English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A Material Point Method (MPM) algorithm is developed and utilized to investigate how the dynamics of (Langrangian) Navier-Stokes fluids as well as that of elastic solids is affected by trauma due to finite barriers. For the fluid simulations, material point particles are placed in a two dimensional pipe with various initial and boundary conditions and stationary perturbations to fluid flow. Results show that eddy currents are present not only in the wake of the perturbing object but are also responsible for disruption of laminar flow upstream from the barrier. An unfortunately relevant application for sudden finite trauma to an elastic solid involves simulations of an aircraft striking a large building under varying system conditions. The work presented here is introductory in nature; the potential ramifications and importance of continued study is discussed and emphasized. I. BACKGROUND AND IMPORTANCE Material Point Method (MPM) simulations have a wide variety of applications and can be used in computational modeling of systems having length scales spanning several orders of magnitude. Recent research on biological and geological systems has shown that fluid flow in ducts and pipes having small, abrupt obstructions can dramatically affect the behavior of the system vis a vis the character of fluid flow. In fact it is thought that the onset of certain types of heart attacks involves the transition from laminar blood flow to chaotic, which can be triggered by the presence of plaque or other sources of roughness on the vessel interior [1]. Because of the rapid change in behavior of fluid flow given even small obstructions, it seems that much could be gained by conducting computer simulations of fluidic flow around finite barriers. The MPM method conserves mass and momentum and is nicely suited to simulate a special case of the Navier-Stokes equation, which must be modified in order to deal with a AMERICAN JOURNAL OF UNDERGRADUATE RESEARCH VOL. 7, NO. 4 (2009) 8 reasonable model of fluid flow. However, the fluid-fluid viscosity interaction as well as that for the fluid-boundary present in the NavierStokes equations is absent in MPM and so we have developed an algorithm to simulate fluids which is a wedding of the two methods. The interaction of a fluid with a finite obstruction can be thought of as a trauma to the fluid. Since a fluid has elasticity but does not support shear forces except those incurred by viscosity (for example, those at a stationary boundary for no slip conditions) it is also of interest to examine the effect of finite trauma to an elastic body. A painfully obvious application is an aircraft impacting a large building. Since September 11, 2001 many such studies have been done and we would like to augment the current body of studies by comparing simulations of aircraft – building collisions. This paper presents preliminary results for simulations of collisions which investigate structural destruction due to beam pressure wave propagation, and sets the stage for a more detailed study where we may better understand how the post – collision pressure wave propagates throughout the building. Ultimately, with sophisticated enough simulations we may be able to gain practical insight into the construction of buildings that can withstand incredibly traumatic events. II. COMPUTATIONAL DETAILS The simulation of choice for our 2D fluid flow as well as 3D collision simulations is the Material Point Method (MPM) [2] with an algorithm developed and evaluated by Z. Chen and R. Brannon.[2] MPM is advantageous because it doesn't require a complex algorithm to simulate collisions or material failure. Instead, MPM maps the mass and momentum of groups of particles in the simulation to a background grid and utilizes the conservation equations of mass as well as that of momentum to ultimately advance the system through time. The use of the background grid also avoids entanglement associated with other contactbased algorithms. To begin with, the initial conditions for the simulation include a collection of particles with initial positions { 0 p x  }, velocities { 0 p v  } and boundary conditions chosen so as to reflect the important physics of the actual system as much as possible. Next, the background grid is defined, where computational space is separated into a defined number of grid cells in which nodes are placed in each corner of each cell. The mass Mp of each particle p at time t is mapped to the nodes i of the grid cells based on the shape function Ni ( t p x  ), resulting in the mass mi t of node i at time t:

Material Point Method Investigations of Trauma to Fluids and Elastic Solids Due to Finite Barriers