Hill condition and overall properties of composites

Hazanov, S.

doi:10.1007/s004190050173

Cited by 84 publications

(41 citation statements)

References 10 publications

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“…The effective isotropic elastic modulus E eff is plotted with respect to average grey-value for seven segment models covering a range of grey-values, representative of the spread of grey-values observed in the scans. From the results it can be noted that E eff KUBC > E eff MUBC > E eff SUBC , consistent with the expectations of the windowing approach on the effects of the different boundary condition types and the generation of upper and lower bounds to effective elastic modulus, as described in 3,20,41 . However it is observed that overall the differences between E eff KUBC and E eff SUBC are not that significant and indeed in one case E eff KUBC ≈ E eff MUBC ≈ E eff SUBC indicating that a Representative Volume Element (RVE) has been identified 3 .…”

supporting

confidence: 84%

“…In the case where high resolution images of the real material microstructure are available, effective properties for the material microstructure can be evaluated using uniform boundary conditions 20 . This approach has been applied to a range of applications including random heterogeneous materials 22 , cancellous bone 43 and silicon carbide fibre reinforced composites 7 .…”

Section: Introductionmentioning

confidence: 99%

“…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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confidence: 84%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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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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“…Under the plane strain condition that is applied to the system, the indices i, j, k can be 1 or 2, and K differs from its three-dimensional counterpart while G remains the same. We impose an orthogonal mixed boundary condition (where displacements are applied on all sides of the specimen without friction), as the static (uniform traction) and kinematic (uniform displacement) conditions usually lead to a lower and upper bound for the effective elastic properties [29,30]. Finite element calculations are carried out using quadratic triangular elements and an adaptive re-meshing technique that yields finer meshes at high stress locations, to ensure a reliable and sufficiently resolved continuum solution for the stress and strain fields; the mesh size is therefore generally much smaller than the phase domain size.…”

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Elasticity of Random Multiphase Materials: Percolation of the Stiffness Tensor

Chen

Schuh

2015

J Stat Phys

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Topology and percolation effects play an important role in heterogeneous materials, but have rarely been studied for higher-order tensor properties. We explore the effective elastic properties of random multiphase materials using a combination of continuum computational simulations and analytical theories. The effective shear and bulk moduli of a class of symmetric-cell random composites with high phase contrasts are determined, and reveal shortcomings of classical homogenization theories in predicting elastic properties of percolating systems. The effective shear modulus exhibits typical percolation behavior, but with its percolation threshold shifting with the contrast in phase bulk moduli. On the contrary, the effective bulk modulus does not exhibit intrinsic percolation but does show an apparent or extrinsic percolation transition due to cross effects between shear and bulk moduli. We also propose an empirical approach for bridging percolation and homogenization theories and predicting the effective shear and bulk moduli in a manner consistent with the simulations.Keywords Percolation · Homogenization theory · Elastic theory · Effective elastic moduli · Random multiphase materials · Composite materials Predicting the effective elastic properties of heterogeneous materials is a fundamental interdisciplinary problem in physics, materials, and mechanics due to the pervasive presence of random multiphase materials in nature and engineering [1,2]. Many composite homogenization theories for effective elastic properties have quantitatively incorporated the effects of phase geometry and anisotropy, but largely overlook the role of disorder, topology, and per-B Ying Chen

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“…More detailed explanation on methods of applying the boundary conditions could be found in [48], [25], [24], [30] and [23].…”

Section: Strain Energy Methodsmentioning

confidence: 99%

Characterization of Homogenized Mechanical Properties of Porous Ceramic Materials Based on Their Realistic Microstructure

Rastkar¹

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The recent advances in the Materials Engineering have led to the development of new materials with customized microstructure in which the properties of its constituents and their geometric distribution have a considerable effect on determination of the macroscopic properties of the substance. Direct inclusion of the material microstructure in the analysis on a macro level is challenging since spatial meshes created for the analysis should have enough resolution to be able to accurately capture the geometry of the microstructure. In most cases this leads to a huge finite element model which requires a substantial amount of computational resources.To circumvent this limitation a number of homogenization techniques were developed. By considering a small element of the material, referred to as Representative Volume Element (RVE), homogenization methods make it possible to include the effects of a materials microstructure on the overall properties at the macro level.However, complexity of the microstructure geometry and the necessity of satisfying periodic boundary conditions introduce additional difficulties into the analysis procedure.In this dissertation we propose a hybrid homogenization method that combines Asymptotic homogenization with MeshFree Solution Structures Method (SSM). Our vi approach allows realistic inclusion of complex geometry of the microstructure that can be captured from micrographs or micro CT scans. In addition to unprecedented flexibility in handling complex geometries, this method also provides a completely automatic analysis procedure. Using meshfree solution structures simplifies meshing to creating a simple cartesian grid which only needs to contain the domain. This also eliminates manual modifications which usually needs to be performed on meshes created from image data.A computational platform is developed in C++ based on meshfree/asymptotic method. In this platform also a novel meshfree solution structure is designed to provide exact satisfaction of periodic boundary conditions for boundary value problems such as homogenization. Performance of the developed platform is tested over 2D and 3D domains against previously published data and/or conventional finite element methods. After getting satisfactory results, homogenized properties are used to compute localized stress and strain distributions over inhomogeneous structures.Furthermore, effects of geometric features of pores/inclusions on homogenized mechanical properties is investigated and it is demonstrated that the developed platform could provide an automated quantitative analysis tool for studying effects of different design parameters on homogenized properties.

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Hill condition and overall properties of composites

Cited by 84 publications

References 10 publications

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

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

Elasticity of Random Multiphase Materials: Percolation of the Stiffness Tensor

Characterization of Homogenized Mechanical Properties of Porous Ceramic Materials Based on Their Realistic Microstructure

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