2023/04/18 by Patrick Dondl, Dondl, Patrick, Yongming Luo +5
Computer Science · Decision Sciences · Engineering · #65C05 #65N30 #74B05 #74Q05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Probabilistic and Robust Engineering Design #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2304.08785
openalex publication_date 2023/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 Γ-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.