A finite strain integral-type anisotropic damage model for fiber-reinforced materials: Application in soft biological tissues

Fathi, Farshid; Ardakani, Saeed Hatefi; Dehaghani, Peyman Fatemi; Mohammadi, Soheil

doi:10.1016/j.cma.2017.04.009

Cited by 24 publications

(12 citation statements)

References 52 publications

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“…The distance l between these two points is defined as

l = \sqrt{(x - y) \cdot (x - y)}

α (x, y)

is the nonlocal average operator defined as,

α false(boldx, boldy false) = \frac{α_{0} false(boldx, boldy false)}{0true \int_{V} α_{0} (x, y) d V} .

α_{0} false(boldx, boldy false)

denotes the weight function defined as

α_{0} false(boldx, boldy false) = {(() 1 - \frac{(x - y) \cdot (x - y)}{L_{r}^{2}})}^{2} .

Here,

L_{r}

is a scalar related to the intrinsic length, which is defined as the largest possible distance of a material point influencing the pitting behaviour of the material point x .…”

Section: Computational Modelling Methodsmentioning

confidence: 99%

Numerical simulation of the tissue differentiation and corrosion process of biodegradable magnesium implants during bone fracture healing

Zhou

Markert

2018

Z Angew Math Mech

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Biodegradable magnesium implants are considered as promising fixation devices in the orthopaedic application to replace the conventional implants with unexpected properties. Extensive applications of magnesium implants are still limited by the uncontrolled corrosion rate in the body fluid and their interactions with the tissue differentiation during bone healing. In addition, the evaluation of the mechanical integrity of implants is essential for stabilisation fractured bones. Therefore, a modelling approach is required to investigate the effect of the degradation process of implants on the healing efficiency of fractured bones. In the present work, a mechanoregulatory model based on the biphasic stimuli is used to simulate tissue differentiation of fractured tibia. A corrosion damage model is extended by employing a nonlocal integral formulation to describe the pitting corrosion of magnesium implants.The physiological loadings are taken into account in 3D simulations. The simulation results are consistent with the experimental observation in the literature. The present modelling approach provides an efficient tool in the design and the performance evaluation of biodegradable magnesium implants. K E Y W O R D Sbiodegradable magnesium, bone healing, numerical simulation, pitting corrosion modelling, tissue differentiation M S C ( 2 0 1 0 ) 00-xx

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“…The distance l between these two points is defined as

l = \sqrt{(x - y) \cdot (x - y)}

α (x, y)

is the nonlocal average operator defined as,

α false(boldx, boldy false) = \frac{α_{0} false(boldx, boldy false)}{0true \int_{V} α_{0} (x, y) d V} .

α_{0} false(boldx, boldy false)

denotes the weight function defined as

α_{0} false(boldx, boldy false) = {(() 1 - \frac{(x - y) \cdot (x - y)}{L_{r}^{2}})}^{2} .

Here,

L_{r}

is a scalar related to the intrinsic length, which is defined as the largest possible distance of a material point influencing the pitting behaviour of the material point x .…”

Section: Computational Modelling Methodsmentioning

confidence: 99%

Numerical simulation of the tissue differentiation and corrosion process of biodegradable magnesium implants during bone fracture healing

Zhou

Markert

2018

Z Angew Math Mech

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“…Fathi et al [ 69 ] had implemented a non-local integral-damage model to overcome the numerical artefacts such as mesh dependency and spurious localization in soft tissues. This damage model, which considers large deformation, was used to simulate aortic dissections.…”

Section: Damage Modelsmentioning

confidence: 99%

“…The damage model proposed by Fathi et al [ 69 ] was simulated with an integral-type non-local scheme that can be implemented on geometrically nonlinear soft tissue by overcoming mesh dependency. The role of the collagen fibres is also studied with the damage model and was found to be predominant.…”

Section: Damage Modelsmentioning

confidence: 99%

See 1 more Smart Citation

A Review on Damage and Rupture Modelling for Soft Tissues

et al. 2022

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Computational modelling of damage and rupture of non-connective and connective soft tissues due to pathological and supra-physiological mechanisms is vital in the fundamental understanding of failures. Recent advancements in soft tissue damage models play an essential role in developing artificial tissues, medical devices/implants, and surgical intervention practices. The current article reviews the recently developed damage models and rupture models that considered the microstructure of the tissues. Earlier review works presented damage and rupture separately, wherein this work reviews both damage and rupture in soft tissues. Wherein the present article provides a detailed review of various models on the damage evolution and tear in soft tissues focusing on key conceptual ideas, advantages, limitations, and challenges. Some key challenges of damage and rupture models are outlined in the article, which helps extend the present damage and rupture models to various soft tissues.

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“…Examples for spatially regularized damage models may be found, for example, in References 1,2,18‐23. Also for the finite‐strain regime, they have been used, compare References 24‐31. Such models may be applied to arbitrary loading velocities since any dependence of the material behavior on this boundary condition is included in a physically sound manner.…”

Section: Introductionmentioning

confidence: 99%

Efficient and robust numerical treatment of a gradient‐enhanced damage model at large deformations

Junker

Riesselmann

Balzani

2021

Numerical Meth Engineering

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The modeling of damage processes in materials constitutes an ill‐posed mathematical problem which manifests in mesh‐dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution, we present an extension of the efficient numerical treatment, which has been proposed by Junker et al. in 2019, to materials that are subjected to large deformations. Along with the model derivation, we present a technique for element erosion in the case of severely damaged materials. Efficiency and robustness of our approach is demonstrated by two numerical examples including snapback and springback phenomena.

show abstract

A finite strain integral-type anisotropic damage model for fiber-reinforced materials: Application in soft biological tissues

Cited by 24 publications

References 52 publications

Numerical simulation of the tissue differentiation and corrosion process of biodegradable magnesium implants during bone fracture healing

Numerical simulation of the tissue differentiation and corrosion process of biodegradable magnesium implants during bone fracture healing

A Review on Damage and Rupture Modelling for Soft Tissues

Efficient and robust numerical treatment of a gradient‐enhanced damage model at large deformations

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