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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Flow visualization

Flow visualization techniques are reviewed, with particular attention given to those applicable to liquid helium flows. Three techniques capable of obtaining qualitative and quantitative measurements of complex 3D flow fields are discussed including focusing schlieren, particle image volocimetry, and holocinematography (HCV). It is concluded that the HCV appears to be uniquely capable of obtaining full time-varying, 3D velocity field data, but is limited to the low speeds typical of liquid helium facilities.

Weinstein, Leonard M.↗
NASA NTRS2021

High Performance, Web-Based, Real-Time Telemetry Visualization for Deep Space Mission Support and Operations

The Jet Propulsion Laboratory’s Mission ControlSystems Section and Mobility and Robotic Systems Section havepartnered to developed a high-performance telemetry visualizationsystem, based on our mature, web-based, 3D visualizationsoftware technology, that provides mission trajectory designers,operations personnel and reconstruction analysts with a highlyaccurate, re-usable, multi-mission solution to interactively visualizeresults from Entry, Descent and Landing (EDL) simulations,real-time mission test beds, live telemetry streams during criticalmission events, such as landing, as well as post-event reconstructionanalysis. This work builds on previous mission visualizationsystems that we have deployed for a variety of flight missions andJPL organizations including NASA’s Mars Science Laboratory(MSL), NASA’S Low Density Supersonic Decelerator (LDSD),NASA’s Soil Moisture Active Passive (SMAP), JPL’s MoonRiseLunar sample return proposal. JPL’s mission design teams, JPL’sOffice of Naval Research tasks, and JPL’s Education and PublicOutreach Office.

Wenzel, Sean↗
NASA NTRS2017

3D-Sonification for Obstacle Avoidance in Brownout Conditions

Helicopter brownout is a phenomenon that occurs when making landing approaches in dusty environments, whereby sand or dust particles become swept up in the rotor outwash. Brownout is characterized by partial or total obscuration of the terrain, which degrades visual cues necessary for hovering and safe landing. Furthermore, the motion of the dust cloud produced during brownout can lead to the pilot experiencing motion cue anomalies such as vection illusions. In this context, the stability and guidance control functions can be intermittently or continuously degraded, potentially leading to undetected surface hazards and obstacles as well as unnoticed drift. Safe and controlled landing in brownout can be achieved using an integrated presentation of LADAR and RADAR imagery and aircraft state symbology. However, though detected by the LADAR and displayed on the sensor image, small obstacles can be difficult to discern from the background so that changes in obstacle elevation may go unnoticed. Moreover, pilot workload associated with tracking the displayed symbology is often so high that the pilot cannot give sufficient attention to the LADAR/RADAR image. This paper documents a simulation evaluating the use of 3D auditory cueing for obstacle avoidance in brownout as a replacement for or compliment to LADAR/RADAR imagery.

3D audio↗
NASA NTRS2002

The Science Behind the NASA/NOAA Electronic Theater 2002

Details of the science stories and scientific results behind the Etheater Earth Science Visualizations from the major remote sensing institutions around the country will be explained. The NASA Electronic Theater presents Earth science observations and visualizations in a historical perspective. Fly in from outer space to Temple Square and the University of Utah Campus. Go back to the early weather satellite images from the 1960s see them contrasted with the latest US/Europe/Japan global weather data. See the latest images and image sequences from NASA & NOAA missions like Terra, GOES, NOAA, TRMM, SeaWiFS, Landsat 7 visualized with state-of-the art tools. A similar retrospective of numerical weather models from the 1960s will be compared with the latest "year 2002" high-resolution models. See the inner workings of a powerful hurricane as it is sliced and dissected using the University of Wisconsin Vis-5D interactive visualization system. The largest super computers are now capable of realistic modeling of the global oceans. See ocean vortexes and currents that bring up the nutrients to feed phitoplankton and zooplankton as well as draw the crill fish, whales and fisherman. See the how the ocean blooms in response to these currents and El Nino/La Nina climate regimes. The Internet and networks have appeared while computers and visualizations have vastly improved over the last 40 years. These advances make it possible to present the broad scope and detailed structure of the huge new observed and simulated datasets in a compelling and instructive manner. New visualization tools allow us to interactively roam & zoom through massive global images larger than 40,000 x 20,000 pixels. Powerful movie players allow us to interactively roam, zoom & loop through 4000 x 4000 pixel bigger than HDTV movies of up to 5000 frames. New 3D tools allow highly interactive manipulation of detailed perspective views of many changing model quantities. See the 1m resolution before and after shots of lower Manhattan and the Pentagon after the September 11 disaster as well as shots of Afghanistan from the Space Imaging IKONOS as well as debris plume images from Terra MODIS and SPOT Image. Shown by the SGI-Octane Graphics-Supercomputer are visualizations of hurricanes Michelle 2001, Floyd, Mitch, Fran and Linda. Our visualizations of these storms have been featured on the covers of the National Geographic, Time, Newsweek and Popular Science. Highlights will be shown from the NASA's large collection of High Definition TV (HDTV) visualizations clips New visualizations of a Los Alamos global ocean model, and high-resolution results of a NASA/JPL Atlantic ocean basin model showing currents, and salinity features will be shown. El Nino/La Nina effects on sea surface temperature and sea surface height of the Pacific Ocean will also be shown. The SST simulations will be compared with GOES Gulf Stream animations and ocean productivity observations. Tours will be given of the entire Earth's land surface at 500 m resolution from recently composited Terra MODIS data, Visualizations will be shown from the Earth Science Etheater 2001 recently presented over the last years in New Zealand, Johannesburg, Tokyo, Paris, Munich, Sydney, Melbourne, Honolulu, Washington, New York City, Pasadena, UCAR/Boulder, and Penn State University. The presentation will use a 2-CPU SGI/CRAY Octane Super Graphics workstation with 4 GB RAM and terabyte disk array at 2048 x 768 resolution plus multimedia laptop with three high resolution projectors. Visualizations will also be featured from museum exhibits and presentations including: the Smithsonian Air & Space Museum in Washington, IMAX theater at the Maryland Science Center in Baltimore, the James Lovell Discovery World Science museum in Milwaukee, the American Museum of Natural History (NYC) Hayden Planetarium IMAX theater, etc. The Etheater is sponsored by NASA, NOAA and the American Meteorological Society. This presentation is brought to you by the University of Utah College of Mines and Earth Sciences and, the Utah Museum of Natural History.

Hasler, A. Fritz↗
NASA NTRS1991

Perceiving environmental structure from optical motion

Generally speaking, one of the most important sources of optical information about environmental structure is known to be the deforming optical patterns produced by the movements of the observer (pilot) or environmental objects. As an observer moves through a rigid environment, the projected optical patterns of environmental objects are systematically transformed according to their orientations and positions in 3D space relative to those of the observer. The detailed characteristics of these deforming optical patterns carry information about the 3D structure of the objects and about their locations and orientations relative to those of the observer. The specific geometrical properties of moving images that may constitute visually detected information about the shapes and locations of environmental objects is examined.

Lappin, Joseph S.↗
NASA NTRS2009

J-2X, The Engine of the Future

My project was two-fold, with both parts involving the J-2X Upper Stage engine (which will be used on both the Ares I and V). Mainly, I am responsible for using a program called Iris to create visual represen tations of the rocket engine's telemetry data. Also, my project includes the application of my newly acquired Pro Engineer skills in develo ping a 3D model of the engine's nozzle.

Smith, Gail↗
NASA NTRSDate not supplied

Virtual Diagnostics Interface (ViDI) for Planning Laser-Based Wind Tunnel Experiments

Virtual Diagnostics Interface (ViDI), originally introduced by Richard Schwartz in 2004 and described again by Alderfer, et. al., in 2007, is an interactive 3D software tool developed at NASA Langley Research Center to serve three main purposes: assist in pre-test planning, enhance post-test image analysis and visualization, and serve as a central location for data storage and distribution.1,2 ViDI is composed of custom-developed software and Autodesk® 3ds Max® as it incorporates Computer Aided Design (CAD) models with the results obtained from optical diagnostics.3 This software tool has proven useful in the field of optical diagnostics where pre-test planning of beam paths, optical elements, and test articles must be carried out to avoid interference, ensure spatial resolution is sufficient, and the camera Field of View (FoV) is adequate for the field of interest. Typically, practical considerations such as the distance a camera is from the region of interest, the angles at which the camera is oriented and issues such as the size of the camera and its sensor and size and focal length lens as well as the path of the laser need to be taken into account to predict a successful measurement. An example application of ViDI is shown in Fig.1 where an experiment to investigate flow separation over the wing of the High Lift Common Research Model (HL-CRM) is currently being planned in the National Transonic Facility (NTF) at NASA Langley Research Center.

virtual diagnostics interface↗
DOE OSTI2025

rcsb-api : Python Toolkit for Streamlining Access to RCSB Protein Data Bank APIs

The Protein Data Bank (PDB) was founded in 1971 as the first open-access digital data resource in biology to serve as the single global archive for three-dimensional (3D) macromolecular structure data. Current PDB holdings exceed 230,000 experimentally determined structures of proteins, nucleic acids, viruses, and macromolecular machines. The RCSB Protein Data Bank RCSB.org research-focused web portal facilitates search, analyses, and visualization of every PDB structure along with more than one million Computed Structure Models from AlphaFold DB and the ModelArchive. It is powered by a set of publicly available Application Programming Interfaces (APIs) that both support RCSB.org users and provide programmatic access to PDB data. Given the breadth and levels of granularity encompassed in this rich data collection, efficiently accessing the information programmatically may be challenging for new users. RCSB PDB has developed a Python software package, rcsb-api , that facilitates easy and efficient use of RCSB PDB APIs within a Python environment. This software tool is designed to streamline access to the extensive corpus of data housed within the PDB, enabling researchers to search, retrieve, and analyze 3D biostructure data seamlessly. Its use will accelerate research in structural biology, molecular biology and biochemistry, drug discovery, and bioinformatics by providing more efficient tools for data integration and analysis. The new toolkit is available on GitHub (github.com/rcsb/py-rcsb-api) and published to the public Python package repository (PyPI) to foster wider usage and support basic and applied research in fundamental biology, biomedicine, and the energy sciences.

FAIR principles↗
DOE OSTI2024

Modular Subsurface Sensors and Integrated Software for Advanced Subsurface Characterization and Monitoring using Unoccupied Vehicles

The advent and subsequent proliferation of autonomous airborne, waterborne, and groundbased vehicles (i.e., “drones”) promises to broadly transform the geosciences and associated industries, including fossil energy exploration and development, mineral resource exploration and development, water-resource management, and environmental remediation. For geophysical characterization and monitoring, the prospect of programming highly repeatable and low-cost drone missions for subsurface imaging will allow for deployments in hazardous and previously inaccessible areas. Coupled with autonomous workflows for data processing, management, and visualization, drone-based geophysical characterization and monitoring will enable unprecedented, real-time insight into diverse subsurface properties and processes of scientific and engineering importance. Toward this end, the objectives of this Lab Directed Research and Development (LDRD) project were to develop new (1) instrumentation for dronebased electromagnetic induction (EMI) geophysical imaging, including separated transmitter and receivers and associated electronics, (2) software for real-time data telemetry, processing, management, and visualization. Although EMI has been previously deployed using unoccupied aerial systems (UASs), these applications failed to capitalize on the game-changing capabilities of drone platforms. Whereas drone-based data acquisition allows for collection of rich, three-dimensional (3D) multi-offset/multi-angle configurations between transmitters and receivers, past efforts have relied on conventional instrumentation that was designed for ground-based data collection with the transmitter and a single receiver housed in the same unit; nor did these previous applications demonstrate real-time delivery of results to support rapid management decisions in the field. In this 1-year project, we (1) designed and constructed new lightweight independent transmitter and receiver antenna platforms that communicate with a laptop computer; (2) developed software to control data acquisition, manage/transfer data, and visualize data as its collected; and (3) demonstrated the operation of the new hardware and software systems in a ground-based field test. Our work entails major technological advances for EMI and established a foundation on which to build a new drone-based, real-time geophysical EMI imaging capability to support diverse challenges facing the nation.

47 OTHER INSTRUMENTATION↗
NASA NTRS2019

A Streamlined Approach to Spatial Mapping of Complex 3D Thermal Boundary Condition Data

Spatial mapping of 1D, 2D, and particularly 3D thermal boundary condition data is essential for accurate thermal simulation of spacecraft and launch vehicles. This information typically is available in simple ASCII file format but can be problematic to use for thermal simulations. Difficulties that can be encountered include the ability to directly use the available file format, transformation of the data into the desired reference coordinate system in 3D space, and accurate interpolation of the data onto the thermal calculation domain. This paper presents a streamlined approach to spatial mapping of complex unsymmetrical 3D cold wall heat flux data using the fields’ capability in Simcenter3D. A recent example of 3D thermal plume simulation at MSFC will be employed to illustrate the use of text, csv, and Excel files, specifying coordinate systems for transformation of data in 3D space, and use of the various interpolation schemes available for spatial mapping. Spatial boundary condition verification is also very important, and the spacecraft thermal analyst needs effective visualization tools to develop confidence in the boundary condition definitions. Visualization of the spacecraft plume raw field data, the calculated field data, and the interpolated field data onto the thermal calculation domain will be discussed, with a particular focus on real-time viewing of the interpolated data for available interpolation schemes. The objective of this paper is to outline the modeling techniques used with the integrated thermal analysis of a terrestrial lunar lander demonstrator. Specifically, the techniques outlined herein focus on spatial mapping of convective and radiative exhaust plume results from a computational fluid dynamics (CFD) analysis. Two cases were investigated, however, the modeling techniques that were utilized translate to both cases seamlessly. Those two cases were as follows: • Lunar lander demonstrator firing on-pad (worst case). • Lunar lander demonstrator hovering at an elevated position above the launch pad. For the purposes of information control, this paper will focus on the modeling techniques only, using altered or dimensionless data where necessary. BACKGROUND The thermal model examined in this paper is of the lunar lander demonstrator known as XL-1T (terrestrial), born from a collaborative effort between Masten Space Systems (MSS) and NASA, under NASA’s Lunar CATALYST (also known as Lunar Cargo Transportation and Landing by Soft Touchdown) initiative. The lander is a reusable vertical takeoff/vertical landing (VTVL) test bed which is controlled by four throttleable main engines utilizing green hypergolic propellants.

Hawkins, Robert F.↗
NASA NTRS2022

On-board Absolute Localization Based on Orbital Imagery for a Future Mars Science Helicopter

Future Mars Rotorcraft require advanced navigationcapabilities to enable all terrain access over long distance flightsthat are executed fully autonomously. A critical component toenable precision navigation during long traverses is the abilityto perform on-board absolute localization to eliminate drift inposition estimates of the on-board odometry algorithm. Inthis paper, we present an approach for on-board map-basedlocalization to provide global reference position based on orbitalor aerial image maps. Our approach builds on a vision-basedlocalization method to localize against a map derived fromHiRISE image products – an ortho-projected image (orthoimage) and a corresponding digital elevation map. The mapis pre-computed using a feature-based approach. Features arestored with their 3D world coordinates, and a descriptor to codethe local image intensity information in the vicinity of the featurelocation. An on-board matching algorithm uses this informationto match visual features in a query image acquired during flight,guided by a pose prior from the on-board range-visual-inertialstate estimator (Range-VIO). Valid matches are then used bya perspective-n-point (PnP) algorithm to estimate the absolutepose of the vehicle in a global frame. We demonstrate andevaluate our approach on simulated data, and data from UASflights.

Balaram, J. Bob↗
NASA NTRS2005

Solar System Visualizations

Solar System Visualization products enable scientists to compare models and measurements in new ways that enhance the scientific discovery process, enhance the information content and understanding of the science results for both science colleagues and the public, and create.visually appealing and intellectually stimulating visualization products. Missions supported include MER, MRO, and Cassini. Image products produced include pan and zoom animations of large mosaics to reveal the details of surface features and topography, animations into registered multi-resolution mosaics to provide context for microscopic images, 3D anaglyphs from left and right stereo pairs, and screen captures from video footage. Specific products include a three-part context animation of the Cassini Enceladus encounter highlighting images from 350 to 4 meter per pixel resolution; Mars Reconnaissance Orbiter screen captures illustrating various instruments during assembly and testing at the Payload Hazardous Servicing Facility at Kennedy Space Center; and an animation of Mars Exploration Rover Opportunity's 'Rub al Khali' panorama where the rover was stuck in the deep fine sand for more than a month. This task creates new visualization products that enable new science results and enhance the public's understanding of the Solar System and NASA's missions of exploration.

Brown, Alison M.↗
NASA NTRS2008

Vision System Measures Motions of Robot and External Objects

A prototype of an advanced robotic vision system both (1) measures its own motion with respect to a stationary background and (2) detects other moving objects and estimates their motions, all by use of visual cues. Like some prior robotic and other optoelectronic vision systems, this system is based partly on concepts of optical flow and visual odometry. Whereas prior optoelectronic visual-odometry systems have been limited to frame rates of no more than 1 Hz, a visual-odometry subsystem that is part of this system operates at a frame rate of 60 to 200 Hz, given optical-flow estimates. The overall system operates at an effective frame rate of 12 Hz. Moreover, unlike prior machine-vision systems for detecting motions of external objects, this system need not remain stationary: it can detect such motions while it is moving (even vibrating). The system includes a stereoscopic pair of cameras mounted on a moving robot. The outputs of the cameras are digitized, then processed to extract positions and velocities. The initial image-data-processing functions of this system are the same as those of some prior systems: Stereoscopy is used to compute three-dimensional (3D) positions for all pixels in the camera images. For each pixel of each image, optical flow between successive image frames is used to compute the two-dimensional (2D) apparent relative translational motion of the point transverse to the line of sight of the camera. The challenge in designing this system was to provide for utilization of the 3D information from stereoscopy in conjunction with the 2D information from optical flow to distinguish between motion of the camera pair and motions of external objects, compute the motion of the camera pair in all six degrees of translational and rotational freedom, and robustly estimate the motions of external objects, all in real time. To meet this challenge, the system is designed to perform the following image-data-processing functions: The visual-odometry subsystem (the subsystem that estimates the motion of the camera pair relative to the stationary background) utilizes the 3D information from stereoscopy and the 2D information from optical flow. It computes the relationship between the 3D and 2D motions and uses a least-mean-squares technique to estimate motion parameters. The least-mean-squares technique is suitable for real-time implementation when the number of external-moving-object pixels is smaller than the number of stationary-background pixels.

Talukder, Ashit↗
NASA NTRS2007

Automated Recognition of 3D Features in GPIR Images

A method of automated recognition of three-dimensional (3D) features in images generated by ground-penetrating imaging radar (GPIR) is undergoing development. GPIR 3D images can be analyzed to detect and identify such subsurface features as pipes and other utility conduits. Until now, much of the analysis of GPIR images has been performed manually by expert operators who must visually identify and track each feature. The present method is intended to satisfy a need for more efficient and accurate analysis by means of algorithms that can automatically identify and track subsurface features, with minimal supervision by human operators. In this method, data from multiple sources (for example, data on different features extracted by different algorithms) are fused together for identifying subsurface objects. The algorithms of this method can be classified in several different ways. In one classification, the algorithms fall into three classes: (1) image-processing algorithms, (2) feature- extraction algorithms, and (3) a multiaxis data-fusion/pattern-recognition algorithm that includes a combination of machine-learning, pattern-recognition, and object-linking algorithms. The image-processing class includes preprocessing algorithms for reducing noise and enhancing target features for pattern recognition. The feature-extraction algorithms operate on preprocessed data to extract such specific features in images as two-dimensional (2D) slices of a pipe. Then the multiaxis data-fusion/ pattern-recognition algorithm identifies, classifies, and reconstructs 3D objects from the extracted features. In this process, multiple 2D features extracted by use of different algorithms and representing views along different directions are used to identify and reconstruct 3D objects. In object linking, which is an essential part of this process, features identified in successive 2D slices and located within a threshold radius of identical features in adjacent slices are linked in a directed-graph data structure. Relative to past approaches, this multiaxis approach offers the advantages of more reliable detections, better discrimination of objects, and provision of redundant information, which can be helpful in filling gaps in feature recognition by one of the component algorithms. The image-processing class also includes postprocessing algorithms that enhance identified features to prepare them for further scrutiny by human analysts (see figure). Enhancement of images as a postprocessing step is a significant departure from traditional practice, in which enhancement of images is a preprocessing step.

Park, Han↗
NASA NTRS2004

Science Opportunity Analyzer (SOA): Science Planning Made Simple

.For the first time at JPL, the Cassini mission to Saturn is using distributed science operations for developing their experiments. Remote scientists needed the ability to: a) Identify observation opportunities; b) Create accurate, detailed designs for their observations; c) Verify that their designs meet their objectives; d) Check their observations against project flight rules and constraints; e) Communicate their observations to other scientists. Many existing tools provide one or more of these functions, but Science Opportunity Analyzer (SOA) has been built to unify these tasks into a single application. Accurate: Utilizes JPL Navigation and Ancillary Information Facility (NAIF) SPICE* software tool kit - Provides high fidelity modeling. - Facilitates rapid adaptation to other flight projects. Portable: Available in Unix, Windows and Linux. Adaptable: Designed to be a multi-mission tool so it can be readily adapted to other flight projects. Implemented in Java, Java 3D and other innovative technologies. Conclusion: SOA is easy to use. It only requires 6 simple steps. SOA's ability to show the same accurate information in multiple ways (multiple visualization formats, data plots, listings and file output) is essential to meet the needs of a diverse, distributed science operations environment.

observation planning operations↗
NASA NTRS2005

Combined Feature Based and Shape Based Visual Tracker for Robot Navigation

We have developed a combined feature based and shape based visual tracking system designed to enable a planetary rover to visually track and servo to specific points chosen by a user with centimeter precision. The feature based tracker uses invariant feature detection and matching across a stereo pair, as well as matching pairs before and after robot movement in order to compute an incremental 6-DOF motion at each tracker update. This tracking method is subject to drift over time, which can be compensated by the shape based method. The shape based tracking method consists of 3D model registration, which recovers 6-DOF motion given sufficient shape and proper initialization. By integrating complementary algorithms, the combined tracker leverages the efficiency and robustness of feature based methods with the precision and accuracy of model registration. In this paper, we present the algorithms and their integration into a combined visual tracking system.

Deans, J.↗
NASA NTRS2015

Spherical Coordinate Systems for Streamlining Suited Mobility Analysis

Introduction: When describing human motion, biomechanists generally report joint angles in terms of Euler angle rotation sequences. However, there are known limitations in using this method to describe complex motions such as the shoulder joint during a baseball pitch. Euler angle notation uses a series of three rotations about an axis where each rotation is dependent upon the preceding rotation. As such, the Euler angles need to be regarded as a set to get accurate angle information. Unfortunately, it is often difficult to visualize and understand these complex motion representations. It has been shown that using a spherical coordinate system allows Anthropometry and Biomechanics Facility (ABF) personnel to increase their ability to transmit important human mobility data to engineers, in a format that is readily understandable and directly translatable to their design efforts. Objectives: The goal of this project was to use innovative analysis and visualization techniques to aid in the examination and comprehension of complex motions. Methods: This project consisted of a series of small sub‐projects, meant to validate and verify a new method before it was implemented in the ABF's data analysis practices. A mechanical test rig was built and tracked in 3D using an optical motion capture system. Its position and orientation were reported in both Euler and spherical reference systems. In the second phase of the project, the ABF estimated the error inherent in a spherical coordinate system, and evaluated how this error would vary within the reference frame. This stage also involved expanding a kinematic model of the shoulder to include the rest of the joints of the body. The third stage of the project involved creating visualization methods to assist in interpreting motion in a spherical frame. These visualization methods will be incorporated in a tool to evaluate a database of suited mobility data, which is currently in development. Results: Initial results demonstrated that a spherical coordinate system is helpful in describing and visualizing the motion of a space suit. The system is particularly useful in describing the motion of the shoulder, where multiple degrees of freedom can lead to very complex motion paths.

Benson, Elizabeth↗
DOE OSTI2025

Toward engineering lattice structures with the material point method (MPM)

This study examines the potential of two variants of the material point method—the generalized interpolation material point (GIMP) and dual domain material point (DDMP) methods—in developing a robust computational framework for engineering lattice structures under different loading conditions. The study begins with assessing the ability of the two methods in predicting elastic buckling phenomena using column geometries with and without initial geometric imperfections. The results indicate that both methods effectively capture buckling phenomena when initial geometric imperfections are introduced. After this verification step, we create several models of tetrahedral lattice structures with varying strut diameter and orientation and subject them to quasi-static loading. We then validate the numerical results using laboratory test results. The results show that, while both methods accurately predict load–displacement curves in the pre-buckling regime, their predictive capabilities diminish in the post-buckling regime. Through visual comparison between the numerical and experimental deformed shapes, it appears that the discrepancies between model and experimental results are attributed to initial geometric imperfections in the lattices that occurred during 3D printing. We then establish a second set of lattice models where different types of initial geometric imperfections are considered. The results from these models show that imperfections have a negligible influence in the pre-buckling regime but affect the behavior considerably in the post-buckling regime. As a final step in this work, we subject the lattice models to impact loading and employ hypothetical soft and stiff materials. These results show that the lattice stiffness, which depends on material stiffness, strut diameter, and orientation, significantly influences the ability of a lattice structure to resist impact. In particular, we find that a stiffer lattice (i.e., one made with a stiff material and thicker struts) is capable of absorbing more energy than a softer one during impact. Although material nonlinearities, inelasticity, and detailed contact formulations are not considered in this study, the findings obtained herein lay the groundwork for engineering lattice structures under extreme loading conditions through a simulation-driven framework based on particle-based methods.

97 MATHEMATICS AND COMPUTING↗