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. 1. Introduction The design of accident-resistant hazmat tank cars or the improvement of existing ones requires material models that describe the physical mechanisms that occur during the accident. In the case of impact accidents such as collisions, finite deformation, and temperature histories, damage and high rate phenomena are generated in the vicinity of the impact region. Unfortunately, the majority of material models used in the finite element (FE) simulation of hazmat tank car impact scenarios do not account for such physical features (unavoidably, this will under- or overestimate, for instance, the numerical prediction of the puncture resistance of hazmat tank cars’ structural integrity). Furthermore, in the few models that do, a mathematical length scale aimed at solving the postbifurcation problem is absent. As a consequence, when one material point fails in the course of the numerical simulations, the boundary value problem for such material models changes, from a hyperbolic to an elliptical system of differential equations in dynamic problems, and the reverse in statics. In both cases, the boundary value problem becomes ill posed, Muhlhaus [1], Tvergaard and Needleman [2], de Borst [3], and Ramaswamy and Aravas [4], as the boundary and initial conditions for one system of differential equations are not suitable for the other. Consequently, discontinuities in
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