*3.5. Eulerian LIW Simulation*

In order to mimic the material jetting phenomenon, an Eulerian model of the LIW process was run in Abaqus/Explicit. In this model, the material's Eulerian volume fraction (EVF) was computed within each element and its movement was tracked as it flowed through the fixed mesh. A material EVF of one means the element is completely filled with that material while a material EVF of zero shows that the material is not at all present in the element. More than one material may be present in Eulerian elements at the same time. If after adding all the material EVFs in an element, the sum is less than one, the software fills the remainder of the element's volume with "void" material which has zero mass and strength [44]. Since Eulerian models in true 2D space are not available in the particular software, a 3D model was created with a thickness of 0.02 mm (four elements thick) in the out-of-plane (depth) direction. However, motion in the depth direction was constrained by a symmetry condition at all nodes, thus rendering the model an equivalent 2D plane strain simulation (due to plate thicknesses being much smaller than other dimensions). An Eulerian grid (meshed control volume) encompassed the entire model in order to track material movement during LIW. Exploiting symmetry, only half of the full geometry was modeled. Approximately 300,000 hexahedral 8-node Eulerian brick elements of 5-micron edge length with reduced integration and hourglass control (EC3D8R) were utilized, which in turn employed predefined volume fractions at the locations of the flyer and target plates. Two fixed discrete rigid bodies were used as the transparent overlay and the metal specimen. Consistent with an Eulerian model description, Abaqus/Explicit allows for load application only at fixed nodes in the meshed control volume. The pressure load described earlier was applied to the top surface of the flyer based on measured spatial and temporal profiles of the laser pulse. Implementation of the measured spatial and temporal profiles as the distribution and amplitude of the load was similar to that of axisymmetric simulation. The only di fference was that the load was apportioned among nodal layers of the initial flyer position in the out-of-plane direction, accelerating the flyer towards the target, resulting in jetting and interlocking of the foils along the weld interface upon collision. The general contact method was implemented between all surface pairs using a "hard" contact interaction property allowing separation after contact. A schematic of the LIW in the Eulerian simulation is shown in Figure 9b. Details on the Eulerian simulation results are provided in Section 4.
