Modeling and simulation of microstructures using power diagrams: Proof of the concept

Kuhn, Martin R.; Steinhauser, Martin Oliver

doi:10.1063/1.2959733

Cited by 18 publications

(22 citation statements)

References 7 publications

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“…[25] use Voronoi tessellations to create 3D geometrical models of 2-phase ferrite/pearlite steel with periodic boundary conditions. Kühn and Steinhauser [26] model polycrystalline materials using power diagrams which are a generalisation of Voronoi diagrams for arbitrary dimensions. Voronoi tessellations have also been used to investigate fracture.…”

Section: Introductionmentioning

confidence: 99%

Analysis of two-phase ceramic composites using micromechanical models

Alveen

McNamara

Carolan

et al. 2014

Computational Materials Science

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Micromechanical models of two-phase ceramic composites are created using a modified Voronoi tessellation approach. These representative Finite Volume (FV) microstructures are used to investigate the role of microstructure on fracture of advanced ceramics. An arbitrary crack propagation model using a cell-centred finite volume based method is implemented. In particular the effect of matrix content is examined. It is shown that the underlying microstructure significantly affects the local stress and strain distributions for a two-phase ceramic containing hard particles in a softer matrix. Simulation results indicate that an increase in the volume fraction of these hard grains leads to an increase in strength of the composite material. Furthermore, it is found that the homogeneity of the microstructure affects the overall strength.

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Section: Introductionmentioning

confidence: 99%

Analysis of two-phase ceramic composites using micromechanical models

Alveen

McNamara

Carolan

et al. 2014

Computational Materials Science

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“…PDs are a well studied generalization of Voronoi diagrams for arbitrary dimensions [165] and have some major advantages over Voronoi diagrams as outlined in [168]. The suggested optimization is based on the statistical characterization of the grains in terms of the distribution of the grain areas A and the grain perimeters P obtained from cross-section micro-photographs, cf.…”

Section: Application: Simulating the Effect Of Shock Waves In Polycrymentioning

confidence: 99%

“…Then, the calculated histograms are compared with the experimental histograms A i exp and P i exp by calculating the first k central moments of the area and perimeter distributions A i and P i , respectively. A figure of merit m of conformity is defined according to which the PDs are optimized [168]:

m = \sum_{i = 1}^{k} {(\frac{P_{i} - P_{i}^{exp}}{P_{i}^{exp}})}^{2} + (\frac{A_{i} - A_{i}^{exp}}{A_{i}^{italicexp}}) .

The figure of merit m in Equation (46) is first calculated from the initial PD generated by a Poisson distribution of generator points. Using a reverse Monte-Carlo scheme, one generator point is chosen at random, its position modified and m is checked again.…”

Section: Application: Simulating the Effect Of Shock Waves In Polycrymentioning

confidence: 99%

A Review of Computational Methods in Materials Science: Examples from Shock-Wave and Polymer Physics

Steinhauser

Hiermaier

2009

IJMS

108

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This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment.

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“…In this work, however, a representative synthetically generated geometry is produced. Numerous studies have been carried out to produce numerical microstructures using Voronoi tessellation [5,6]. However there is little in the literature to show that numerical microstructures are actually representative of the real microstructures they were created to replace.…”

Section: Introductionmentioning

confidence: 99%

Micromechanical Modelling of Advanced Ceramics Using Statistically Representative Microstructures

Alveen

McNamara

Carolan

et al. 2013

KEM

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Abstract. Advanced ceramics are a class of materials used as cutting tools in some of the most demanding material removal operations. Their high hardness makes them extremely suited for use at these extreme conditions. However they have a relatively low fracture toughness when compared to other conventional tool materials.A combined experimental-numerical method was used to investigate the role of microstructure on the fracture of advanced ceramics. In particular, the effect of grain size and matrix content were examined. Representative finite volume (FV) microstructures were created using Voronoi tessellation. It is shown, by comparing with real micrographs, that the method captures the features of real microstructures in terms of grain size distribution and grain aspect ratio. It was found that the underlying microstructure significantly affects the failure of this class of materials. Furthermore, it was found that by altering the microstructural parameters in the numerical model, such as grain size and matrix content, it is possible to specify material improvements.

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Modeling and simulation of microstructures using power diagrams: Proof of the concept

Cited by 18 publications

References 7 publications

Analysis of two-phase ceramic composites using micromechanical models

Analysis of two-phase ceramic composites using micromechanical models

A Review of Computational Methods in Materials Science: Examples from Shock-Wave and Polymer Physics

Micromechanical Modelling of Advanced Ceramics Using Statistically Representative Microstructures

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