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Modelling and Simulation in Engineering
Volume 2013, Article ID 815158, 11 pages
Research Article

Modeling the Dynamic Failure of Railroad Tank Cars Using a Physically Motivated Internal State Variable Plasticity/Damage Nonlocal Model

1Center for Advanced Vehicular Systems, Mississippi State University, 200 Research Boulevard, Mississippi State, MS 39762, USA
2School of Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85287, USA
3Mechanical Engineering Department, Mississippi State University, Mississippi State, MS 39762, USA

Received 28 September 2012; Revised 11 December 2012; Accepted 14 January 2013

Academic Editor: Chung-Souk Han

Copyright © 2013 Fazle R. Ahad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We used a physically motivated internal state variable plasticity/damage model containing a mathematical length scale to idealize the material response in finite element simulations of a large-scale boundary value problem. The problem consists of a moving striker colliding against a stationary hazmat tank car. The motivations are (1) to reproduce with high fidelity finite deformation and temperature histories, damage, and high rate phenomena that may arise during the impact accident and (2) to address the material postbifurcation regime pathological mesh size issues. We introduce the mathematical length scale in the model by adopting a nonlocal evolution equation for the damage, as suggested by Pijaudier-Cabot and Bazant in the context of concrete. We implement this evolution equation into existing finite element subroutines of the plasticity/failure model. The results of the simulations, carried out with the aid of Abaqus/Explicit finite element code, show that the material model, accounting for temperature histories and nonlocal damage effects, satisfactorily predicts the damage progression during the tank car impact accident and significantly reduces the pathological mesh size effects.