Texas Differential Equations Conference 2018

Date: March 24, 2018
Location:Downtown UTSA Campus, Durango Building
Time: 1:30 PM - 2:30 PM


Mathematical Ideas and Techniques in Impact and Penetration Mechanics October 06, 2017 Seminars

Dr. James Walker

Director of the Engineering Dynamics Department

Southwest Research Institute

Modeling the response of materials and systems experiencing intense dynamic load is a challenging and interesting problem in classical mechanics. In this talk we discuss some of the analytical and numerical modeling approaches that are taken. The basic background is continuum mechanics (the graduate school version of F = ma, which in our situation are nonlinear hyperbolic partial differential equations) and the essential idea is taking data from simplified materials tests, which exhibit very nonlinear and path dependent behavior, and utilizing this material response data to model dynamic systems that undergo impact, shock waves, deformation, damage, and failure. The material data is collected at a scale of 0.1 to 1 cm and the systems are at a scale of 1 cm to 10s of meters. In the area of protection equipment and armor, we use the material all the way through total failure – it gives everything it has in the process of stopping a threat because we want to make the protection and safety equipment as light as possible. Metal plasticity theory is extensively used and has been very successful in modeling these events. Ceramics and fiber-based composites will be discussed with meso-scale modeling. Finally, the issue of scaling will be discussed. With an example taken from hypervelocity impact tests (impacts at speeds greater than 2 km/s = 4474 miles per hour), it will be seen that different scaling effects occur for the deformation/plasticity behavior than occur for the damage/ejecta behavior. Both processes occur concurrently in an event where the impulsive load lasts only microseconds (millionths of a second). Examples presented in the talk include impacts related to body armor worn by soldiers and police, the foam impact that caused the loss of the space shuttle Columbia, and impacts quantifying momentum enhancement that underlie the potential use of hypervelocity impactors to deflect asteroids.


Figure1.  A sequence of four frames from a high-speed video of a 4.45-cm diameter aluminum sphere striking a 1-meter diameter granite sphere at 2.1 km/s (SwRI).

Friday, October 27

FLN 2.02.06

4:00 - 5:00 PM