Isotropic continuum damage/repair model for alveolar bone remodeling

Mengoni, Marlène; Ponthot, Jean‐Philippe

doi:10.1016/j.cam.2009.08.061

Cited by 16 publications

(13 citation statements)

References 23 publications

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“…), as discussed in Hillsley and Frangos (1994), Cowin (2002), Qin et al (2003), McGarry et al (2005), Kafka (1993), and Nguyen et al (2010) for instance. Other approaches rely on 'solid' quantities arising from additional constitutive mechanisms, such as micro-damage, see Zidi (1999, 2001), Mengoni and Ponthot (2010), with or without the influence of an interstitial fluid, as in Tami et al (2002), and Rouhi et al (2006), or viscosity in Baïotto and Zidi (2009) that leads to a first-order system, introducing a constitutive characteristic time. The present work also introduces a characteristic time, relying on hydraulic diffusion.…”

Section: Introductionmentioning

confidence: 99%

Numerical model of bone remodeling sensitive to loading frequency through a poroelastic behavior and internal fluid movements

Malachanne

Dureisseix

Jourdan

2011

Journal of the Mechanical Behavior of Biomedical Materials

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In this article, a phenomenological numerical model of bone remodeling is proposed. This model is based on the poroelasticity theory in order to take into account the effects of fluid movements in bone adaptation. Moreover, the proposed remodeling law is based on the classical 'Stanford' law, enriched in order to take into account the loading frequency, through fluid movements. This coupling is materialized by a quadratic function of Darcy velocity. The numerical model is carried out, using a finite element method, and calibrated using experimental results at macroscopic level, from the literature. First results concern cyclic loadings on a mouse ulna, at different frequencies between 1 Hz and 30 Hz, for a force amplitude of 1.5 N and 2 N. Experimental results exhibit a sensitivity to the loading frequency, with privileged frequency for bone remodeling between 5 Hz and 10 Hz, for the force amplitude of 2 N. For the force amplitude of 1.5 N, no privileged frequencies for bone remodeling are highlighted. This tendency is reproduced by the proposed numerical computations. The model is identified on a single case (one frequency and one force amplitude) and validated on the other ones. The second experimental validation deals with a different loading regime, an internal fluid pressure at 20 Hz on a turkey ulna. The same framework is applied, and the numerical and experimental data are still matching in terms of gain in bone mass density.

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Section: Introductionmentioning

confidence: 99%

Numerical model of bone remodeling sensitive to loading frequency through a poroelastic behavior and internal fluid movements

Malachanne

Dureisseix

Jourdan

2011

Journal of the Mechanical Behavior of Biomedical Materials

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“…In the present work, Doblaré and García (2002); García et al (2002)'s model is firstly enhanced to be coupled to an elasto-plastic material behaviour in a finite strain framework (see Mengoni and Ponthot (2010) for an isotropic version of this elasto-plastic damage coupling). The new model can therefore capture 24 permanent strains of the tissue beyond the ones due to the density variation only.…”

Section: The Remodelling Ratementioning

confidence: 99%

“…The yield criterion is expressed for the undamaged material, here the fully mineralised bone. Actually, this anisotropic model is applied to trabecular bone only while the cortical bone is considered as initially isotropic and remaining isotropic during remodelling, thus following an isotropic version of this anisotropic model (Mengoni and Ponthot, 2010).…”

Section: Phenomenological Remodelling Model Expressed In the Continuumentioning

confidence: 99%

A generic anisotropic continuum damage model integration scheme adaptable to both ductile damage and biological damage-like situations

Mengoni¹,

Ponthot²

2015

International Journal of Plasticity

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This paper aims at presenting a general versatile time integration scheme applicable to anisotropic damage coupled to elastoplasticity, considering any damage rate and isotropic hardening formulations. For this purpose a staggered time integration scheme in a finite strain framework is presented, together with an analytical consistent tangent operator. The only restrictive hypothesis is to work with an undamaged isotropic material, assumed here to follow a J 2 plasticity model. The only anisotropy considered is thus a damage-induced anisotropy.The possibility to couple any damage rate law with the present algorithm is illustrated with a classical ductile damage model for aluminium, and a biological damage-like application. The later proposes an original bone remodelling law coupled to trabecular bone plasticity for the simulation of orthodontic tooth movements. All the developments have been considered in the framework of the implicit non-linear finite element code Metafor (developed at the LTAS/MN 2 L, University of Liège, Belgium -www.metafor.ltas.ulg.ac.be).

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“…Our choice was dictated by the potential of application of the phenomenological models to other classes of materials, such as composite materials [35], or living tissues for biomechanical applications. In the latest case, the damage/remodeling processes associated to living bones can be easily dealt with using phenomenological models because in such a situation the damage variable is not an actual damage of the tissue but a measure of the bone density that can increase or decrease as a function of the biological processes involved [28].Moreover, authors who use a damage formulation generally tend to limit their model to only one hardening law coupled to one damage model. The present work is based on a generic phenomenological damage formulation that allows us to couple any hardening law with any damage model.…”

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confidence: 99%

An efficient 3D implicit approach for the thermomechanical simulation of elastic–viscoplastic materials submitted to high strain rate and damage

Jeunechamps

Ponthot

2013

Numerical Meth Engineering

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SUMMARYThis paper aims at presenting a general consistent numerical formulation able to take into account, in a coupled way, strain rate, thermal and damage effects on the behavior of materials submitted to quasistatic or dynamic loading conditions in a large deformation context. The main features of this algorithmic treatment are as follows: A unified treatment for the analysis and implicit time integration of thermo‐elasto‐viscoplastic constitutive equations including damage that depends on the strain rate for dynamic loading conditions. This formalism enables us to use dynamic thermomechanically coupled damage laws in an implicit framework. An implicit framework developed for time integration of the equations of motion. An efficient staggered solution procedure has been elaborated and implemented so that the inertia and heat conduction effects can be properly treated. An operator split‐based implementation, accompanied by a unified method to analytically evaluate the consistent tangent operator for the (implicit) coupled damage–thermo‐elasto‐viscoplastic problem. The possibility to couple any hardening law, including rate‐dependent models, with any damage model that fits into the present framework.All the developments have been considered in the framework of an implicit finite element code adapted to large strain problems. The numerical model will be illustrated by several applications issued from the impact and metal‐forming domains. All these physical phenomena have been included into an oriented object finite element code (implemented at LTAS‐MN 2L, University of Liège, Belgium) named Metafor.Copyright © 2013 John Wiley & Sons, Ltd.

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Isotropic continuum damage/repair model for alveolar bone remodeling

Cited by 16 publications

References 23 publications

Numerical model of bone remodeling sensitive to loading frequency through a poroelastic behavior and internal fluid movements

Numerical model of bone remodeling sensitive to loading frequency through a poroelastic behavior and internal fluid movements

A generic anisotropic continuum damage model integration scheme adaptable to both ductile damage and biological damage-like situations

An efficient 3D implicit approach for the thermomechanical simulation of elastic–viscoplastic materials submitted to high strain rate and damage

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