# Scaling analysis and experiments for the apparent stiffness of woodpile lattices with tubular struts

## TL;DR

Researchers studied how the stiffness of 3D-printed woodpile lattices with tubular struts changes with their geometry and material properties.

## Contribution

They discovered a new structure-property relationship that does not follow a simple power law and showed tubular struts significantly reduce stiffness.

## Key findings

- Replacing solid struts with tubular ones reduces stiffness by up to an order of magnitude at the same porosity.
- A new structure-property relationship was identified: ⟨E⟩(r/t)^{1/2} ∼ (ρ̄)^2.
- 3D-printed tubular lattices offer customizable mechanical performance for multifunctional applications.

## Abstract

The apparent stiffness of woodpile lattices with tubular struts compressed diametrically in the stacking direction is investigated theoretically, experimentally and computationally. This architecture is inspired by multifunctional application in tissue engineering, where hierarchical porosity is important. A key result presented here is the absence of a simple power law of the form \documentclass[12pt]{minimal}
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\begin{document}$$\langle E\rangle \sim (\overline{\rho })^{m}$$\end{document} relating the apparent modulus to the apparent density, where m is an exponent. Here we show that the relationship \documentclass[12pt]{minimal}
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\begin{document}$$\langle E \rangle (r/t)^{\frac{1}{2}} \sim (\overline{\rho })^{2}$$\end{document} holds between the apparent modulus of elasticity and the geometric and materials parameters. This structure-property relationship is further examined computationally and experimentally. We successfully fabricated these structures using affordable commercial 3D printing machines that allow us to control properties by adjusting tube dimensions, thus offering new possibilities for optimizing structural performance. Compression tests confirm that replacing solid struts with tubular ones significantly reduces stiffness—up to an order of magnitude—at equivalent porosity levels. This reduction in stiffness underscores the crucial role of tubular strut geometry in determining the mechanical response of engineered lattices. Our findings provide valuable insights into the design and manufacture of advanced lattice structures, paving the way for customisable multifunctional materials.