A physically motivated internal state variable plasticity/damage model embedded with a length scale for hazmat tank cars' structural integrity applications

In this study, we use a physically-motivated internal state variable plasticity/damage model containing a mathematical length scale to represent the material behavior in finite element (FE) simulations of a large scale boundary value problem. This 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 which arise during the impact and (2) to address the pathological mesh size dependence of the FE solution in the post-bifurcation regime. 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 (1987) in the context of concrete. We implement this evolution equation into existing implicit and explicit versions of the FE subroutines of the plasticity/failure model. The results of the FE simulations, carried out with the aid of Abaqus/Explicit FE 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.