Cosserat Modeling of Trimmed Helicoid Soft Arms with a Separated-Section Constitutive Law
Cosserat rod models for soft robots usually construct sectional stiffness by summing material properties over a common cross-section. This assumption becomes inaccurate for trimmed helicoid arms, where load-bearing helix domains are separated and connected only through sparse fused crossings. This paper formulates a separated-section constitutive law that evaluates each helix domain in its local frame and pulls its constitutive response back to the backbone, yielding an effective backbone stiffness. Sparse-fusion mechanics captures the additional compliance caused by relative motion between neighboring domains and determines channel-wise reduction profiles $η_c(s/L)$ for bending, torsion, and extension. The resulting effective sectional stiffness is strongly anisotropic: bending and extension are reduced by about one order of magnitude, whereas torsion remains close to the effective backbone stiffness. The resulting sectional law is embedded in a geometrically exact dynamic Cosserat model with GVS discretization and routed-tendon actuation. Across 103 measured configurations, the three datasets give pooled normalized position errors of $7.7 \ \%$, $6.7 \ \%$, and $7.8 \ \%$, while each full-arm solve requires approximately $0.3 \ \mathrm{s}$ on one CPU core (Intel Xeon, Cascade Lake, $2.8 \mathrm{GHz}$), enabling rapid model-based planning, state and load estimation, and morphology--control co-design for architected soft robots.