A Micromechanical Anisotropic Damage Model for Brittle Rocks With Non-Associated Plastic Flow Rule Under True Triaxial Compressive Stresses

A micromechanical anisotropic damage model with a non-associated plastic flow rule is developed for describing the true triaxial behaviors of brittle rocks. We combine the Eshelby’s solution to the inclusion problem with the framework of irreversible thermodynamics. The main dissipative mechanisms of inelastic deformation due to the frictional sliding and damage by microcrack propagation are strongly coupled to each other. A Coulomb-type friction criterion is formulated in terms of the local stress applied onto the microcracks as the yielding function. The back-stress term contained in this local stress plays a critical role in describing the material’s hardening/softening behaviors. With a non-associated flow rule, a potential function is involved. Some analytical analysis of the non-associated micromechanical anisotropic damage model are conducted, which are useful for the model parameters calibration. The proposed model is used to simulate the laboratory tests on Westerly granite under true triaxial stresses. Comparing the numerical simulation results provided by the models with associated/non-associated plastic flow rule and experimental results, it is clear that the proposed non-associated model gives a better prediction than the previous associated model.

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A new elastoplastic constitutive model for coarse granular aggregates incorporating particle breakage

Canadian Geotechnical Journal ◽

10.1139/t04-025 ◽

2004 ◽

Vol 41 (4) ◽

pp. 657-671 ◽

Cited By ~ 115

Author(s):

Wadud Salim ◽

Buddhima Indraratna

Keyword(s):

Constitutive Model ◽

Plastic Flow ◽

Current Model ◽

Particle Breakage ◽

Flow Rule ◽

Peak Strain ◽

Stress Strain ◽

Coarse Aggregates ◽

Stress Changes ◽

Plastic Flow Rule

A new elastoplastic stressstrain constitutive model is developed for granular coarse aggregates incorporating the degradation of particles during triaxial shearing. Coarse granular aggregates are subjected to breakage during excessive stress changes. Most of the available constitutive models do not consider the degradation of particles during shearing. In the current model, a plastic flow rule has been developed incorporating the energy consumption due to particle breakage during shear deformation. A non-associated flow and a kinematic type yield locus have been adopted in the model. A general formulation for the rate of particle breakage during shearing has been developed and incorporated in the plastic flow rule. The effects of particle breakage on the plastic distortional and volumetric deformations are incorporated in the current model. The stressstrain formulations are developed within the general critical state framework. The model can accurately predict the stressstrain and volume change behaviour of coarse granular aggregates. The plastic dilation and contraction features of coarse aggregates at various confining pressures are well captured, and the strain-hardening and post-peak strain-softening behaviour of coarse granular media is adequately represented. A particular feature of the model is its capability to predict the degree of particle breakage at any stage of shear deformation.Key words: constitutive modelling, coarse granular aggregates, particle breakage, dilatancy, non-associated flow, plasticity.

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Generalized plastic flow rule

International Journal of Plasticity ◽

10.1016/j.ijplas.2003.12.003 ◽

2005 ◽

Vol 21 (2) ◽

pp. 321-351 ◽

Cited By ~ 27

Author(s):

K HASHIGUCHI

Keyword(s):

Plastic Flow ◽

Flow Rule ◽

Plastic Flow Rule

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A Plastic Flow Rule at a Yield Corner

Buckling of Structures ◽

10.1007/978-3-642-50992-6_9 ◽

1976 ◽

pp. 95-97

Author(s):

M. J. Sewell

Keyword(s):

Plastic Flow ◽

Flow Rule ◽

Plastic Flow Rule

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Non-orthogonal elastoplastic constitutive model for sand with dilatancy

10.31224/osf.io/umxv9 ◽

2021 ◽

Author(s):

Jingyu Liang ◽

Dechun Lu ◽

Xiuli Du ◽

Wei Wu ◽

Chao Ma

Keyword(s):

Constitutive Model ◽

Plastic Flow ◽

Flow Direction ◽

Model Performance ◽

Yield Function ◽

Flow Rule ◽

Shear Process ◽

Hardening Parameter ◽

Elastoplastic Constitutive Model ◽

Plastic Flow Rule

A non-orthogonal elastoplastic constitutive model for sand with dilatancy is presented in the characteristic stress space. Dilatancy of sand is represented by the direction of plastic ﬂow, which can be directly determined by applying the non-orthogonal plastic ﬂow rule to an improved elliptic yield function. A new hardening parameter is developed to describe the contractive and dilative volume change during the shear process, which is co-ordinated with the non-orthogonal plastic ﬂow direction. The combination of the non-orthogonal plastic ﬂow rule and the proposed hardening parameter renders the proposed model with the ability to reasonably describe the stress-strain relationship of sand with dilatancy. The model performance is evaluated by comparing with the experimental data of sand under triaxial stress conditions.

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Non-orthogonal elastoplastic constitutive model with the critical state for clay

10.31224/osf.io/vpwq3 ◽

2021 ◽

Author(s):

Jingyu Liang ◽

Dechun Lu ◽

Xin Zhou ◽

Xiuli Du ◽

Wei Wu

Keyword(s):

Plastic Flow ◽

Critical State ◽

Flow Direction ◽

Volumetric Strain ◽

Yield Function ◽

Triaxial Tests ◽

Flow Rule ◽

Model Framework ◽

Plastic Strain Increment ◽

Plastic Flow Rule

A non-orthogonal elastoplastic model for clay is proposed by combining the non-orthogonal plastic flow rule with the critical state concept, and the model framework is presented from the perspective of the magnitude and direction of the plastic strain increment. The magnitude is obtained based on the improved elliptical yield function and the plastic volumetric strain dependent hardening parameter. The direction is determined by ap-plying the non-orthogonal plastic flow rule with the Riemann-Liouville fractional derivative to the yield function without the necessity of additional plastic potential function. The presented approach gives rise to a simple model for soil with five parameters. All parameters have clear physical meaning and can be easily identified by triaxial tests. The model performance is shown by analyzing the evolution process of the yield surface, the hardening rule and the plastic flow direction. The capability of the proposed model to capture the mechanical behaviours of clay with different stiffness is also confirmed by predicting test results from the literature.

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Formability prediction of substrate-supported metal layers using a non-associated plastic flow rule

Journal of Materials Processing Technology ◽

10.1016/j.jmatprotec.2020.116694 ◽

2021 ◽

Vol 287 ◽

pp. 116694

Author(s):

Mohamed Ben Bettaieb ◽

Farid Abed-Meraim

Keyword(s):

Plastic Flow ◽

Flow Rule ◽

Formability Prediction ◽

Metal Layers ◽

Plastic Flow Rule ◽

Supported Metal

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Coupling Analysis between Stress Induced Anisotropic Damage and Permeability Variation in Brittle Rocks

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.340-341.1133 ◽

2007 ◽

Vol 340-341 ◽

pp. 1133-1138 ◽

Cited By ~ 3

Author(s):

Hui Zhou ◽

Jian Fu Shao ◽

Xia Ting Feng ◽

Da Wei Hu

Keyword(s):

Damage Model ◽

Coupling Model ◽

Mechanical Analysis ◽

Effective Porosity ◽

Anisotropic Damage ◽

Permeability Evolution ◽

Coupling Analysis ◽

Brittle Rocks ◽

Permeability Variation ◽

Set Up

In this paper, a coupling constitutive model is proposed for anisotropic damage and permeability variation in brittle rocks before cracks fully coalesce. In this coupling model, an anisotropic damage model is employed to perform the mechanical analysis, and a statistical penetration model is set up to describe the effective porosity and permeability evolution in brittle rocks. For the coupling analysis, anisotropic damage model offers statistical penetration model the crack length in various directions, and statistical penetration model inversely provides anisotropic damage model with permeability of rock for coupling hydro-mechanical analysis. The proposed coupling model is applied to Lac du Bonnet granite, and generally a good agreement is obtained between numerical simulations and experimental data.

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Micromechanics-Based Elastoplastic and Damage Modeling of Particle Reinforced Composites

Materials ◽

10.1115/imece2004-59303 ◽

2004 ◽

Author(s):

H. T. Liu ◽

Lizhi Sun ◽

J. W. Ju

Keyword(s):

Damage Model ◽

Local Stress ◽

Damage Mechanism ◽

Elastic Stiffness ◽

Interfacial Debonding ◽

Isotropic Hardening ◽

Flow Rule ◽

Elastoplastic Behavior ◽

Micromechanical Damage ◽

The Matrix

A micromechanical damage model is proposed to predict the effective elastoplastic behavior of ductile composites containing randomly dispersed particles. The interfacial debonding between particles and the matrix is considered as the primary micromechanical damage mechanism. The debonded isotropic elastic reinforcements are replaced by equivalent anisotropic elastic inclusions. The interfacial debonding process is simulated by three-dimensional debonding angles. After the local stress field in the matrix is calculated, the homogenization averaging procedure is employed to estimate the effective elastic stiffness and yield function of the composites. The associative plastic flow rule and the isotropic hardening law are postulated based on the continuum plasticity theory. As applications, the overall elastoplastic and damage constitutive behavior of the composites under various loading conditions is numerically simulated and compared with available experimental results.

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