and f

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32

Kendall, K., N. McN Alford, S. R. Tan, and J. D. Birchall. "Influence of toughness on Weibull modulus of ceramic bending strength." Journal of Materials Research 1, no. 1 (1986): 120–23. http://dx.doi.org/10.1557/jmr.1986.0120.

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It is demonstrated both theoretically and experimentally that fracture toughness does not directly influence the Weibull modulus of ceramic bending strength for materials that obey the Griffith criterion for crack propagation. Weibull modulus remains unchanged as toughness is increased. However, toughness variations with crack length do affect the Weibull modulus. Thus materials that display R-curve behavior or Dugdale character give an increased Weibull modulus and appear more reliable.

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33

Zhang, Shuang, Hai Jun Wu, Zheng Jun Tan, and Feng Lei Huang. "Theoretical Analysis of Dynamic Spherical Cavity Expansion in Reinforced Concretes." Key Engineering Materials 715 (September 2016): 222–27. http://dx.doi.org/10.4028/www.scientific.net/kem.715.222.

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This paper aims to establish a model that considers the penetration resistance caused by the constraint effects of steel reinforcements on concrete. Firstly, based on the experiment phenomena that reinforcements increase the toughness and tensile strength of concretes, the fitting relational expression between toughness of reinforced concrete and ratio of reinforcement was used to improve the Griffith yield criterion for reinforced concrete. Then, the dynamic spherical cavity expansion analysis was developed using the improved Griffith yield criterion as constitutive model and the dilation equ

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34

Atkins, A. G. "Comments on ‘The Griffith-Orowan fracture theory revisited: The T-criterion’." International Journal of Mechanical Sciences 29, no. 4 (1987): 293–94. http://dx.doi.org/10.1016/0020-7403(87)90042-7.

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35

Liu, Feng, Qiheng Tang, and Tzu-Chiang Wang. "Intrinsic Notch Effect Leads to Breakdown of Griffith Criterion in Graphene." Small 13, no. 25 (2017): 1700028. http://dx.doi.org/10.1002/smll.201700028.

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36

Ballico, Edoardo, and Francesco Malaspina. "Qregularity and an extension of the Evans–Griffiths criterion to vector bundles on quadrics." Journal of Pure and Applied Algebra 213, no. 2 (2009): 194–202. http://dx.doi.org/10.1016/j.jpaa.2008.06.002.

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37

Aleksandrov, Anatoly, Natalya Aleksandrova, Vasiliy Chusov, and Aleksandr Riabov. "Ways of application of the provisions of mechanics of bodies with cracks to the calculation of asphalt concrete on strength and plasticity." MATEC Web of Conferences 239 (2018): 05018. http://dx.doi.org/10.1051/matecconf/201823905018.

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The report discusses the principles of two major theories of fracture mechanics of bodies with cracks, which include the theory of accumulation of damage Kachanov–Rabotnov and theory of brittle fracture Griffith–Irwin, including the invariant integral Cherepanov–Rice, describing the criterion of growth the crack. To assess the application of these theories to the calculation of asphalt concrete, laboratory test data are given and based on their analysis the appropriate conclusions.

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38

Makhutov, N. A., and Yu G. Matvienko. "Griffith theory and development of fracture mechanics criteria." Materials Science 29, no. 3 (1993): 316–19. http://dx.doi.org/10.1007/bf00558976.

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39

Lakirouhani, Ali, Mohammad Bahrehdar, Jurgis Medzvieckas, and Romualdas Kliukas. "COMPARISON OF PREDICTED FAILURE AREA AROUND THE BOREHOLES IN THE STRIKE-SLIP FAULTING STRESS REGIME WITH HOEK-BROWN AND FAIRHURST GENERALIZED CRITERIA." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 27, no. 5 (2021): 346–54. http://dx.doi.org/10.3846/jcem.2021.15020.

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Breakout is a shear failure due to compression that forms around the borehole due to stress concentration. In this paper, the breakout theory model is investigated by combining the equilibrium elasticity equations of stress around the borehole with two Hoek-Brown and Fairhurst generalized fracture criteria, both of which are based on the Griffith criterion. This theory model provides an explicit equation for the breakout failure width, but the depth of failure is obtained by solving a quartic equation. According to the results and in general, in situ stresses and rock strength characteristics

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40

Zhou, Zhen Gong, and Lin Zhi Wu. "The Non-Local Theory Solution of a Crack in the Functionally Graded Piezoelectric Materials Subjected to the Harmonic Anti-Plane Shear Stress Waves." Key Engineering Materials 353-358 (September 2007): 258–62. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.258.

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In this paper, the non-local theory of elasticity was applied to obtain the dynamic behavior of a Griffith crack in functionally graded piezoelectric materials under the harmonic anti-plane shear stress waves. The problem can be solved with the help of a pair of dual integral equations. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips, thus allows us to use the maximum stress as a fracture criterion.

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41

Marsh, P. G., and W. W. Gerberich. "A microscopically-shielded Griffith criterion for cleavage in grain oriented silicon steel." Acta Metallurgica et Materialia 42, no. 3 (1994): 613–19. http://dx.doi.org/10.1016/0956-7151(94)90257-7.

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42

Meshkov, Yu Ya. "Griffith energy criterion in the fracture micro-and macromechanics of brittle bodies." Metal Science and Heat Treatment 38, no. 1 (1996): 28–32. http://dx.doi.org/10.1007/bf01153869.

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43

Eldred, Roger J. "Effect of Oriented Platy Filler on the Fracture Mechanism of Elastomers." Rubber Chemistry and Technology 61, no. 4 (1988): 619–29. http://dx.doi.org/10.5254/1.3536208.

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Abstract Through an investigation of tension fatigue failure modes, oriented platy fillers have been found to provide elastomers with a unique failure mechanism which allows the elastomer to resist destructive crack growth. Samples of chlorosulfonated polyethylene containing talc as a reinforcing agent failed in an interlaminar shear mode, parallel to the applied stress. This fracture pattern resulted from diversion of the classical Griffith-type crack which would normally proceed perpendicularly to the stress. The theoretical criterion for diversion requires the adhesive fracture energy, Gad,

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44

Wang, E. Z., and N. G. Shrive. "On the griffith criteria for brittle fracture in compression." Engineering Fracture Mechanics 46, no. 1 (1993): 15–26. http://dx.doi.org/10.1016/0013-7944(93)90300-h.

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45

Xie, Y. J., Xiao Zhi Hu, and X. H. Wang. "A Theoretical Note on Mode I Crack Kinking and Branching." Advanced Materials Research 118-120 (June 2010): 314–18. http://dx.doi.org/10.4028/www.scientific.net/amr.118-120.314.

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An energy-based fracture mode has been derived for the mode I crack kinking and branching. The classic -integral has been further explored by a new partial integral path and the analytical solution of the energy release rate for crack kinking and branching from a mode-I crack tip has been established. The crack kinking/branching angle has also been analytically derived. It shows that the Griffith’s theorem and conservation law can be applied to both model I crack extension and model I crack kinking and branching. The branching mechanism for quasi-static mode-I crack has been theoretically inve

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46

Jeulin, D. "Fracture Statistics Models and Crack Propagation in Random Media." Applied Mechanics Reviews 47, no. 1S (1994): S141—S150. http://dx.doi.org/10.1115/1.3122809.

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Crack propagation in heterogeneous media is of primary interest for engineering purposes, in order to predict the overall toughness and the probability of fracture from data on the microstructure. Probabilistic models for mode I crack propagation in two dimensions are presented. They are developed for brittle elastic materials with a random distribution of fracture energy. These models enable us to calculate in a closed form the probability of fracture involving crack nucleation and propagation that differ from the usual fracture statistics models based on the weakest link model. The use of th

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47

Chen, Bin, Jing Hong Fan, J. Wang, X. Peng, and Xiao Lin Wu. "Research of Nanostructure of Bivalva Shell." Journal of Metastable and Nanocrystalline Materials 23 (January 2005): 83–86. http://dx.doi.org/10.4028/www.scientific.net/jmnm.23.83.

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Molluscan shells is a natural ceramic composite with excellent fracture strength and fracture toughness, which are attributed to their unique microstructures. Sanning electron microscope (SEM) observation on Bivalva shell showed that the shell consists of laminated aragonite and organic layers. These aragonite and organic layers are provided with the scale and characteristics of nanometer. The effect and function of these nanometer structures were analyzed based on Griffith criterion and energy-dissipation idea. The higher fracture strength and fracture roughness of bionanocomposite-molluscan

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48

Dienes, J. K. "Comments on “a generalized griffith criterion for crack propagation” by L. G. Margolin." Engineering Fracture Mechanics 23, no. 3 (1986): 615–17. http://dx.doi.org/10.1016/0013-7944(86)90165-7.

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49

Almi, Stefano. "Quasi-static hydraulic crack growth driven by Darcy’s law." Advances in Calculus of Variations 11, no. 2 (2018): 161–91. http://dx.doi.org/10.1515/acv-2016-0029.

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AbstractIn the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain {\epsilon\in\mathbb{R}} and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V, and ϵ. Then we study the problem of quasi-static evolution for our model, imposing that the fluid volume

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Keer, Leon M. "Mechanics of Contact Fatigue." Applied Mechanics Reviews 47, no. 6S (1994): S194—S198. http://dx.doi.org/10.1115/1.3124405.

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Abstract:

Contact fatigue between typical machine elements such as gears, roller followers, bearings and other components involves many complex interacting features. There are the effects of geometry, mechanical properties, material properties and surface chemistry. The present discussion will center around analytical prediction techniques that are concerned only with the mechanical aspects of contact fatigue between two elements. Aspects related to the initiation of a crack under repeated loading will be discussed. The application of an approach developed by Mura, analogous to Griffith’s criterion for

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