Spherenes: A New Class of Minimal Surfaces
Interview with Christian
Waldvogel
While many new software tools may claim to allow designers and engineers to ‘think outside the box‘, only Spherene can claim to allow them to ‘think outside the sphere‘, with their metamaterial software based on the premise of ‘the opposite of a sphere‘.
Christian Waldvogel, founder and CEO of Spherene will be discussing their software and it’s capabilities at CDFAM Berlin.
To prepare attendees for his presentation, we asked Christian about the origin of their software, how a spherene compares to the beloved gyroid, and what people can expect from his talk at CDFAM.
What is Spherene?
Could you start by telling us about the meaning of the word spherene?
Yes, of course. I spent the better part of 2011 on an artist grant in Berlin, working towards creating the shape that represents the opposite of a sphere. A friend coined the term Spherene for it, as a portmanteau blending ‹sphere› + ‹serene›, alluding to a calm, wide and open space, to the view of an ocean, revealing the curvature of the Earth.
When, a few years after having founded spherene Ltd., it became clear that our software produces a metamaterial based that opposite of the sphere, the less poetic but more substantial ‹sphere› + ‹graphene› portmanteau was equally fitting.
I like the fact that our name offers two almost contradictory readings, just like the spherene metamaterial itself, which is random and regular at the same time.
Could you provide an overview of Spherene software, outlining its core functionalities and the specific needs it was designed to fulfill?
A ‹spherene› is a new type of minimal surface that is generated specifically for each design, taking into account all of the part’s requirements in one single step. This is fundamentally different from TPMS, which are generated by repeating, grading and trimming unit cells.
We had started out generating repetitive partial tilings of the hyperbolic plane and quasi-periodic minimal surfaces. When we introduced these pristine mathematics into the practice of design for manufacturing, we understood that what was needed was an adaptation to the erratic reality as it were, where designs need to amalgamate functional requirements, material properties, looks and branding, along with the constraints inherent to a certain production method. Thus we refocused on ‹Adaptive Density Minimal Surfaces› (ADMS) and began working on what has become the spherene metamaterial.
In order to create a spherene one needs to specify three things: an ‹Envelope› — the geometry that defines the shape inside of which it will be generated — and at least one value for the Density, Thickness, and Surface Bias fields.
These inputs control stiffness and springing behavior on global and local levels, and allow to crossfade between solid bulk, minimal surface and lattice-like structures of various volume fractions and thicknesses. Optional inputs include geometries that control the connections to a bounding shape or interfacing geometries, to create open or closed regions, and repulsors that locally inhibit surface generation.
From these inputs our cloud-based algorithm will create a surface conformal minimal surface, which means that it is fitted into its envelope such that its outer ends are perpendicular to the bounding shape. Material is placed just where needed and to the necessary amount, ascertaining that the mechanical requirements and printability are met in the most efficient way in terms of material and energy use.
Once finished, the result is delivered into the CAD client as an error-free, compressed mesh at adequate resolution and ready to be printed or integrated into more complex assemblies.
Two things stand out: (one) because of the regular characteristics of the spherene metamaterial, the performance of parts based on spherene can be precisely anticipated and, once ‹calibrated›, a design can be transformed in a purely computational manner to meet changing requirements. And (two) the fact that spherenes are at the same time isotropic and surface conformal leaves a user not with dealing with systemic interfaces and production limitations, but allows for higher level thinking.
Spherenes vs. Gyroids
Gyroids, gyroids, gyroids, it’s always about the gyroids with AM people. How do spherenes as Adaptive Density Minimal Surfaces (ADMS) differentiate itself from ‘traditional’ Triply Periodic Minimal Surface (TPMS) structures such as gyroids, both in terms of its underlying principles and practical benefits?
The name ‹ADMS› implies a fundamental relation to TPMS: both are Minimal Surfaces, with global zero mean curvature and two separate labyrinthine spaces. But that’s basically where the similarities end.
Let me use an image: think of a gyroid unit as a brick with which you can build a wall. This works very well, but around the doors and windows, and in the corners, you’ll probably need to cut some of the bricks. You’ll need to insert beams or prefabricated lintels above the openings, or do arches and extra brick cutting. A spherene, on the other hand, is the entire wall, including windows, doors, niches; round or rectangular.
Here the power of spherene becomes manifest: it is computed outside-in, going from the part shape and the entirety of interface situations to the interior. Inherently surface conformal. A complex part with keep-out zones, varying thickness, joints and latches is no more complicated to handle than a plain cube. Or a sphere.
Now imagine filling a sphere with a gyroid. The unit cell is simple to generate and quickly repeated. But there ends the facile phase, as joining a cubic pattern to any shape other than a cube is tedious and difficult. Think about how hard it is to distort a doubly curved surface so that it matches another, while trying not to destroy the zero mean curvature condition. And consider that we just saw that cutting bricks was tedious.
So to create the gyroid sphere you’re typically left with only one practical option: make too much gyroid, and trim everything outside of the sphere. Not only will this generate irregular and hardly controllable geometry, but the boolean trimming and data bloating might involve a whole set of other problems.
Aside from this, there is an even more fundamental difference: spherenes are isotropic, gyroids (and all other TPMS) are not. Because a periodic pattern needs to ‹end› on one side at the same place and inclination as it ‹began› on the other, it cannot have a balanced distribution of face normals. Spherenes and spheres however share the perfectly smooth face normal distribution that is unique to shapes that are the same in all directions. Even if, as is the case with spherenes, they are somewhat random from up close.
And the third difference is in how they are configured. To make a gyroid structure more or less dense, one will adjust the size of the unit cell and the wall thickness, hence probably not choosing the most efficient combination. In so doing one might distort the structure, hence losing the zero mean curvature condition. A spherene, on the other hand, is natively able to change density, and adjust its thickness-to-density ratio to be most efficient given the loads and printing method.
Applications at CDFAM Berlin
At the upcoming CDFAM Symposium in Berlin, what applications of Spherene will you be demonstrating?
Aside from introducing spherene and sharing our research insights, we might do a short software demo, and present some projects like a study for an ESA satellite bracket, research into stability and bone ingrowth in ceramic spherene structures for resorbable bone replacements, emulating the mass of an aluminum part in a steel print, or manufacturing personalized wheelchair cushions.
How do these examples underscore the value and capabilities of your software in addressing these design challenges?
When designing a real-world part for a certain type of load, one must account for this load being applied from differing directions either by adding material through guesswork, experience or safety factors, or include several load cases into one’s design. The former is the classical approach, the latter can be seen in methods like topology optimization.
With a design making use of spherene, a part being dimensioned for that load will perform equally well in adjacent load cases because spherenes are isotropic. Once perfected over the course of a few simulation/input correction iterations, virtually no stress concentrations occur under load and deformation, which makes such a part almost indestructible.
Needless to say that a physical part is first of all defined by the material it is made from, but it is interesting to note that spherene metamaterial allows to shift the natural behavior of a material: Titanium can become rather elastic, Ceramics might be comparatively ductile.
In the case of the satellite bracket, for example, a combination of using both the envelope geometry as well as the spherene configuration to control the vibration response in different directions, we were able to switch out the initially requested, harder, but less desirable Titanium for Aluminium.
In the bone ingrowth study we learned that our geometry performed at state of the art level in terms of ingrowth, but with a stability three times above the other samples.
The wheelchair cushion study (an independent university thesis) revealed that FDM printed spherene performs equal to the baseline foam, and injection mold applications showed an exceptionally high design efficiency with spherene as an infill providing both dimensional stability as well as autonomously generated surface tempering.
Integration with Existing Tools
Integration with existing design, engineering, and simulation software ecosystems is crucial for seamless workflow. How does Spherene connect with these tools, and what has been your approach to ensuring compatibility and interoperability?
Owing to its setup as a cloud API that receives simple control information, and returns spherene geometry, our system allows for access from many sources. At present, Rhino 3D is used as the host software, but spherene API access from other CAD systems will be enabled in the future.
Input geometries such as envelope and interfaces are uploaded as meshes after being imported or converted from any CAD system. Field information consists of values with coordinates, and can be created inside of host software, or imported from any other source such as a simulation result or a text editor.
Result geometries are returned as meshes ready for simulation or printing. In order to facilitate interoperability, our API caters to different types of simulation: one can generate the massless single surface geometry (sheet simulation, slicing for single pass printing), or the thickened solid surface (voxel-based simulation, printing), or two solids representing the hollow labyrinths (fluid simulation).
Effortless evacuation of powder or slurry is given, as is largely support-free printability. This means that our algorithm offers itself to occupy the last modeling slot in the manufacturing workflow, right before validation and print preprocessing.
API Functionality for Automated Workflows
Is there API functionality available with Spherene that would allow users to establish automated workflows for batch processing, design of experiments, or mass customization applications?
Yes, there is, in a way. You know, the beauty of spherenes is that performance prognosis and control inputs can be derived directly from a solid body simulation — a spherene is like an abstract bulk material with adjustable density. A spherene-based workflow is less about designing an object and then assessing its performance, but more about specifying performance and then calibrating the algorithm and validating the autonomously created design.
Once the requirements and generation parameters are properly defined, first results will already be fairly close to a workable solution. Variants using different random seeds are not all that different from one another; we see performance varying in the single digit percentage range. This means that the number of iterations needed for a satisfactory result is typically an order of magnitude smaller than with variant-based methods like topology optimization.
And once a configuration is ‹stable›, a workflow for mass customization only needs to take into account the way certain generation parameters react to changing requirements. So batch processing is possible, as are repetitive customization workflows; both are handled by the client rather than the API.
Key Takeaways and Goals for CDFAM Presentation
As participants of the CDFAM Symposium, what key insights do you hope they will take away from your presentation on Spherene?
As an artist, I’ve spent almost twenty years inventing, designing and producing things. This modus operandi continued well into the early days of our company, with plenty of joyfully endless sessions contemplating what one could do with our technology.
Having now boiled this down to a reliable piece of software, easy to understand and with just a few tools, the time has come to pass the baton, to have the world have these brainstorms.
We hope to instill in our audience an impulse to try it out, to invent, make things better, faster. And maybe simpler by making them more complicated.
What are your goals for participating in this event, and are there specific areas of collaboration or knowledge exchange you are particularly interested in exploring?
At the CDFAM Symposium we want to make most of this moment in our fledgling industry, which still consists of colleagues rather than competitors.
We work to getting the word out and to establish trust in our technology — which is a fundamentally new approach coming out of a small startup rather than a state-funded research institution.
We hope to establish collaborations to make the spherene technology trusted and widely accessible, and as often used as possible, in order to maximise its potential for savings in material and energy and reducing the manufacturing carbon footprint.
Our overarching aim, however, is to help shift human effort from solving design and manufacturing problems to dealing with the fundamental questions of what to produce and why, not having to turn a blind eye to what is happening in the world.
Register to attend CDFAM Berlin to connect with Christian and other experts in computational geometry and its applications at every scale for design and engineering, from metamaterials to architectural systems.
May 7-8, 2024 at AXICA, Berlin
