Three-scale finite element analysis of heterogeneous media by asymptotic homogenization and mesh superposition methods

Takano, Naoki; Okuno, Yoshihiro

doi:10.1016/j.ijsolstr.2004.02.049

Cited by 33 publications

(19 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The average macroscopic stress in Table 1 can be used to assess the material yield at the microscopic level of the lattice struts. For unit cells located at the implant boundary, where non-periodic local heterogeneity and nonuniform macroscopic field exist, the finite element mesh superposition method integrated with AH is better suited to capture the microscopic stress distribution with higher accuracy (Takano et al, 2010;Takano and Okuno, 2004;Takano et al, 2000;Takano et al, 2003). This would significantly reduce the computational cost of the numerical simulations, since a fully detailed FEA of the implant might be unfeasible.…”

Section: Verification Of the Numerical Resultsmentioning

confidence: 99%

“…These defects result in local non-periodic heterogeneities and stress concentrations which affect the stiffness and strength of the lattice. A multiscale finite element analysis (Takano et al, 2010;Takano and Okuno, 2004;Takano et al, 2003) combining enhanced mesh superposition method with AH theory could be implemented. In addition, further work is required to examine the sensitivity of the results to variations of bulk material properties.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Fatigue design of a mechanically biocompatible lattice for a proof-of-concept femoral stem

Khanoki

Pasini

2013

Journal of the Mechanical Behavior of Biomedical Materials

View full text Add to dashboard Cite

A methodology is proposed to design a spatially periodic microarchitectured material for a twodimensional femoral implant under walking gait conditions. The material is composed of a graded lattice with controlled property distribution that minimizes concurrently bone resorption and interface failure. The periodic microstructure of the material is designed for fatigue fracture caused by cyclic loadings on the hip joint as a result of walking. The bulk material of the lattice is Ti6AL4V and its microstructure is assumed free of defects. The Soderberg diagram is used for the fatigue design under multiaxial loadings. Two cell topologies, square and Kagome, are chosen to obtain optimized property gradients for a two-dimensional implant. Asymptotic homogenization (AH) theory is used to address the multiscale mechanics of the implant as well as to capture the stress and strain distribution at both the macro and the microscale. The microstress distribution found with AH is also compared with that obtained from a detailed finite element analysis. For the maximum value of the von Mises stress, we observe a deviation of 18.6 % in unit cells close to the implant boundary, where the AH assumption of spatial periodicity of the fluctuating fields ceases to hold. In the second part of the paper, the metrics of bone resorption and interface shear stress are used to benchmark the graded cellular implant with existing prostheses made of fully dense titanium implant.The results show that the amount of initial postoperative bone loss for square and kagome lattice implants decreases, respectively, by 53.8% and 58%. In addition, the maximum shear interface failure at the distal end is significantly reduced by about 79%.A set of proof-of-concepts of planar implants have been fabricated via Electron Beam Melting (EBM) to demonstrate the manufacturability of Ti6AL4V into graded lattices with alternative cell size. Optical microscopy has been used to measure the morphological parameters of the cellular microstructure, including cell wall thickness and pore size, and compared them with the nominal values. No sign of fracture or incomplete cell walls was observed, an assessment that shows the satisfactory metallurgical bond of cell walls and the structural integrity of the implants.

show abstract

Section: Verification Of the Numerical Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Fatigue design of a mechanically biocompatible lattice for a proof-of-concept femoral stem

Khanoki

Pasini

2013

Journal of the Mechanical Behavior of Biomedical Materials

View full text Add to dashboard Cite

show abstract

“…• Cette idée est reprise dans [58], où les auteurs nous proposent d'associer l'homogé- Si on écrit le déplacement, en adoptant l'indice G pour le maillage global et l'indice L pour le maillage local ( Fig. 2.6), sous la forme :…”

Section: Méthodes Multi-niveauxunclassified

A new fully coupled two-scales modelling for mechanical problems involving microstructure: The 95/5 technique

Missoum-Benziane

Ryckelynck

Chinesta

2007

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

“…To solve this problem, this paper utilized the multiscale computational methods, i.e., asymptotic homogenization method (Lions, 1981, Guedes andKikuchi, 1990) and finite element mesh superposition method (or s-version FEM) (Fish, 1982, Takano, et al, 1999, Takano and Okuno, 2004 to analyze microscopic stress around acetabular cup implant in THA. The microstructure model of trabecular bone was obtained by micro-CT with 0.017 mm resolution.…”

Section: Introductionmentioning

confidence: 99%

Multiscale stress analysis of trabecular bone around acetabular cup implant by finite element mesh superposition method

Tsukino¹,

Takano²,

Michel

et al. 2015

Mechanical Engineering Letters

Self Cite

View full text Add to dashboard Cite

Microscopic stress was calculated with 0.017 mm resolution in a macroscopic model with approximately 100 mm size using the finite element mesh superposition method. To bridge the large gap in resolution, an intermediate finite element model was newly used. This multiscale computational procedure was applied to the biomechanical problem to analyze the microscopic stress in the trabecular bone around acetabular cup implant in total hip arthroplasty, which occurs by direct contact of the implant with trabecular bone. In the microstructural modeling of highly porous media such as the trabecular bone, special attention was paied to the boundary of microstructure model for both homogenization procedure and mesh superposition procedure. Three demonstrative numerical results revealed that higher stress occured at microscale due to macroscopic stress concentration, which is hardly estimated by only bone volume fraction.

show abstract

Three-scale finite element analysis of heterogeneous media by asymptotic homogenization and mesh superposition methods

Cited by 33 publications

References 34 publications

Fatigue design of a mechanically biocompatible lattice for a proof-of-concept femoral stem

Fatigue design of a mechanically biocompatible lattice for a proof-of-concept femoral stem

A new fully coupled two-scales modelling for mechanical problems involving microstructure: The 95/5 technique

Multiscale stress analysis of trabecular bone around acetabular cup implant by finite element mesh superposition method

Contact Info

Product

Resources

About