2023/06/19 by Dondl, Patrick, Hounkpe, Coffi Aristide, Jesenko, Martin
#35A15 #49M25 #74K10 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.10936
This work is motivated by the classical discrete elastic rod model by Audoly et al. We derive a discrete version of the Kirchhoff elastic energy for rods undergoing bending and torsion and prove Γ-convergence to the continuous model. This discrete energy is given by the bending and torsion energy of an interpolating conforming polynomial curve and provides a simple formula for the bending energy depending in each discrete segment only on angle and adjacent edge lengths. For the \liminf-inequality, we need to introduce penalty terms to ensure arc-length parametrization in the limit. For the recovery sequence a discretization with equal Euclidean distance between consecutive points is constructed. Particular care is taken to treat the interaction between bending and torsion by employing a discrete version of the Bishop frame.