Numerical Method of Fabric Dynamics Using Front Tracking and Spring Model

Abstract

We use front tracking data structures and functions to model the dynamic evolution of fabric surface. We represent the fabric surface by a triangulated mesh with preset equilibrium side length. The stretching and wrinkling of the surface are modeled by the mass-spring system. The external driving force is added to the fabric motion through the “Impulse method” which computes the velocity of the point mass by superposition of momentum. The mass-spring system is a nonlinear ODE system. Added by the numerical and computational analysis, we show that the spring system has an upper bound of the eigen frequency. We analyzed the system by considering two spring models and we proved in one case that all eigenvalues are imaginary and there exists an upper bound for the eigen-frequency This upper bound plays an important role in determining the numerical stability and accuracy of the ODE system. Based on this analysis, we analyzed the numerical accuracy and stability of the nonlinear spring mass system for fabric surface and its tangential and normal motion. We used the fourth order Runge-Kutta method to solve the ODE system and showed that the time step is linearly dependent on the mesh size for the system.

On the verification and validation of a spring fabric for modeling parachute inflation

“…The numerical framework employed is based on the previous analysis and numerical verification in Li et al (2013) and Kim et al (2013). These previous analyses proved that the spring-mass system without external force is a conservative system and the motion of point mass in its tangential direction to the surface (or string on 2D) is purely oscillatory, and that there exists an upper bound for the eigen frequency of the oscillation:…”

“…v f , μ, and ρ are fluid velocity, viscosity, and density respectively. In the FronTier-airfoil Li et al, 2013) code used here, the pressure difference is computed after the velocity projection into the divergence-free space. We can then use the pressure difference on two sides of the canopy to compute v f and add it to the advection solver as flux from the immersed elastic surface.…”

“…The authors' previous studies of Kim et al (2013) and Li et al (2013) discuss the application of the mesoscale model in effects to mimic the dynamic motion of a fabric surface while coupled with an incompressible fluid solver for parachute inflating and descending. The numerical simulations demonstrated good agreement with the experimental results both qualitatively and quantitatively, but questions remain on the validity of the model and its relation to the continuum model of the fabric surface as an elastic membrane.…”

Verification and Validation of the Spring Model Parachute Air Delivery System in Subsonic Flow

“…When no external driving force is applied, the fabric surface, which is represented by the spring-mass system, is a conservative system whose total energy (kinetic energy plus potential energy) is a constant. Assuming each mesh point represents a point mass m in the spring system with position vector x i , the kinetic energy of the mass point i is T i = The original spring model [17] that serves as the basis for this effort is a simplified mesoscale model which assumes the force required to bend the surface is negligible and the force to stretch the surface is proportional to the displacement from the equilibrium distance between adjacent mass points. In this model, the kinetic energy and the potential energy of the triangulated mesh is given by…”

Front Tracking on Problems of US Air Force Interests SFFP (Preprint)

“…Figure 6 is a schematic plot of the spring-mass fabric model. In our previous papers [7,6], we introduced the use of spring-mass system as a meso-scale model to mimic the dynamic motion of fabric surface and incorporate this model into the numerical modeling and simulation of parachute system. We showed that the system is a conservative system (without external force and damping) and the motion is purely oscillatory in the direction tangential to the fabric surface.…”