Many natural structures, while being lightweight and porous, exhibit respectable levels of stiffness. Natural structural designs are complex and hierarchical, and with the surge in societal demand for lighter weight, durable, yet resilient materials, there is a concurrent research need to consider biomimetic materials as alternatives to traditional materials since these can be manufactured more easily now than ever before, with significant advancements made in the area of digital design and manufacture. Our study considered porous Bouligand structures, which are structures built up of twisting fibrous architecture, but with spaces set between the fibres which induce porosity into the structure. These are more complicated than non-porous Bouligand structures, since the addition of porosity into the material creates a secondary variable besides fibre pitch. As such, there is currently no analytical model available to predict the modulus of such materials.

Our paper explores the correlation between porosity, polymer fibre pitch angle, and flexural modulus in porous-Bouligand-structured polymers. Our structures were digitally manufactured using SLA additive manufacturing methods, after which they were subjected to three-point bending tests. Our aim was to simply and parametrically develop an analytical model that would capture the influences of both porosity and polymer fibre pitch angle on the flexural modulus of the material.

Our model is shown below and we derive this by applying non-linear regression to our experimental data.

This model predicts the flexural modulus, , of porous-Bouligand-structured polymer as a function of both porosity and pitch angle. Here, is a linear reduction of the modulus as a function of increasing porosity and is defined as the solid material modulus, , multiplied by porosity, , while signifies the polymer fiber pitch angle. This relationship is relatively accurate within the range of 10⁰ ≤ ≤ 50⁰ and for porosity values in the range 0.277 ≤ ≤ 0.356, as supported by our evidence to date.