Book•
Random Heterogeneous Materials: Microstructure and Macroscopic Properties
19 Oct 2001-
TL;DR: In this article, a unified approach for the characterization of 2-dimensional (2-3D) moduli is presented. But the approach is not suitable for 3-dimensional moduli.
Abstract: Motivation and overview * PART I Microstructural characterization * Microstructural descriptors * Statistical mechanics of particle systems * Unified approach * Monodisperse spheres * Polydisperse spheres * Anisotropic media * Cell and random-field models * Percolation and clustering * Some continuum percolation results * Local volume fraction fluctuation * computer simulation and image analysis * PART II Microstructure property connections * Local and homogenized equations * Variational Principles * Phase-interchange relations * Exact results * Single-inclusion solutions * Effective medium approximations * Cluster expansions * Exact contrast expansions * Rigorous bounds * Evaluation of bounds * Cross-property relations * Appendix A Equilibrium Hard disk program * Appendix B Interrelations among 2-3D moduli* References * Index
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TL;DR: The integration of CTD with SFF to build designer tissue-engineering scaffolds is reviewed and the mechanical properties and tissue regeneration achieved using designer scaffolds are details.
Abstract: A paradigm shift is taking place in medicine from using synthetic implants and tissue grafts to a tissue engineering approach that uses degradable porous material scaffolds integrated with biological cells or molecules to regenerate tissues. This new paradigm requires scaffolds that balance temporary mechanical function with mass transport to aid biological delivery and tissue regeneration. Little is known quantitatively about this balance as early scaffolds were not fabricated with precise porous architecture. Recent advances in both computational topology design (CTD) and solid free-form fabrication (SFF) have made it possible to create scaffolds with controlled architecture. This paper reviews the integration of CTD with SFF to build designer tissue-engineering scaffolds. It also details the mechanical properties and tissue regeneration achieved using designer scaffolds. Finally, future directions are suggested for using designer scaffolds with in vivo experimentation to optimize tissue-engineering treatments, and coupling designer scaffolds with cell printing to create designer material/biofactor hybrids.
3,487 citations
TL;DR: In this article, the effects of particle size, particle/matrix interface adhesion and particle loading on the stiffness, strength and toughness of such particulate polymer composites are reviewed.
Abstract: There have been a number of review papers on layered silicate and carbon nanotube reinforced polymer nanocomposites, in which the fillers have high aspect ratios. Particulate–polymer nanocomposites containing fillers with small aspect ratios are also an important class of polymer composites. However, they have been apparently overlooked. Thus, in this paper, detailed discussions on the effects of particle size, particle/matrix interface adhesion and particle loading on the stiffness, strength and toughness of such particulate–polymer composites are reviewed. To develop high performance particulate composites, it is necessary to have some basic understanding of the stiffening, strengthening and toughening mechanisms of these composites. A critical evaluation of published experimental results in comparison with theoretical models is given.
2,767 citations
Cites background from "Random Heterogeneous Materials: Mic..."
...In addition, Hashin and Shtrikman [102] and others (see [103] and references therein) have developed sharper bounds (namely in a narrower range between the two bounds) for elastic moduli of composites....
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...Besides the abovementioned empirical or semi-empirical formulas and the bounding techniques micromechanics has already made a great success in prediction of the overall effective elastic moduli of composites [103,122]....
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...In addition, the statistical micromechanical theory, stochastic defect theory, and some other micromechanical theories [103] may be considered to elucidate the effects of particulate interaction....
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06 May 2002
TL;DR: Some of the greatest scientists including Poisson, Faraday, Maxwell, Rayleigh, and Einstein have contributed to the theory of composite materials Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients Although extensively studied for more than a hundred years, an explosion of ideas in the last five decades has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective moduli which govern the macroscopic behavior as mentioned in this paper.
Abstract: Some of the greatest scientists including Poisson, Faraday, Maxwell, Rayleigh, and Einstein have contributed to the theory of composite materials Mathematically, it is the study of partial differential equations with rapid oscillations in their coefficients Although extensively studied for more than a hundred years, an explosion of ideas in the last five decades (and particularly in the last three decades) has dramatically increased our understanding of the relationship between the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective (electrical, thermal, elastic) moduli which govern the macroscopic behavior This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification This 2002 book surveys these exciting developments at the frontier of mathematics
2,455 citations
TL;DR: In this paper, the basic principles involved in designing hierarchical biological materials, such as cellular and composite architectures, adapative growth and as well as remodeling, are discussed, and examples that are found to utilize these strategies include wood, bone, tendon, and glass sponges.
2,274 citations
Cites background from "Random Heterogeneous Materials: Mic..."
...Classical theoretical models to produce random cellular solids use Voronoi tessellations or level-cut Gaussian random fields [16,106]....
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...Main ideas about composite materials can be found in [15,16]....
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TL;DR: An analytical expression for the cluster coefficient is derived, which shows that the graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality are distinctly different from standard random graphs, even for infinite dimensionality.
Abstract: We analyze graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size of the largest cluster. We derive an analytical expression for the cluster coefficient, which shows that the graphs are distinctly different from standard random graphs, even for infinite dimensionality. Insights relevant for graph bipartitioning are included.
1,271 citations