Physical Finite Elements

Calisch, S. E. "Physical Finite Elements"


Engineering with digital materials, by discretely and reversibly assembling structure and function from a mass-produced construction kit of parts, is indeed an exciting vision. The ability to decouple conventionally linked material properties and reach new territory in parameter space has already been demonstrated by the fabrication of ultralight samples with extreme specific stiffness. Further, these material properties can be spatially varied, opening new possibilities in engineering design. The discrete assembly process also frees us from constraints of monolithic manufacturing and the corresponding supply chains. Thus, this approach offers compelling promise for the design, manufacture, and deployment of large structures.

In this thesis, we argue that digital materials offer a further benefit in the power and accuracy of simulation possible, as compared to modeling materials with less order. At the most general level, this comes from mirroring the discrete nature of the structure in the mathematical model, creating a hierarchical representation of the assembly and treating each level independently. The results can reduce the cost to design and validate complex structures, in both the required computational resources, as well as the time and testing cycles of human engineers.

We outline several techniques for structural modeling of such digital material assemblies, focusing on workflow flexibility and engineering empowerment through custom design tools. We demonstrate two effective table-top part production techniques: one for producing many tightly toleranced parts for validating simulations and one for producing high performance, directionally aligned composite parts in an out-of-autoclave process. We implement several structural tests in hardware and software, comparing results from modeling with empirical data. We show that at both the scale of individual parts, as well as of large assemblies, models synthesized from beam bending equations outperform more complicated and computationally intensive finite element simulations. Finally, we undertake an ambitious design study using these tools, using both simulation and physical testing to predict performance. The results suggest the feasibility of building skinned, lighter-than-air digital material structures, capable of withstanding atmospheric crush pressures and floating under the lift generated by the displaced air.

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