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Purpose <p>This study presents an energy-consistent reduced-order model designed to simulate the dynamics of slender bodies falling through Newtonian and non-Newtonian fluids. The primary objective is to create a computationally efficient framework that captures the complex interplay between fluid rheology (memory and yield) and structural flexibility while maintaining a strict discrete energy balance.</p> Methods <p>The model couples rigid-body degrees of freedom (surge, heave, pitch) with a modal bending coordinate. It incorporates potential-flow-consistent added mass, hydrostatic buoyancy, and quadratic sectional drag extended to include power-law scaling and Papanastasiou yield regularization. Non-Newtonian effects are modeled via finite-mode viscoelastic memory (Prony/Oldroyd-type projection) and a rate-sensitive modal viscoplastic return-map with direct plastic dissipation accounting. All generalized forces are evaluated using Gauss–Legendre projection. The numerical implementation is verified through memory ODE unit tests, quadrature and integrator convergence studies, and RK4 reference solutions, supported by explicit energy-decomposition diagnostics.</p> Results <p>Simulations quantify several rheology-dependent phenomena: under the tested conditions, shear-thinning increases terminal descent speed by approximately 10–15%. When the finite viscoelastic memory relaxation time is comparable to the pitch period, the model predicts ≈ 20–40% larger modal amplitudes and a similar prolongation of oscillation decay. Furthermore, moderate plastic yielding is shown to produce discrete elastic-energy drops and permanent changes to the body’s trajectory. The framework also provides a reproducible pathway for calibrating finite-mode memory parameters directly from rheometric data (G′, G′′).</p> Conclusions <p>The model clarifies the mechanistic pathways by which non-Newtonian physics alter falling-body dynamics. For robust production runs, the study recommends specific quadrature and time-integration practices (Nq ≥32). Future improvements highlight the implementation of structure-preserving integrators as a means to strictly isolate physical dissipation from algorithmic damping, thereby enhancing the predictive fidelity of the reduced-order approach.</p>

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Falling-body Dynamics in Complex Types of Rheology: An Energetic Modal Reduction with Memory, Yield and Plasticity

  • 期刊论文

  • 发表日期：

    2026年3月31日

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  • Jacob Nagler

摘要

Purpose

This study presents an energy-consistent reduced-order model designed to simulate the dynamics of slender bodies falling through Newtonian and non-Newtonian fluids. The primary objective is to create a computationally efficient framework that captures the complex interplay between fluid rheology (memory and yield) and structural flexibility while maintaining a strict discrete energy balance.

Methods

The model couples rigid-body degrees of freedom (surge, heave, pitch) with a modal bending coordinate. It incorporates potential-flow-consistent added mass, hydrostatic buoyancy, and quadratic sectional drag extended to include power-law scaling and Papanastasiou yield regularization. Non-Newtonian effects are modeled via finite-mode viscoelastic memory (Prony/Oldroyd-type projection) and a rate-sensitive modal viscoplastic return-map with direct plastic dissipation accounting. All generalized forces are evaluated using Gauss–Legendre projection. The numerical implementation is verified through memory ODE unit tests, quadrature and integrator convergence studies, and RK4 reference solutions, supported by explicit energy-decomposition diagnostics.

Results

Simulations quantify several rheology-dependent phenomena: under the tested conditions, shear-thinning increases terminal descent speed by approximately 10–15%. When the finite viscoelastic memory relaxation time is comparable to the pitch period, the model predicts ≈ 20–40% larger modal amplitudes and a similar prolongation of oscillation decay. Furthermore, moderate plastic yielding is shown to produce discrete elastic-energy drops and permanent changes to the body’s trajectory. The framework also provides a reproducible pathway for calibrating finite-mode memory parameters directly from rheometric data (G′, G′′).

Conclusions

The model clarifies the mechanistic pathways by which non-Newtonian physics alter falling-body dynamics. For robust production runs, the study recommends specific quadrature and time-integration practices (Nq ≥32). Future improvements highlight the implementation of structure-preserving integrators as a means to strictly isolate physical dissipation from algorithmic damping, thereby enhancing the predictive fidelity of the reduced-order approach.