On structural computations until fracture based on an anisotropic and unilateral damage theory

Genet, Martin; Marcin, Lionel

doi:10.1177/1056789513500295

Cited by 15 publications

(16 citation statements)

References 43 publications

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“…The present work is based on fracture mechanics [2][3][4][5][6][7][8][9][10][11][12] framework rather than on continuum damage mechanics [13,14] because we model the propagation of sharp cracks in the material. Majority of the existing computational methods employing fracture mechanics principles utilize either one of the following frameworks:…”

Section: Brief Overview Of Relevant Methodsmentioning

confidence: 99%

Mesh refitting approach: a simple method to model mixed-mode crack propagation in nonlinear elastic solids

Sudhakar

Wall

2017

Adv. Model. and Simul. in Eng. Sci.

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We devise a finite element methodology to trace quasi-static through-thickness crack paths in nonlinear elastic solids. The main feature of the proposed method is that it can be directly implemented into existing large scale finite element solvers with minimal effort. The mesh topology modifications that are essential in propagating a crack through the finite element mesh are accomplished by utilizing a combination of a mesh refitting procedure and a nodal releasing approach. The mesh refitting procedure consists of two steps: in the first step, the nodes are moved by solving the elastostatic equations without touching the connectivity between the elements; in the next step, if necessary, quadrilateral elements attached to crack tip nodes are split into triangular elements. This splitting of elements allows the straightforward modification of element connectivity locally, and is a key step to preserve the quality of the mesh throughout the simulation. All the geometry related operations required for crack propagation are addressed in detail with full emphasis on computer implementation. Solving several examples involving single and multiple cracks, and comparing them with experimental or other numerical approaches indicate that the proposed method captures crack paths accurately.

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Section: Brief Overview Of Relevant Methodsmentioning

confidence: 99%

Mesh refitting approach: a simple method to model mixed-mode crack propagation in nonlinear elastic solids

Sudhakar

Wall

2017

Adv. Model. and Simul. in Eng. Sci.

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“…Since growth is driven by the elastic strains

\underset{E^{e}}{true}

, which are in turn affected by growth as

\underset{F^{e}}{true} = \underset{F}{true} \cdot {\underset{true‗}{F^{g}}}^{- 1}

, we iteratively determine the growth multiplier ϑ g at the integration point level at every global iteration step. Rather than using a consistent Newton-Raphson procedure, which requires a consistent algorithmic linearization (Göktepe, Abilez and Kuhl, 2010; Göktepe, Abilez, et al, 2010), we adopt a local fixed-point iteration, supplemented by Aitken’s relaxation (Genet, Marcin and Ladeveze, 2013). For the time integration, we use an implicit mid-point rule.…”

Section: Methodsmentioning

confidence: 99%

Heterogeneous growth-induced prestrain in the heart

Genet

Rausch²,

Lee³

et al. 2015

Journal of Biomechanics

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Even when entirely unloaded, biological structures are not stress-free, as shown by Y.C. Fung’s seminal opening angle experiment on arteries and the left ventricle. As a result of this prestrain, subject-specific geometries extracted from medical imaging do not represent an unloaded reference configuration necessary for mechanical analysis, even if the structure is externally unloaded. Here we propose a new computational method to create physiological residual stress fields in subject-specific left ventricular geometries using the continuum theory of fictitious configurations combined with a fixed-point iteration. We also reproduced the opening angle experiment on four swine models, to characterize the range of normal opening angle values. The proposed method generates residual stress fields which can reliably reproduce the range of opening angles between 8.7±1.8 and 16.6 ± 13.7 as measured experimentally. We demonstrate that including the effects of prestrain reduces the left ventricular stiffness by up to 40%, thus facilitating the ventricular filling, which has a significant impact on cardiac function. This method can improve the fidelity of subject-specific models to improve our understanding of cardiac diseases and to optimize treatment options.

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“…In this paper, we use a classical approach, based on the idea that only positive deformations will turn existing defects into propagating cracks, which has been experimentally evidenced for robocast scaffolds [Miranda et al, 2007], and used in several models e.g. for concrete [Desmorat, 2006] and ceramic matrix composites [Genet et al, 2012b]. Thus, we will consider the following probability law:

P^{F} = 1 - \exp (- \frac{1}{V_{0}} \int_{V} {true(\frac{{∥ 〈 \underset{\underline{∊}}{true} 〉 ∥}_{+}}{∊_{0}} true)}^{m} d V)

where

{〈 \underset{\underline{∊}}{true} 〉}_{+}

is the positive part of the deformation tensor, built by removing all non-positive eigenvalues from

\underset{\underline{∊}}{true}

.…”

Section: Modeling and Methodsmentioning

confidence: 99%

A two-scale Weibull approach to the failure of porous ceramic structures made by robocasting: Possibilities and limits

Genet

Houmard

Eslava

et al. 2013

Journal of the European Ceramic Society

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This paper introduces our approach to modeling the mechanical behavior of cellular ceramics, through the example of calcium phosphate scaffolds made by robocasting for bone-tissue engineering. The Weibull theory is used to deal with the scaffolds’ constitutive rods statistical failure, and the Sanchez-Palencia theory of periodic homogenization is used to link the rod- and scaffold-scales. Uniaxial compression of scaffolds and three-point bending of rods were performed to calibrate and validate the model. If calibration based on rod-scale data leads to over-conservative predictions of scaffold’s properties (as rods’ successive failures are not taken into account), we show that, for a given rod diameter, calibration based on scaffold-scale data leads to very satisfactory predictions for a wide range of rod spacing, i.e. of scaffold porosity, as well as for different loading conditions. This work establishes the proposed model as a reliable tool for understanding and optimizing cellular ceramics’ mechanical properties.

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On structural computations until fracture based on an anisotropic and unilateral damage theory

Cited by 15 publications

References 43 publications

Mesh refitting approach: a simple method to model mixed-mode crack propagation in nonlinear elastic solids

Mesh refitting approach: a simple method to model mixed-mode crack propagation in nonlinear elastic solids

Heterogeneous growth-induced prestrain in the heart

A two-scale Weibull approach to the failure of porous ceramic structures made by robocasting: Possibilities and limits

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