Theoretical Scaling Analysis of Hydrostatic Skeleton Principles: Projecting Mechanics from Earthworm to Infrastructure

Abstract

Nature has optimized hydrostatic skeletons over 500 million years, yet engineering applications have historically been limited to small-scale soft robotics. This paper presents a theoretical scaling analysis of hydrostatic principles, projecting their performance from the biological scale (earthworm Lumbricus terrestris, ∼0.001 m³) to infrastructure dimensions (10–100 m³)—an 83,000× volumetric increase.Using a modified Gibson-Ashby cellular solids model adapted for fluid-filled constraints, we analyze the structural mechanics of the proposed Adaptive Matrix Ecosystem (AME). Our analysis suggests that key biological performance metrics—including operating pressure (5–15 kPa), elastic coupling moduli (2–8 MPa), and damping ratios (ζ ≈ 0.50–0.63)—can theoretically be preserved across this scale gap.Computational validation using discrete element analysis indicates stress reduction of 8.1× compared to equivalent monolithic structures. Furthermore, topological network analysis predicts that hierarchical cellular organization can yield load distribution advantages through network connectivity. This work establishes a mathematical basis for the design of large-scale, resilient water-based infrastructure.