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High-Order Arbitrary Lagrangian-Eulerian Methods and Model Order Reduction for Plasticity to Simulate Melting and Solidification of Metals During Extreme Events

Problems in which solids, particularly metals, start to flow, or deform plastically, are ubiquitous in army applications, including traditional ballistic penetration problems of armor, structural integrity under fire, welding, and additive manufacturing processes. In many of these problems the plastic deformation is propelled by localized increases in temperature, such as those induced by friction between the projectile and its surroundings, by the appearance of shear bands, or by laser heating,  As the temperature approaches the melting point, the yield stress of the material decreases and the material progressively deforms more and more like a fluid. Once the yield stress is identically zero, the material loses all of its elastic response and is entirely a fluid. The temperature eventually decreases, melted parts solidify, and the elastoplastic response is recovered.

 

This type of scenario is truly a nightmare for simulation algorithms, for at least the following reasons:

   1.  The material in the simulation can transition from a solid to a fluid and back to a solid in different regions of the domain of the problem. As we discuss below, this scenario calls for the formulation of suitable high-order Arbitrary Lagrangian-Eulerian methods.

   2.  In the absence of contact events, the most costly part of a simulation at each time step by far is the evaluation of the plastic response and evolution of the material. The computational cost becomes directly overwhelming in the presence of materials that require complex, multiscale models, such as a crystal plasticity model. To make accurate simulations of this type even possible, a promising path to explore is the formulation and construction of reduced-order models for plasticity and plastic evolution.