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One of the essential challenges of metamaterial design is being able to generate a material with specified material properties, like compression stiffness for example. It is reasonably straightforward to design new materials, then simulate or even physically test their properties. This is the forward problem. But the inverse problem — generating a material given a desired property — has remained elusive. A solution to this problem is exactly what is described in the recent paper Inverse-designed spinodoid metamaterials, by ETH researchers Siddhant Kumar, Stephanie Tan, Li Zheng and Dennis M. Kochmann (Nature NPJ Computational Materials, 2020).

After reading this paper I became a little obsessed with spinodoids. These are a class of materials that have a remarkable range of material expressions (both visually and in physical response), and a shockingly simple parametrization. It is a beautiful, clear and well-written paper that I highly recommend reading. I will only briefly summarize it here, then focus on a few of its fascinating themes. …


The study of metamaterials aims to extract extraordinary behaviours from ordinary materials through careful design on the scale of microstructure. At MESH we are particularly interested in the role of geometry in determining the macrostructural behaviour of such an “architected material”.

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An example of a metamaterial: the geometry of the lattice determines the emergent material property of the volume.

Additive manufacturing is a promising method for developing metamaterials: while the material (resin, polymer etc.) printed by the machine is typically of one type (with a predetermined stiffness etc.), we can achieve varying properties and compressive behaviours by changing the geometry of the print. Symmetric lattices are particularly appealing from a design perspective, and it is possible to attain a huge spectrum of material behaviour through a variation of the underlying geometry (one of my favourite papers on this topic is Panetta et al., 2015, which we draw on to generate our lattice data). However, the material properties of these lattices are typically assessed through a finite element simulation, which can be costly and time-consuming. …


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City of Toronto Building permits closed in 2018 by Forward Sortation Area

I developed a lot of respect for the work of data scientists last week, when I did a little project involving a data set of building permits for the city of Toronto. Like any good research project, it raised more questions than it answered, but I will record some of what I did learn here.

In broad strokes, I was interested in answering the following questions:
1. How has the rate and price of home renovation in Toronto changed over time?
2. How has the incidence of renovation by location in the city changed over time?
3. …


Like everyone everywhere these days, architects want to use machine learning. They want machine learning to design their buildings, to streamline their documentation burden, to provide realtime simulation results, and to close the feedback loop between design and engineering. Unfortunately, architects have a data problem.

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Let’s back up. Isn’t it true that architects feel that they are drowning in data? After all, the practice of BIM (Building Information Models) layers 3D geometry together with metadata representing everything from material choices to environmental analyses to spatial relationships. It could be argued that contemporary architecture projects are as much about data management as they are about designing anything. …


Have you ever noticed that most illustrations in math articles look the same? The same basic style, the same LaTeX’ed labels, similar lineweights and the same arrowheads? Why is this? Similarly, have you ever noticed that every single math article is written with a single font, Computer Modern (it IS a nice font, but still!)? Do you think it is odd that our disciplinary conventions of presentation are so very rigid?

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An example of a mathematical illustration.

Mathematical figures in journal articles serve an expository purpose. They are there to explain, not to prove. Proof by figure is not a concept mathematicians are fond of. In fact, algebra was effectively invented to do away with geometry, or at least to formalize it to try to avoid some misleading errors of accuracy. And it seems that mathematicians remain suspicious of figures, with the guiding principle that fewer is better. However, perhaps one of the reasons that figures are used so sparingly is that nice mathematical figures are hard to make! …

About

Elissa Ross

Mathematician working in the design industry.

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