A Short Introduction to Continuum Micromechanics

Böhm, H.J.

doi:10.1007/978-3-7091-2776-6_1

Cited by 83 publications

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“…Unlike the effective properties, the apparent ones are affected by the boundary conditions. Yet, a multitude of embedding approaches can smoothen this impact and relax the periodicity constraints (Böhm 2016). The idea is to measure the properties of a core region embedded in larger outer region on which loads are applied.…”

Section: Introductionmentioning

confidence: 99%

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

Daszkiewicz

Maquer

Zysset

2016

Biomech Model Mechanobiol

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word count: 249 Total word count: 3393Attachments: 5 figures and 2 tables + 1 figure and 4 tables in the appendices 2 Disclosure pageThe authors have no conflict of interest to report. AcknowledgmentsThe script manager Medtool (www.dr-pahr.at) was used to generate the µFE models, start the computations and analyse the results. The authors would like to thank Prof. Bert van Rietbergen for sharing the µCT data. Karol Daszkiewicz is supported by grants from the are also gratefully acknowledged. AbstractBoundary conditions (BCs) and sample size affect the measured elastic properties of cancellous bone. Samples too small to be representative appear stiffer under kinematic uniform BCs (KUBCs) than under periodicity-compatible mixed uniform BCs (PMUBCs). To avoid those effects, we propose to determine the effective properties of trabecular bone using an embedded configuration. Cubic samples of various sizes (2.63, 5.29, 7.96, 10.58 and 15.87 mm) were cropped from µCT scans of femoral heads and vertebral bodies. They were converted into µFE models and their stiffness tensor was established via six uniaxial and shear load cases. PMUBCs-and KUBCs-based tensors were determined for each sample. "In situ" stiffness tensors were also evaluated for the embedded configuration, i.e. when the loads were transmitted to the samples via a layer of trabecular bone. The Zysset-Curnier model accounting for bone volume fraction and fabric anisotropy was fitted to those stiffness tensors and model parameters ν0 (Poisson's ratio), E0 and µ0 (elastic and shear moduli) were compared between sizes. BCs and sample size had little impact on ν0. However, KUBCs-and PMUBCs-based E0 and µ0 respectively decreased and increased with growing size, though convergence was not reached even for our largest samples. Both BCs produced upper and lower bounds for the in situ values that were almost constant across samples dimensions, thus appearing as an approximation of the effective properties. PMUBCs seem also appropriate for mimicking the trabecular core, but they still underestimate its elastic properties (especially in shear) even for nearly orthotropic samples.

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Section: Introductionmentioning

confidence: 99%

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

Daszkiewicz

Maquer

Zysset

2016

Biomech Model Mechanobiol

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“…The experimentally evaluated elastic modulus for PCL (E PCL ) of 277MPa, as per Section 4.1.1 below, was used for PCL phases and the elastic modulus of β-TCP was taken as 24.6GPa, as 13 per Section 3.3.1.2. A Poisson's ratio of 0.3 was assumed for both phases in all simulations and Abaqus/Standard V6.10 was used with NLGEOM selected.Given that, in this particular implementation, material segment size has been fixed for the micromechanical model by the full strut model element size (edge length of 28.8µm), the "windowing approach" is used to generate the effective elastic constants (and specifically in this case an effective isotropic elastic modulus (E eff ) and Poisson's ratio (ν eff )), as described for example in references 3,20,41 . Consistent with the windowing approach, three different sets of uniform boundary conditions were applied to the models as follows: Segments with significant porosity were excluded due to the complications of assigning KUBC and SUBC to these segments.…”

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Predicting the Elastic Properties of Selective Laser Sintered PCL/β-TCP Bone Scaffold Materials Using Computational Modelling

2013

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Publication InformationDoyle, H., Lohfeld, S., McHugh, P.E. (2013) 'Predicting the elastic properties of selective laser sintered PCL/b-TCP bone scaffold materials using computational modelling'. Annals Of Biomedical Engineering, 42 (3):661-677. Publisher SpringerLink to publisher's version http://link.springer.com/article/10.1007%2Fs10439-013-0913-4Item record http://hdl.handle.net/10379/5524 DOI http://dx.doi.org/10.1007/s10439-013-0913-4Accepted manuscript, published in Annals of Biomedical Engineering 09/2013; 42(3), pp 661-677. The final publication is available at Springer via http://dx.doi.org/10.1007/s10439-013-0913-4Title: Predicting the elastic properties of selective laser sintered PCL/β-TCP bone scaffold materials using computational modelling. AbstractThis study assesses the ability of finite element models to capture the mechanical behaviour of sintered orthopaedic scaffold materials. Individual scaffold struts were fabricated from a 50:50 wt% poly-ε-caprolactone (PCL) /β-tricalcium phosphate (β-TCP) blend, using selective laser sintering (SLS). The tensile elastic modulus of single struts was determined experimentally. High resolution finite element models of single struts were generated from micro-CT scans (28.8µm resolution) and an effective strut elastic modulus was calculated from tensile loading simulations. Three material assignment methods were employed: (1) homogeneous PCL elastic constants, (2) composite PCL/ β-TCP elastic constants based on rule of mixtures, and (3) heterogeneous distribution of micromechanically-determined elastic constants. In comparison with experimental results, the use of homogeneous PCL properties gave a good estimate of strut modulus; however it is not sufficiently representative of the real material as it neglects the β-TCP phase. The rule of mixtures method significantly overestimated strut modulus, while there was no significant difference between strut modulus evaluated using the micromechanically-determined elastic constants and experimentally evaluated strut modulus. These results indicate that the multi-scale approach of linking micromechancial modelling of the sintered scaffold material with macroscale modelling gives an accurate prediction of the mechanical behaviour of the sintered structure.Keywords: selective laser sintering; polycaprolactone, B-tricalcium phosphate; micromechanical modelling; bone tissue engineering; mechanical properties; finite element analysis.3 IntroductionThe purpose of bone tissue engineering scaffolds is to fill defects and support mechanical loading while providing a template on which new bone will form. The remodelling of native bone in response to mechanical loading occurs when cells convert mechanical stimuli to chemical signals to direct the formation of new tissue or resorption through mechanotransduction 30,44 . The mechanical stimuli that influence bone formation in vivo are a combination of both fluid shear over the cells 36,55 and mechanical loading of the cells 16,24,58 , therefore it is important to be able to acc...

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“…Figura 3: Schema di array esagonale periodico di inclusioni circolari (ad esempio fibre di rinforzo immerse in una matrice continua) e definizione di 11 possibili celle unitarie e delle relative condizioni al contorno [2].…”

Section: Metodi Basati Su Microstrutture Discreteunclassified

“…Figura 5: Tecniche di modellazione basate su microstrutture discrete: PMA, ECA e windowing approach (SVEs) [2].…”

Section: Metodi Basati Su Microstrutture Discreteunclassified

“…Tipici esempi di materiali eterogenei sono i materiali compositi, fibro-rinforzati o particellari, i materiali porosi, gli stessi metalli policristallini, ma anche il legno e l'osso. Una diretta conseguenza di questo concetto è l'approccio cosiddetto multiscala allo studio del comportamento meccanico dei materiali microstrutturati, associato a fenomeni e meccanismi peculiari della dimensione in cui si conduce l'analisi [1,2]. Un gran numero di problemi della Meccanica dei Solidi e della Scienza dei Materiali non può di fatto essere risolto tramite gli approcci convenzionali, poiché alla base delle effettive proprietà meccaniche di un materiale eterogeneo vi è la crescente necessità di incorporare informazioni fisiche sui micromeccanismi di deformazione e danneggiamento all'interno di modelli fenomenologici di plasticità o rottura, caratteristici dei materiali omogenei.…”

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La modellazione microstrutturale di materiali a struttura eterogenea: princìpi ed applicazioni

Collini

2010

Frattura Ed Integrità Strutturale

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sono facilmente risolvibili con gli approcci tradizionali. Oltre allo studio delle proprietà effettive dei solidi eterogenei, vi è la crescente necessità di incorporare un maggiore numero di informazioni sui meccanismi di deformazione e danneggiamento generati alla microscala, anche per i materiali abitualmente considerati omogenei. Micromeccanismi di cavitazione e concentrazioni locali di tensione e deformazione, sono indispensabili per spiegare fenomeni non-lineari come la rottura di fatica o il cedimento duttile, altrimenti non inquadrabili con approcci classici di tensioni e deformazioni medie. La micromeccanica si occupa della determinazione precisa, o di una stima accurata, di grandezze di campo microstrutturali locali. In questo lavoro sono illustrati i princìpi che sono alla base dell'approccio micromeccanico, come i concetti di multiscala, di distribuzione statistica delle fasi, di descrizione mediante volumi di riferimento e di omogeneizzazione e localizzazione, e, attraverso alcune applicazioni pratiche delle principali tecniche di modellazione, sono illustrati e discussi criticamente i risultati della ricerca effettuata su varie strutture di ghisa nodulare. ABSTRACT.There are many problems in Solid Mechanics, Physics of Solids and Materials Science that can not been solved using conventional approaches. Besides the effective properties of non-homogeneous bodies, there is an increasing need for incorporating more physical information about small-scale mechanisms of deformation and damage into phenomenological models of plasticity and rupture of materials which are usually considered homogeneous. Cavitation, local stress or strain concentrations at small scale are essential to explain nonlinear phenomena, such as fatigue or ductile rupture, which are not understandable from the simple point of view of average stresses or strains. Precise determination or accurate estimation of local fields is the domain of micromechanics. This work treats the basic concepts of the micromechanics in a simple way, with some practical suggestion on the most commonly used modelling techniques and some applications made by the author on various nodular cast iron microstructures. KEYWORDS.Modellazione micromeccanica; Materiali a struttura eterogenea; Compositi; Comportamento elasto-plastico. INTRODUZIONE ALLA MECCANICA DEI MATERIALI MICROSTRUTTURATIMateriali microstrutturati e concetto di scala di osservazione a Micro-e Meso-Meccanica del Continuo è una branca relativamente giovane della Meccanica dei Materiali, che studia il comportamento meccanico dei materiali a livello microstrutturale. Molti dei materiali di interesse industriale ed ingegneristico, e la maggior parte dei materiali "naturali", presentano una struttura eterogenea, formata cioè da più costituenti o "fasi", distinguibili ad una certa (ridotta) scala di osservazione. In altre parole, ciò che al L

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A Short Introduction to Continuum Micromechanics

Cited by 83 publications

References 138 publications

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

The effective elastic properties of human trabecular bone may be approximated using micro-finite element analyses of embedded volume elements

Predicting the Elastic Properties of Selective Laser Sintered PCL/β-TCP Bone Scaffold Materials Using Computational Modelling

La modellazione microstrutturale di materiali a struttura eterogenea: princìpi ed applicazioni

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