The variational multiscale method has been shown to perform well for large-eddy simulation ͑LES͒ of turbulent flows. The method relies upon a partition of the resolved velocity field into large-and small-scale components. The subgrid model then acts only on the small scales of motion, unlike conventional LES models which act on all scales of motion. For homogeneous isotropic turbulence and turbulent channel flows, the multiscale model can outperform conventional LES formulations. An issue in the multiscale method for LES is choice of scale partition and sensitivity of the computed results to it. This is the topic of this investigation. The multiscale formulation for channel flows is briefly reviewed. Then, through the definition of an error measure relative to direct numerical simulation ͑DNS͒ results, the sensitivity of the method to the partition between large-and small-scale motions is examined. The error in channel flow simulations, relative to DNS results, is computed for various partitions between large-and small-scale spaces, and conclusions drawn from the results.

The ballistic properties of the aluminium alloy AA6070 in different tempers are studied, using target plates of 20 mm thickness in tempers O (annealed), T4 (naturally aged), T6 (peak strength) and T7 (overaged). The stressstrain behaviour of the different tempers was characterised by quasi-static tension tests and was found to vary considerably with temper in regards to strength, strain hardening and ductility. Ballistic impact tests using 7.62 mm APM2 bullets were then carried out, and the ballistic limit velocities were obtained for all tempers. In the material tests it was shown that the O-temper was most ductile and almost no fragmentation took place during the ballistic impact tests. The T6-temper proved to be least ductile, and fragmentation was commonly seen. The experiments show that despite fragmentation, strength is a more important feature than ductility in ballistic impact for this alloy, at least for the given projectile and within the velocity range investigated. A thermoelasticthermoviscoplastic constitutive relation and a ductile fracture criterion were determined for each temper, and finite element analyses were performed using the IMPETUS Afea Solver with fully integrated 3 rd -order 64-node hexahedrons. The numerical simulations predicted the same variation in ballistic limit velocity with respect to temper condition as found in the experiments, but the results were consistently to the conservative side. In addition, analytical calculations using the cylindrical cavity expansion theory (CCET) were carried out. The ballistic limit velocities resulting from these calculations were found to be in good agreement with the experimental data.

In this paper an experimental program investigating the behavior of monolithic and multi-layered configurations of 0.8 mm and 1.8 mm medium-strength steel plates is presented. We have considered impacts by blunt-ended and ogival-ended impactors in the low-velocity regime (≤ 16 m/s). Experimental outputs include measurements of force and velocity, and deformation fields. Force and velocity readings were provided by a strain-gauge instrumented striker, while digital image correlation was used to obtain the displacement field from the rear side of the bottom plate. For the 0.8 mm plates a near linear relationship between the number of layers and the ballistic limit velocity was found. The plates' resistance against perforation was found to be higher for the blunt-ended impactor than for the ogival-ended impactor. This can be explained by the failure mechanisms. The monolithic plates have a higher capacity than layered plates with the same total thickness: this is particularly clear for plates struck by the ogival-ended impactor. The experiments provide ample data to validate the subsequent 3D numerical simulations. The analysis model is double-symmetric in simulations using the ogival-ended impactor, while only a 10 • slice of the plate and impactor is needed in simulations using the blunt-ended impactor. A thermoelastic-thermoviscoplastic constitutive relation combined with the Cockcroft-Latham criterion for failure is implemented in IMPETUS Afea Solver, and used in all simulations. The simulations predict the failure modes fairly well, and the numerical results are within the range seen in previous publications. Sensitivity studies regarding friction, mesh refinement, thermal formulation and strain-rate dependence are conducted and discussed.

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In this study, we use a discrete particle method in combination with finite element analysis to describe the interaction between structures and granular media during ballistic impact. By applying a discrete particle method to model granular materials, issues like mesh distortion and element deletion can be avoided. This paper presents experiments and numerical simulations on the perforation of empty and sand-filled aluminum alloy panels subjected to impacts by small-arms bullets. The simulations of the sand-filled panels were conducted using a combined discrete particle-finite element approach that accounts for the coupling between structure and sand. The ballistic capacity of the sand-filled aluminum panels was more than 40 % higher than that of the empty aluminum panels. Overall, the results from the numerical simulations describe the trends from the experiments. The predicted ballistic capacity of the empty panels was within 5 % of the experimentally determined value and the critical velocity of the sand-filled panels was predicted within 11 % of the experimentally determined critical velocity. The scatter in residual velocity was similar in simulations and experiments. However, in its current form the discrete particle method needs different calibrations for different velocity regimes to obtain accurate description of the sand behavior.

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a b s t r a c tPerforation of welded aluminum structures by small-arms bullets is studied both experimentally and numerically in this paper. From the chemical composition, artificial aging history, and welding procedure, the spatial distribution of the flow stress at ambient temperature of MIG-welded AA6082-T6 aluminum extrusions was determined by using a thermal finite element model and a nano-scale material model. The resulting flow-stress curves which are functions of the distance from the weld center line were used in a mechanical 3D finite element model to investigate the effect of the heat affected zone (HAZ) on the ballistic properties of welded aluminum extrusions. For experimental validation, 10 mm, 20 mm and 30 mm thick extruded profiles were processed and welded to correspond to the numerical method. Hardness measurements and ballistic impact experiments were performed in the weld metal, HAZ, and base material. Uniaxial tension tests were conducted for the base material of the 10 mm and 30 mm profiles. These tests provided sufficient data for experimental validation of the numerical method. Temperature distribution, hardness values, equivalent stress-strain curves, and ballistic limit curves are reported from both the experiments and the numerical simulations. In general, the experimental results correspond well with the numerical predictions and the predicted ballistic limit velocities are within 10% of the experimental ones, suggesting that this method is a possible alternative to performing expensive and time consuming experimental testing in the early stages of the design of protective aluminum structures. The HAZ was found to impair the ballistic performance locally, but the difference between the ballistic limit for the base material and HAZ was never more than 10% in this study.

Finite element simulations of AA6070 aluminium plates struck by ogival-nose projectiles are performed. The aluminium plates are 20 mm thick and heat treated to temper O, T4, T6 and T7. A nano-scale material model, consisting of three parts: a precipitation model, a yield-strength model and a work-hardening model, is used to predict the flow-stress curves of the materials at ambient temperature based on the chemical composition of the alloy and the thermal history defined by the heat treatment. Finite element simulations of the perforation process are then carried out using both 3D solid and 2D axisymmetric elements. The numerically-obtained ballistic limit velocities, predicted without any use of data from mechanical tests, are compared with available experimental data and found to be in excellent agreement with the experimental ones for all tempers. The same holds for the predicted residual velocities at striking velocities higher than the ballistic limit.