The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials. This allows us to derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design. Thus it is shown that the so-called artificial interpolation model in many circumstances actually falls within the framework of microstructurally based models. Single material and multi-material structural design in elasticity as well as in multi-physics problems is discussed.

/pdf/material-interpolation-schemes-in-topology-optimization-1ps0tr57ei.pdf

Material interpolation schemes in topology optimization

Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsoe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary” and several others. The paper gives an overview, comparison and critical review of the different approaches, their strengths, weaknesses, similarities and dissimilarities and suggests guidelines for future research.

Topology optimization approaches: A comparative review

http://web.stanford.edu/group/cui_group/papers/Hui_Today_2012.pdf

Designing nanostructured Si anodes for high energy lithium ion batteries

Graphene is a two-dimensional (2D) material with over 100-fold anisotropy of heat flow between the in-plane and out-of-plane directions. High in-plane thermal conductivity is due to covalent sp2 bonding between carbon atoms, whereas out-of-plane heat flow is limited by weak van der Waals coupling. Herein, we review the thermal properties of graphene, including its specific heat and thermal conductivity (from diffusive to ballistic limits) and the influence of substrates, defects, and other atomic modifications. We also highlight practical applications in which the thermal properties of graphene play a role. For instance, graphene transistors and interconnects benefit from the high in-plane thermal conductivity, up to a certain channel length. However, weak thermal coupling with substrates implies that interfaces and contacts remain significant dissipation bottlenecks. Heat flow in graphene or graphene composites could also be tunable through a variety of means, including phonon scattering by substrates, edges or interfaces. Ultimately, the unusual thermal properties of graphene stem from its 2D nature, forming a rich playground for new discoveries of heat flow physics and potentially leading to novel thermal management applications.

Thermal properties of graphene: Fundamentals and applications

This review paper provides an overview of different level-set methods for structural topology optimization. Level-set methods can be categorized with respect to the level-set-function parameterization, the geometry mapping, the physical/mechanical model, the information and the procedure to update the design and the applied regularization. Different approaches for each of these interlinked components are outlined and compared. Based on this categorization, the convergence behavior of the optimization process is discussed, as well as control over the slope and smoothness of the level-set function, hole nucleation and the relation of level-set methods to other topology optimization methods. The importance of numerical consistency for understanding and studying the behavior of proposed methods is highlighted. This review concludes with recommendations for future research.

Level-set methods for structural topology optimization: a review

Applying stress/strain on a material provides a mechanism to tune the thermal conductivity of materials dynamically or on demand. Experimental and simulation results have shown that thermal conductivity of bulk materials can change significantly under external pressure (compressive stress). However, stress/strain effects on the thermal conductivity of nanostructures have not been systematically studied. In this paper, equilibrium molecular-dynamics (EMD) simulation is performed to systematically study the strain effects on the lattice thermal conductivity of low-dimensional silicon and carbon materials: silicon nanowires (one dimensional) and thin-films (two dimensional), single-walled carbon nanotube (SWCNT, one dimensional) and single-layer graphene sheet (two dimensional). Spectral analysis of EMD is further developed and then applied to avoid the numerical artifacts such as the neglect of long-wavelength phonons that are often encountered when using EMD with periodic boundary conditions. Intrinsic thermal conductivity of the simulated bulk and nanostructures can be obtained using spectral analysis of EMD. The thermal conductivity of the strained silicon and diamond nanowires and thin films is shown to decrease continuously when the strain changes from compressive to tensile. However, for SWCNT and single-layer graphene, the thermal conductivity has a peak value, and the corresponding applied strain is at $\ensuremath{-}0.06$ or $\ensuremath{-}0.03$ for SWCNTs depending on the chirality and at zero for graphene, respectively. The following two reasons could explain well the effects of strains on the thermal conductivity of the nanowires and thin films that decreases continuously from compressive strain to tensile strain: (1) mode-specific group velocities of phonons decrease continuously from compressive strain to tensile strain and (2) the specific heat of each propagating phonon modes decrease continuously from compressive strain to tensile strain. However, for SWCNT and single-layer graphene, the mechanical instability induces buckling phenomenon when they are under compressive strains. The phonon-phonon scattering rate increases significantly when the structure buckles. This results in the decreasing behavior of thermal conductivity of SWCNT and graphene under compressive stress and explains the peak thermal conductivity value observed in SWCNT and single-layer graphene when they are under strain. The results obtained in this paper has important implications of challenging thermal management of electronics using advanced materials such as carbon nanotubes and graphene. It also points to a potentially new direction of dynamic thermal management.

Strain effects on the thermal conductivity of nanostructures

Reliability-based design of MEMS mechanisms by topology optimization

Material topology optimization is applied to determine the basic layout of a structure. The nonlinear structural response, e.g. buckling or plasticity, must be considered in order to generate a reliable design by structural optimization. In the present paper adaptive material topology optimization is extended to elastoplasticity. The objective of the design problem is to maximize the structural ductility which is defined by the integral of the strain energy over a given range of a prescribed displacement. The mass in the design space is prescribed. The design variables are the densities of the finite elements. The optimization problem is solved by a gradient based OC algorithm. An elastoplastic von Mises material with linear, isotropic work-hardening/softening for small strains is used. A geometrically adaptive optimization procedure is applied in order to avoid artificial stress singularities and to increase the numerical efficiency of the optimization process. The geometric parametrization of the design model is adapted during the optimization process. Elastoplastic structural analysis is outlined. An efficient algorithm is introduced to determine the gradient of the ductility with respect to the densities of the finite elements. The overall optimization procedure is presented and verified with design problems for plane stress conditions.

Kurt Maute

Papers

Topology optimization approaches: A comparative review

Level-set methods for structural topology optimization: a review

Strain effects on the thermal conductivity of nanostructures

Reliability-based design of MEMS mechanisms by topology optimization

Adaptive topology optimization of elastoplastic structures