Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method consists in finding the distribution of material phases that optimizes an objective function (e.g. thermoelastic properties) subject to certain constraints, such as elastic symmetry or volume fractions of the constituent phases, within a periodic base cell. The effective properties of the material structures are found using the numerical homogenization method based on a finite-element discretization of the base cell. The optimization problem is solved using sequential linear programming. To benchmark the design method we first consider two-phase designs. Our optimal two-phase microstructures are in fine agreement with rigorous bounds and the so-called Vigdergauz microstructures that realize the bounds. For three phases, the optimal microstructures are also compared with new rigorous bounds and again it is shown that the method yields designed materials with thermoelastic properties that are close to the bounds. The three-phase design method is illustrated by designing materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void.

Design of materials with extreme thermal expansion using a three-phase topology optimization method

Design of multiphysics actuators using topology optimization - Part I: One-material structures

Dip-in direct-laser-writing (DLW) optical lithography allows fabricating complex three-dimensional microstructures without the height restrictions of regular DLW. Bow-tie elements assembled into mechanical metamaterials with positive/zero/negative Poisson's ratio and with sufficient overall size for direct mechanical characterization aim at demonstrating the new possibilities with respect to rationally designed effective materials.

Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography.

Topology optimization is a computational tool that can be used for the systematic design of photonic crystals, waveguides, resonators, filters and plasmonics. The method was originally developed for mechanical design problems but has within the last six years been applied to a range of photonics applications. Topology optimization may be based on finite element and finite difference type modeling methods in both frequency and time domain. The basic idea is that the material density of each element or grid point is a design variable, hence the geometry is parameterized in a pixel-like fashion. The optimization problem is efficiently solved using mathematical programming-based optimization methods and analytical gradient calculations. The paper reviews the basic procedures behind topology optimization, a large number of applications ranging from photonic crystal design to surface plasmonic devices, and lists some of the future challenges in non-linear applications.

Topology optimization for nano‐photonics

Manufacturing-oriented topology optimization has been extensively studied the past two decades, in particular for the conventional manufacturing methods, for example, machining and injection molding or casting. Both design and manufacturing engineers have benefited from these efforts because of the close-to-optimal and friendly-to-manufacture design solutions. Recently, additive manufacturing (AM) has received significant attention from both academia and industry. AM is characterized by producing geometrically complex components layer-by-layer, and greatly reduces the geometric complexity restrictions imposed on topology optimization by conventional manufacturing. In other words, AM can make near-full use of the freeform structural evolution of topology optimization. Even so, new rules and restrictions emerge due to the diverse and intricate AM processes, which should be carefully addressed when developing the AM-specific topology optimization algorithms. Therefore, the motivation of this perspective paper is to summarize the state-of-art topology optimization methods for a variety of AM topics. At the same time, this paper also expresses the authors' perspectives on the challenges and opportunities in these topics. The hope is to inspire both researchers and engineers to meet these challenges with innovative solutions.

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Current and future trends in topology optimization for additive manufacturing

This paper describes a new way to design and fabricate compliant micromechanisms and material structures with negative Poisson's ratio (NPR). The design of compliant mechanisms and material structures is accomplished in an automated way using a numerical topology optimization method, The procedure allows the user to specify the elastic properties of materials or the mechanical advantages (MA's) or geometrical advantages (GA's) of compliant mechanisms and returns the optimal structures. The topologies obtained by the numerical procedure require practically no interaction by the engineer before they can be transferred to the fabrication unit. Fabrication is carried out by patterning a sputtered silicon on a plasma-enhanced chemical vapor deposition (PECVD) glass with a laser micromachining setup. Subsequently, the structures are etched into the underlying PECVD glass, and the glass is underetched, all in one two-step reactive ion etching (RIE) process. The components are tested using a probe placed on an x-y stage. This fast prototyping allows newly developed topologies to be fabricated and tested within the same day.

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O. Signund

Papers

Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio