  Motivated by an application involving additively manufactured bioresorbable
polymer scaffolds supporting bone tissue regeneration, we investigate the
impact of uncertain geometry perturbations on the effective mechanical
properties of elastic rods. To be more precise, we consider elastic rods
modeled as three-dimensional linearly elastic bodies occupying randomly
perturbed domains. Our focus is on a model where the cross-section of the rod
is shifted along the longitudinal axis with stationary increments. To
efficiently obtain accurate estimates on the resulting uncertainty of the
effective elastic moduli, we use a combination of analytical and numerical
methods. Specifically, we rigorously derive a one-dimensional surrogate model
by analyzing the slender-rod $\Gamma$-limit. Additionally, we establish
qualitative and quantitative stochastic homogenization results for the
one-dimensional surrogate model. To compare the fluctuations of the surrogate
with the original three-dimensional model, we perform numerical simulations by
means of finite element analysis and Monte Carlo methods.
