Micromechanical Approach to Nonlinear Poroelasticity: Application to Cracked Rocks

Deudé, V.; Dormieux, Luc; Kondo, Djimédo; Maghous, Samir

doi:10.1061/(asce)0733-9399(2002)128:8(848)

Cited by 68 publications

(55 citation statements)

References 10 publications

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“…The distinctive matrix-inclusion morphology of RVE II-i.e. cracks and mesopores can be considered as inclusions embedded in the hydroxyapatite polycrystal matrixsuggests the use of a Mori-Tanaka-type homogenization scheme (Mori and Tanaka 1973;Benveniste 1987) for stiffness homogenization; mathematical treatment of the penny-shaped cracks has been dealt with by Deudé et al (2002), Dormieux et al (2004). The stiffness tensor of the pre-cracked, mesoporous granule material, C gran is then governed by the composition and morphology of RVE II, as well as by the stiffness tensors of the hydroxyapatite polycrystal matrix, C polyHA , accessible from stiffness homogenization across RVE I, and of the mesopores, C mesoφ , and by the density of cracks, quantified by the so-called crack density parameter e (Budianksy and O'Connell 1976).…”

Section: Micromechanical Modelingmentioning

confidence: 99%

“…The latter is estimated by means of Eshelby's matrix-inclusion problem (Eshelby 1957); considering the matrixinclusion-type morphology discernible on hierarchical level II, compare Fig. 1, A gran polyHA is defined by (Deudé et al 2002;Dormieux et al 2004)…”

Section: Definition Of Mechanical Input Parametersmentioning

confidence: 99%

“…Here, as a (computationally more efficient) complement, we present a three-step, fully continuum micromechanicsbased macro-to-meso-to-micro (stress and strain) downscaling scheme, linking in the end the quasibrittle failure of single micrometer-or sub-micrometersized hydroxyapatite crystal needles to the overall strength of both millimeter-sized biomaterial scaffolds and composites comprising biomaterial scaffold and bone tissue, respectively. For this purpose, a number of homogenization concepts are adapted, extended, and combined, considering the pioneering contributions of Eshelby (1957), Hill (1963Hill ( , 1965, Laws (1977Laws ( , 1985, Hervé and Zaoui (1993); and also considering more recent contributions of Deudé et al (2002), Dormieux et al (2004), Fritsch et al (2006), Bertrand andHellmich (2009). Following Fritsch et al (2009a, b), we feed the stress of the most unfavorably loaded hydroxyapatite needle into a suitable, Mohr-Coulombtype failure criterion, and deduce then therefrom the corresponding ultimate macroscopic load bearable by the aforementioned granular, hydroxyapatite-based biomaterial (optionally containing ingrown bone tissue).…”

Section: Introductionmentioning

confidence: 99%

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Strength increase during ceramic biomaterial-induced bone regeneration: a micromechanical study

2016

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Bone tissue engineering materials must blend in the targeted physiological environment, in terms of both the materials' biocompatibility and mechanical properties. As for the latter, a well-adjusted stiffness ensures that the biomaterial's deformation behavior fits well to the deformation behavior of the surrounding biological tissue, whereas an appropriate strength provides sufficient load-carrying capacity of the biomaterial. Here, a mathematical modeling approach for estimating the macroscopic load that initiates failure of a hierarchically organized, granular, hydroxyapatite-based biomaterial is presented. For this purpose, a micromechanics model is developed for downscaling macroscopically prescribed stress (or strain) states to the level of the needle-shaped hydroxyapatite crystals. Presuming that the biomaterial fails due to the quasi-brittle failure of the most unfavorably stressed hydroxyapatite needle, the downscaled stress tensors are fed into a suitable, Mohr-Coulomb-

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Section: Micromechanical Modelingmentioning

confidence: 99%

Section: Definition Of Mechanical Input Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strength increase during ceramic biomaterial-induced bone regeneration: a micromechanical study

2016

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“…It is classically formulated by adapting the Eshelby result to this situation. The resulting localization tensor for the r th family of microcracks (r = 1 to N) takes then the form (see for instance [6] or [7]):…”

Section: The Mori-tanaka Scheme Applied To Cracked Mediamentioning

confidence: 99%

A micromechanical approach of crack-induced damage in orthotropic media: Application to a brittle matrix composite

Monchiet¹,

Gruescu²,

Cazacu³

et al. 2012

Engineering Fracture Mechanics

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. A micromechanical approach of crackinduced damage in orthotropic media : application to a brittle matrix composite. Engineering Fracture Mechanics, Elsevier, 2012, 83 (-) AbstractCoupling between initial and damage-induced anisotropies in 3D elastic damaged materials has been so far addressed by homogenization techniques only for particular microcracks configurations. The main difficulty in developing a general 3D micromechanical model lies in the lack of a closed-form solution of the Eshelby tensor corresponding to cracks in an elastic anisotropic medium. In this study, we begin to present closed form expressions of the Eshelby tensor S that we derived for a cylindrical crack embedded in an orthotropic material. The 3D obtained expressions reduce to existing results in the 2D case or in particular 3D cracks configurations. The effective compliance of an orthotropic medium containing arbitrarily oriented cracks is then derived by using the new Eshelby tensor. Finally, a damage model is formulated by combining the above results with classical thermodynamics approach.The ability of the model to capture coupling between initial orthotropy and damage induced anisotropy is demonstrated through a comparison with experimental data available for a ceramic matrix composite (unidirectional SiC-SiC).

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“…For complex microstructures and non-linear behavior, the analytical approach is difficult to apply even though some authors have obtained interesting results [16]. Consistently with the hypothesis of periodic microstructure and scale separability, a different procedure is the one in which the upscaling is performed with numerical computations, the so-called finite element squared FE 2 method.…”

Section: Introductionmentioning

confidence: 99%

Modeling of granular solids with computational homogenization: Comparison with Biot׳s theory

Marinelli

Eijnden

Sieffert

et al. 2016

Finite Elements in Analysis and Design

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a b s t r a c tThis paper discusses the numerical results for a consolidation test studied by using a hydromechanical model formulated within a numerical homogenization approach, the so-called finite element squared method, FE 2 . This model is characterized by two observation scales: at the microscopic scale, the microstructure of the material is described as an assembly of hyperelastic grains connected by cohesive interfaces that define a network of channels in which fluid can percolate. This microstructure, periodically distributed in the small-scale, identifies the Representative Elementary Volume of the material. At the macroscopic scale, the material is treated as a continuum and the corresponding constitutive equations are obtained by means of a numerical homogenization process on the microscopic problem. In this manner, the total stress of the mixture, the density of the mixture, the fluid mass flow and the fluid mass content can be computed. The objective of this work is to compare the numerical results with the analytical solution of a classical oedometric test using the poroelastic theory of Biot (1941) [1]. For this purpose, it is shown that the hydromechanical behavior obtained with the selected FE 2 method is characterized by a classical Biot-like porous medium and the resulting macroscopic properties can be illustrated in light of the hydromechanical mechanisms at the microscopic scale.

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Micromechanical Approach to Nonlinear Poroelasticity: Application to Cracked Rocks

Cited by 68 publications

References 10 publications

Strength increase during ceramic biomaterial-induced bone regeneration: a micromechanical study

Strength increase during ceramic biomaterial-induced bone regeneration: a micromechanical study

A micromechanical approach of crack-induced damage in orthotropic media: Application to a brittle matrix composite

Modeling of granular solids with computational homogenization: Comparison with Biot׳s theory

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