Microplane damage model for fatigue of quasibrittle materials: Sub-critical crack growth, lifetime and residual strength

Kirane, Kedar; Bažant, Zdeněk P.

doi:10.1016/j.ijfatigue.2014.08.012

Cited by 65 publications

(35 citation statements)

References 36 publications

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“…This particular observation documents the ability of the model to capture the stress redistribution in a material point due to anisotropic evolution of damage. As emphasized in [8] this feature is a paramount requirement for a reproduction of damage evolution at subcritical load levels.…”

Section: Hysteretic Loopsmentioning

confidence: 99%

“…The reason for this modification is the fact that the shape of the damage relation with the cumulative sliding strain resulting from the original Lemaitre's damage potential is approaching ω = 1.0 in a nonasymptotic manner. As demonstrated by Kirane and Bažant [8] when linking the damage to a cumulative measure of strain with the goal to cover the high cycle fatigue behavior, damage must be accumulated slowly, within a large range of cumulative strain approaching ω = 1.0 asymptotically. The behavior of the modified damage potential is studied in Fig.…”

Section: Microplane Constitutive Lawsmentioning

confidence: 99%

“…In order to reflect the opening/closure and growth of microcracks and/or the frictional sliding along their lips, the formulation of the dissipative mechanisms has been refined by introducing the internal sliding strain as a fatigue damage driving variable [6]. An approach relating the dissipative terms owing to fatigue damage even closer to the observable disintegration mechanisms within the material structure appeared recently in [8]. The key idea of this model is to relate the damage evolution to the cumulative measure of volumetric strain.…”

Section: Introductionmentioning

confidence: 99%

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Microplane damage plastic model for plain concrete subjected to compressive fatigue loading

Baktheer¹

2019

Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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A thermodynamically based microplane fatigue damage model for plain concrete under compressive loading is introduced. The key idea of the present approach is to relate the fatigue damage to a cumulative measure of inelastic sliding/shear strains. Which reflects the fatigue damage accumulation owing to internal friction at subcritical fatigue loading level. The model is formulated within the microplane framework using a homogenization approach based on the energy equivalence principle with explicit representation of the effective triaxial elastic stiffness. The model can reflect the damage-induced anisotropic behavior of concrete and can reproduce the shape of the hysteretic loops related to the fatigue damage development within the tensorial representation of the material state. Elementary studies of the model response and its applicability to modeling of the fatigue response under compression are presented. The ability to reproduce the typical shape of the hysteretic loops is discussed and compared to the existing phenomenological fatigue models for concrete under compression.1 Table 1: General classification of approaches to modeling of concrete fatigue Lifetime based approaches Strain based approaches Strain approximations Damage approximations Tensorial models Microplane models Discrete models Liu [1] Pfanner [2] Alliche [4] Desmorat [6] Kirane and Bazant [8] Wang [9]

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Section: Hysteretic Loopsmentioning

confidence: 99%

Section: Microplane Constitutive Lawsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Microplane damage plastic model for plain concrete subjected to compressive fatigue loading

Baktheer¹

2019

Proceedings of the 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures

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“…The microplane model describes the material behavior at the mesoscopic scale by formulating the constitutive laws in terms of stress and strain vectors acting on individual microplanes of all possible orientations at a given material point [4,5,7,6,8,9,10,11,12,13,14,15,16,3,17,19,20,21,18,22], instead of using a traditional tensorial constitutive model. These microplanes may be imagined to represent damage planes or weak planes in the mesoscale structures, such as contact layers between aggregate pieces in concrete or defects in composite laminates.…”

Section: Background Of Microplane Modelmentioning

confidence: 99%

“…Since then the microplane model for concrete has been studied extensively, and evolved through several progressively improved versions [4,5,8,9,6,11,10,12,13,18,19,20,21]. Numerous advantages of microplane models were reviewed in Brocca and Bažant [26] and Cusatis et al [27].…”

Section: Background Of Microplane Modelmentioning

confidence: 99%

Elastic Microplane Formulation for Transversely Isotropic Materials

Jin

Salviato

et al. 2016

Journal of Applied Mechanics

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This contribution investigates the extension of the microplane formulation to the description of transversely isotropic materials such as shale rock, foams, unidirectional composites, and ceramics. Two possible approaches are considered: 1) the spectral decomposition of the stiffness tensor to define the microplane constitutive laws in terms of energetically orthogonal eigenstrains and eigenstresses; and 2) the definition of orientationdependent microplane elastic moduli. It is shown that the first approach provides a rigorous way to tackle anisotropy within the microplane framework whereas the second approach represents an approximation which, however, makes the formulation of nonlinear constitutive equations much simpler. The efficacy of the second approach in modeling the macroscopic elastic behavior is compared to the thermodynamic restrictions of the anisotropic parameters showing that a significant range of elastic properties can be modeled with excellent accuracy. Further, it is shown that it provides a very good approximation of the microplane stresses provided by the first approach, with the advantage of a simpler formulation.It is concluded that the spectral stiffness decomposition represents the best approach in such cases as for modeling unidirectional composites, in which accurately capturing the elastic behavior is important. The introduction of orientation-dependent microplane elastic moduli provides a simpler framework for the modeling of transversely isotropic materials with remarked inelastic behavior, as in the case, for example, of shale rock.

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Conversion of explicit microplane model with boundaries to a constitutive subroutine for implicit finite element programs

Nguyen

Caner

Bažant

2020

Numerical Meth Engineering

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Whereas various simplistic microplane models of limited applicability, defined by stress-strain curves on the microplane, can function as either explicit or implicit, the explicit-to-implicit conversion of realistic versatile microplane models for plain or fiber-reinforced concrete, shale and composites has remained a challenge for quarter century. The reason is that these realistic models use microplane stress-strain boundaries defined by inequalities. Here, we show how the conversion can be easily achieved on the microplane level and then transferred to a tangent stiffness tensor or an inelastic stiffness tensor to be used in Newton-Raphson iterations within a loading step. To ensure convergence, a minor adjustment in the M7 algorithm is introduced to achieve continuity. Power-law convergence, almost quadratic in most cases, is also demonstrated. Seven examples of crack-band finite element simulations of challenging laboratory tests document nearly identical implicit and explicit results, as well as good match of test data. Three of them, including the vertex effect in compression-torsion tests, pure Mode II shear fracture, and the "gap test" of the crack-parallel compression effect on Mode I load-deflection curve, have not been reproduced by other models before. The coding of implicit M7 subroutine, usable in, for example, UMAT of ABAQUS, is posted for a free download.

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Microplane damage model for fatigue of quasibrittle materials: Sub-critical crack growth, lifetime and residual strength

Cited by 65 publications

References 36 publications

Microplane damage plastic model for plain concrete subjected to compressive fatigue loading

Microplane damage plastic model for plain concrete subjected to compressive fatigue loading

Elastic Microplane Formulation for Transversely Isotropic Materials

Conversion of explicit microplane model with boundaries to a constitutive subroutine for implicit finite element programs

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