Continuum Damage Mechanics and Numerical Applications

Zhang, Wohua; Cai, Yuanqiang

doi:10.1007/978-3-642-04708-4

Cited by 43 publications

(24 citation statements)

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“…For rock materials, the dilatancy was usually considered by non-associated plastic flow rule with a suitable plastic function (Q p ). For the sake of simplicity, the confining pressuresensitive Drucker-Prager model was used to describe the plastic behavior, whereas the plastic loading function has been modified to consider the effect of damage in plasticity (Zhang & Cai, 2001).…”

Section: Plastic Characterizationmentioning

confidence: 99%

Rock Failure Analysis Based on a Coupled Elastoplastic-Logarithmic Damage Model

Abdia¹,

Molladavoodi²,

Salari-Rad³

2017

Archives of Mining Sciences

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The rock materials surrounding the underground excavations typically demonstrate nonlinear mechanical response and irreversible behavior in particular under high in-situ stress states. The dominant causes of irreversible behavior are plastic flow and damage process. The plastic flow is controlled by the presence of local shear stresses which cause the frictional sliding. During this process, the net number of bonds remains unchanged practically. The overall macroscopic consequence of plastic flow is that the elastic properties (e.g. the stiffness of the material) are insensitive to this type of irreversible change. The main cause of irreversible changes in quasi-brittle materials such as rock is the damage process occurring within the material. From a microscopic viewpoint, damage initiates with the nucleation and growth of microcracks. When the microcracks length reaches a critical value, the coalescence of them occurs and finally, the localized meso-cracks appear. The macroscopic and phenomenological consequence of damage process is stiffness degradation, dilatation and softening response.In this paper, a coupled elastoplastic-logarithmic damage model was used to simulate the irreversible deformations and stiffness degradation of rock materials under loading. In this model, damage evolution & plastic flow rules were formulated in the framework of irreversible thermodynamics principles. To take into account the stiffness degradation and softening on post-peak region, logarithmic damage variable was implemented. Also, a plastic model with Drucker-Prager yield function was used to model plastic strains.Then, an algorithm was proposed to calculate the numerical steps based on the proposed coupled plastic and damage constitutive model. The developed model has been programmed in VC++ environment. Then, it was used as a separate and new constitutive model in DEM code (UDEC). Finally, the experimental Oolitic limestone rock behavior was simulated based on the developed model. The irreversible strains, softening and stiffness degradation were reproduced in the numerical results. Furthermore, the confinement pressure dependency of rock behavior was simulated in according to experimental observations. Keywords 754Zachowanie materiału skalnego otaczającego wyrobiska podziemne w odpowiedzi na wysokie stany lokalnych naprężeń działajacych in situ jest zazwyczaj nieodwracalne i nieliniowe. Reakcje nieodwracalne spowodowane są w głównej mierze przez płynięcie plastyczne i procesy uszkodzeń. Płynięcie plastyczne uwarunkowane jest przez występowanie lokalnych naprężeń ścinających powodujące obsunięcia skał. W trakcie tego procesu ilość wiązań netto pozostaje praktycznie niezmieniona. Całościowy efekt płynięcia plastycznego w skali makroskopowej polega na tym, że właściwości elastyczne (np. sztywność) stają się niewrażliwe na działanie nieodwracalnych procesów tego rodzaju. Podstawową przyczyną reakcji nieodwracalnych reakcji w materiałach quasi-kruchych, do których należą skały, jest powstawanie uszkodzeń wewnątrz materiału. W...

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Section: Plastic Characterizationmentioning

confidence: 99%

Rock Failure Analysis Based on a Coupled Elastoplastic-Logarithmic Damage Model

Abdia¹,

Molladavoodi²,

Salari-Rad³

2017

Archives of Mining Sciences

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“…Important advances in creep damage models for crack growth analysis have been made in the last two decades as scientists and engineers strive to imbue continuum-based models with more realistic details at microstructure damage mechanisms in the creep process [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Such damage models can be also found in [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…Such damage models can be also found in [17][18][19][20]. Knowledge of stress, strain and displacement fields in the vicinity of the crack tip under mixed-mode loading conditions is important for the justification of fracture mechanics criteria and has attracted considerable attention nowadays [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Asymptotic analysis of the mechanical fields in front of stationary and propagating cracks facilitate the understanding of the mechanical and physical state in front of crack tips and they enable prediction of crack growth and failure.…”

Section: Introductionmentioning

confidence: 99%

“…For a crack this results in an alteration of opening mode I, II and III which is why the study of mixed-mode loads is of particular importance [7][8][9]14,24]. In linear fracture mechanics the principle of superposition allows to obtain solutions for mixed mode I/II crack problems whereas in nonlinear fracture mechanics many questions are still open [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Analysis of the near crack-tip fields in power-law hardening (or power-law creeping) damaged materials under mixed-mode loading results in new nonlinear eigenvalue problems in which the whole spectrum of the eigenvalues and orders of stress singularity have to be determined [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

“…The method proposed has been applied to nonlinear eigenvalue problems arising from the problem of the determining the near crack-tip fields in the damaged materials. In continuum damage mechanics [2,6,7,10,12,13,16], the damage state at an arbitrary point in the material is represented by a properly defined integrity (continuity) variable ( , ) r   . The integrity parameter reaches its critical value at fracture.…”

Section: Introductionmentioning

confidence: 99%

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Intermediate asymptotic behavior of the stress and damage fields in the vicinity of the mixed-mode crack tip under creep regime

Степанова¹,

Mironova²

2017

Collection of Selected Papers of the III International Conference on Information Technology and Nanotechnology

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The creep crack problems in damaged materials under mixed mode loading (Mode I and Mode II loading) in the framework of creep-damage coupled formulation are considered. The class of the self-similar solutions to the plane creep crack problems in a damaged medium under mixed-mode loading is given. With the similarity variable and the self-similar representation of the solution for a power-law creeping material and the Kachanov-Rabotnov power-law damage evolution equation the near crack-tip stresses, creep strain rates and continuity distributions for plane stress and plane strain conditions are obtained. The similarity solutions are based on the hypothesis of the existence of the completely damaged zone near the crack tip. It is shown that the asymptotic analysis of the near crack-tip fields gives rise to the nonlinear eigenvalue problems. The technique permitting to find all the eigenvalues numerically is proposed and numerical solutions of the nonlinear eigenvalue problems arising from the mixed-mode crack problems in a power-law medium under plane stress conditions are obtained. Using the approach developed the eigenvalues different from the eigenvalues corresponding to the Hutchinson-Rice-Rosengren (HRR) problem are found. The angular distributions of the stress and the continuity fields are selected as the crack tip fields of interest. Having obtained the eigenspectra and eigensolutions the geometry of the completely damaged zone in the vicinity of the crack tip is found for all values of the mixity parameter.

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Dynamic Damage Evolution in Shale in the Presence of Pre-Existing Microcracks

Fahem

Singh

2022

Dynamic Behavior of Materials, Volume 1

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Continuum Damage Mechanics and Numerical Applications

Cited by 43 publications

References 0 publications

Rock Failure Analysis Based on a Coupled Elastoplastic-Logarithmic Damage Model

Rock Failure Analysis Based on a Coupled Elastoplastic-Logarithmic Damage Model

Intermediate asymptotic behavior of the stress and damage fields in the vicinity of the mixed-mode crack tip under creep regime

Dynamic Damage Evolution in Shale in the Presence of Pre-Existing Microcracks

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