LAUSR

Closed-form expressions are derived for the effective in-plane moduli $$E_{xx}$$ E xx and $$G_{xy}$$ G xy of fused filament fabrication material with aligned mesostructure at low porosity values. The void shape is approximated using a hypotrochoid, allowing stress and displacement fields around a single void to be calculated using the complex-variable method of elasticity. The effective moduli are then calculated by equating strain energies between a unit cell containing a void and an effective unit cell. Experimental results for $$E_{xx}$$ E xx as well as unit cell simulations show good agreement with predictions. Finally, the closed-form solution for the Young’s modulus ratio is compared against several existing models.