Stability analysis of the phase-field method for fracture with a general degradation function and plasticity induced crack generation

Arriaga, Miguel; Waisman, Haim

doi:10.1016/j.mechmat.2017.04.003

Cited by 35 publications

(10 citation statements)

References 69 publications

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“…The strong correlation between river marks and functional properties of implant allows one to estimate the degree of material degradation. Following Griffith’s seminal work [ 8 ] concerning a model predicting the crack initiation, subsequent investigators added to the understanding of plasticity [ 9 ], toughness [ 10 ], and complex geometries [ 11 , 12 , 13 ]. In orthopedic, fracture mechanics has been exploited to study microstructural damage and energy at the implant-bone interface [ 14 , 15 ].…”

Section: Introductionmentioning

confidence: 99%

Fatigue Crack Growth and Fracture of Internal Fixation Materials in In Vivo Environments—A Review

Guo

2021

Materials

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The development of crack patterns is a serious problem affecting the durability of orthopedic implants and the prognosis of patients. This issue has gained considerable attention in the medical community in recent years. This literature focuses on the five primary aspects relevant to the evaluation of the surface cracking patterns, i.e., inappropriate use, design flaws, inconsistent elastic modulus, allergic reaction, poor compatibility, and anti-corrosiveness. The hope is that increased understanding will open doors to optimize fabrication for biomedical applications. The latest technological issues and potential capabilities of implants that combine absorbable materials and shape memory alloys are also discussed. This article will act as a roadmap to be employed in the realm of orthopedic. Fatigue crack growth and the challenges associated with materials must be recognized to help make new implant technologies viable for wider clinical adoption. This review presents a summary of recent findings on the fatigue mechanisms and fracture of implant in the initial period after surgery. We propose solutions to common problems. The recognition of essential complications and technical problems related to various approaches and material choices while satisfying clinical requirements is crucial. Additional investigation will be needed to surmount these challenges and reduce the likelihood of fatigue crack growth after implantation.

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Section: Introductionmentioning

confidence: 99%

Fatigue Crack Growth and Fracture of Internal Fixation Materials in In Vivo Environments—A Review

Guo

2021

Materials

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“…At the same time, recent findings show [4] that a pivotal role in the performance of heterogeneous materials under cyclic loading is played by micro-plasticity. Specifically, the regions of asymptotic concentration of plastic deformations are the likely candidates for fatigue crack initialization [3,4]. Current methods of computing the asymptotic response (see e.g.…”

Section: Introductionmentioning

confidence: 99%

One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model

Gudoshnikov

Kamenskii

Makarenkov

et al. 2020

Math. Model. Nat. Phenom.

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We offer a finite-time stability result for Moreau sweeping processes on the plane with periodically moving polyhedron. The result is used to establish the convergence of stress evolution of a simple network of elastoplastic springs to a unique cyclic response in just one cycle of the external displacement-controlled cyclic loading. The paper concludes with an example showing that smoothing the vertices of the polyhedron makes finite-time stability impossible.

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“…Remark While the smaller the length scale l 0 is, the closer the fracture representation is to true cracks computational limitation preclude extremely small length scales . It is recommended that one should have at least two elements across the smeared crack width, which means the element size must be at least twice smaller than the length scale .…”

Section: Fundamentals Of the Phase Field Methodsmentioning

confidence: 99%

“…While the smaller the length scale l 0 is, the closer the fracture representation is to true cracks computational limitation preclude extremely small length scales. 42,[64][65][66] It is recommended that one should have at least two elements across the smeared crack width, which means the element size must be at least twice smaller than the length scale. 64 Nonetheless, to avoid some of those computational limitations, l 0 can be related to the Young modulus, critical energy and the strength of the material and could directly be calibrated against experimental results, as suggested in Borden 62 and Zhang et al 64 Remark 2.…”

Section: Governing Equationsmentioning

confidence: 99%

A novel phase field method for modeling the fracture of long bones

Shen

Waisman

Yosibash

et al. 2019

Numer Methods Biomed Eng

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A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This could be due to the complex, inhomogeneous bone microstructure, complex geometries, and the limitations of current fracture mechanics methods. In this paper, we develop a novel phase field method to investigate the proximal humerus fracture. To model the fracture in the inhomogeneous domain, we propose a power‐law relationship between bone mineral density and critical energy release rate. The method is validated by an in vitro experiment, in which a human humerus is constrained on both ends while subjected to compressive loads on its head, in the longitudinal direction, that lead to fracture at the anatomical neck. CT scans are employed to acquire the bone geometry and material parameters, from which detailed finite element meshes with inhomogeneous Young modulus distributions are generated. The numerical method, implemented in a high performance computing environment, is used to quantitatively predict the complex 3D brittle fracture of the bone and is shown to be in good agreement with experimental observations. Furthermore, our findings show that the damage is initiated in the trabecular bone‐head and propagates outward towards the bone cortex. We conclude that the proposed phase field method is a promising approach to model bone fracture.

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Stability analysis of the phase-field method for fracture with a general degradation function and plasticity induced crack generation

Cited by 35 publications

References 69 publications

Fatigue Crack Growth and Fracture of Internal Fixation Materials in In Vivo Environments—A Review

Fatigue Crack Growth and Fracture of Internal Fixation Materials in In Vivo Environments—A Review

One-period stability analysis of polygonal sweeping processes with application to an elastoplastic model

A novel phase field method for modeling the fracture of long bones

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