Microplane-damage-based Effective Stress and Invariants

Yang, Qiang; Chen, Xin; Weiyuan, Zhou

doi:10.1177/1056789505048602

Cited by 10 publications

(16 citation statements)

References 10 publications

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“…3 J II (σ) (e.g., Fung 1965, p.80). Here the author took notice of the proportionality between the spherical average of square shear stress magnitude and J II (e.g., Yang et al 2005):…”

Section: Exact Physical Meaningmentioning

confidence: 99%

Physical Meaning of Stress Difference for Fault-Slip Analysis

Sato

2012

Math Geosci

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Recent stress tensor inversion methods for fault-slip analysis are used to distinguish multiple stress states to elucidate spatiotemporal change of the earth's crustal tectonics. An estimator named the "stress difference" has been a practicable tool to measure the difference between stress solutions of inversion analysis. This measure corresponds to the expected difference in shear stress direction on a randomly oriented fault plane, which is, however, an approximation including several degrees of deviation. This study investigated the formula of stress difference and found the exact physical meaning, specifically the expected difference in shear stress vector which carries information on magnitude as well as direction. The present discovery is based on the analytical proportionality between the second invariant of stress tensor and the root mean square magnitude of shear stress for all orientation of fault planes. The meaningless difference in non-dimensional shear stress magnitude was found to be incorporated into the value of stress difference. This fact is not convenient for fault-slip analysis dealing with only orientations.

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“…3 J II (σ) (e.g., Fung 1965, p.80). Here the author took notice of the proportionality between the spherical average of square shear stress magnitude and J II (e.g., Yang et al 2005):…”

Section: Exact Physical Meaningmentioning

confidence: 99%

Physical Meaning of Stress Difference for Fault-Slip Analysis

Sato

2012

Math Geosci

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“…This article is essentially an extension of the work by Yang et al (2005a) who deal with this issue from a viewpoint of effective stress vectors of Kachanov (1958) and Rabotnov (1963). Yang et al (2005a) have shown that the well-known second-order effective stress tensor of Murakami (1988) can be viewed as the second-order fabric tensor of the Kachanov-Rabotnov effective stress vector. Therefore, it seems meaningful to develop higherorder effective stress tensors to characterize highly anisotropic damage states of materials.…”

Section: Introductionmentioning

confidence: 96%

Effective Stress and Vector-valued Orientational Distribution Functions

Yang

Chen

Weiyuan

2007

International Journal of Damage Mechanics

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The original Kachanov-Rabotnov damage variable is inherently microplane-based and should be expressed by a scalar-valued orientation distribution function (ODF), and the corresponding effective stress is a vector-valued ODF. The analysis of vector-valued ODFs is established in this article in the spirit of the analysis of scalar-valued ODFs by Kanatani, K. (1984a). : 531-546. Explicit expansions of vector-valued ODFs up to the sixth-order have been developed, and the relationship of fabric tensors of different order is addressed. The fabric tensors and expansion of the Kachanov-Rabotnov effective stress vector can be fully determined by the scalar-valued ODF characterizing the microplane damage. The second-order effective stress and damage tensors of Murakami, S. (1988). Mechanical Modeling of Material Damage, ASME Journal of Engineering Materials and Technology, 55: 280-286 are related to the second-order expansion of the Kachanov-Rabotnov effective stress vector. Therefore, the analysis of vector-valued ODFs furnishes a rigorous and unified mathematical basis for the damage theory of Kachanov, L.M. (1958).

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“…To provide better insight into the physical mechanism while adhering to the basic framework of continuum damage mechanics, microplane models based on geometric damage were proposed to separate the independent effect of geometrical characteristic . In these models, the concept of effective stress and the hypothesis of strain equivalence were reformulated on the microplane level, and geometric damage variables could be defined on the microplanes so as to represent a different reduction of the net stress‐carrying area fraction in different directions, which is impossible in tensorial models.…”

Section: Introductionmentioning

confidence: 99%

“…By defining a single damage variable on microplanes as an orientation distribution function (ODF) and an effective stress vector on the microplanes, and assuming static constraint between macro nominal stresses and microplane nominal stresses, Yang et al . showed that the second‐order effective stress tensor of Murakami can be recovered as the second‐order fabric tensor of the effective stress vector. Furthermore, they proved that the anisotropic yield criteria of damaged materials whose matrix follows von Mises and Drucker–Prager yield criteria possess the form of the famous Hill criterion and its extension by Liu to pressure‐sensitive materials , in which the parameters are related to the fabric tensors of the microplane damage variable.…”

Section: Introductionmentioning

confidence: 99%

Microplane damage model for jointed rock masses

Chen

Bažant

2014

Num Anal Meth Geomechanics

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The paper presents a new microplane constitutive model for the inelastic behavior of jointed rock masses that takes into account the mechanical behavior and geometric characteristics of cracks and joints. The basic idea is that the microplane modeling of rock masses under general triaxial loading, including compression, requires the isotropic rock matrix and the joints to be considered as two distinct phases coupled in parallel. A joint continuity factor is defined as a microplane damage variable to represent the stress-carrying area fraction of the joint phase. Based on the assumption of parallel coupling between the rock joint and the rock matrix, the overall mechanical behavior of the rock is characterized by microplane constitutive laws for the rock matrix and for the rock joints, along with an evolution law for the microplane joint continuity factor. The inelastic response of the rock matrix and the rock joints is controlled on the microplane level by the stress-strain boundaries. Based on the arguments enunciated in developing the new microplane model M7 for concrete, the previously used volumetric-deviatoric splits of the elastic strains and of the tensile boundary are avoided. The boundaries are tensile normal, compressive normal, and shear. The numerical simulations demonstrate satisfactory fits of published triaxial test data on sandstone and on jointed plaster mortar, including quintessential features such as the strain softening and dilatancy under low confining pressure, as well as the brittle-ductile transition under higher confining pressure, and the decrease of jointed rock strength and Young's modulus with an increasing dip angle of the joint.This leads to the following basic relation between the macrocontinuum stress tensor and the microplane stresses of the rock mass: MICROPLANE DAMAGE MODEL FOR JOINTED ROCK MASSES Figure 12. The normal stress on the microplane μ = 7 versus axial strain: (a) p = 10 MPa, (b) p = 30 MPa, (c) p = 60 MPa, and (d) p = 100 MPa. Figure 13. The shear stress on the microplane μ = 7 versus axial strain: (a) p = 10 MPa, (b) p = 30 MPa, (c) p = 60 MPa, and (d) p = 100 MPa. MICROPLANE DAMAGE MODEL FOR JOINTED ROCK MASSES

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Microplane-damage-based Effective Stress and Invariants

Cited by 10 publications

References 10 publications

Physical Meaning of Stress Difference for Fault-Slip Analysis

Physical Meaning of Stress Difference for Fault-Slip Analysis

Effective Stress and Vector-valued Orientational Distribution Functions

Microplane damage model for jointed rock masses

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