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An explicit formulation for multiscale modeling of bcc metals. (English) Zbl 1421.74024

Summary: Many materials for specialized applications exhibit a body-centered cubic structure; e.g., tantalum, vanadium, barium and chromium. In addition, the successful modeling of body-centered cubic (bcc) metals is a necessary step toward modeling of common structural materials such as iron. Implicit formulations for this class of materials exist
(e.g., [L. Stainier et al., J. Mech. Phys. Solids 50, No. 7, 1511–1545 (2002; Zbl 1071.74553); the first author et al., “A pressure-dependent multiscale model for bcc metals”, Preprint], but are impractical to resolve large-scale dynamic deformation processes. In this article, we describe a procedure analogous to [the first author et al., Int. J. Plast. 22, No. 10, 1988–2011 (2006; Zbl 1136.74310)]. wherein we construct an explicit formulation for the multiscale physics models. This update is based on the model of the first author et al. [Preprint, loc. cit.] using a power law representation for the plastic slip rates. The existing implicit form of the model provides qualitative matching with experiments at quasi-static strain rates. The model is recast in an explicit form and applied first to a high quasi-static strain rate to verify that the two forms of the model return similar predictions for similar input parameters. The explicit model is also applied to several high strain rates, showing that it captures characteristic features observed in experimental tests of high-rate deformations, such as the drop in stress immediately after yield that is present in split Hopkinson pressure bar (SHPB) experiments. This test provides qualitative evidence that the model is suitable for high-strain-rate applications. The utility of the model is further demonstrated by a one-dimensional simulation of a SHPB test. Finally, a test case modeling pressure impact of a Tantalum plate using 600,000 elements is shown. The simulations show that the explicit model is capable of recovering the salient features of the experiments while integrating the constitutive update in a robust manner.

MSC:

74E15 Crystalline structure
74S30 Other numerical methods in solid mechanics (MSC2010)
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