No abstract

A key issue in Arbitrary Lagrangian-Eulerian (ALE) non-linear solid mechanics is the correct treatment of the convection terms in the constitutive equation. These convection terms, which re ect the relative motion between the finite element mesh and the material, are found for both transient and quasistatic ALE analyses. It is shown in this paper that the same explicit algorithms can be employed to handle the convection terms of the constitutive equation for both types of analyses. The most attractive consequence of this fact is that a quasistatic simulation can be upgraded from Updated Lagrangian (UL) to ALE without significant extra computational cost. These ideas are illustrated by means of two numerical examples.

The arbitrary Lagrangian-Eulerian (ALE) formulation, which is already well established in the hydrodynamics and fluid-structure interaction fields, is extended to materials with memory, namely, non-linear path-dependent materials. Previous attempts to treat non-linear solid mechanics with the ALE description have, in common, the implicit interpolation technique employed. Obviously, this implies a numerical burden which may be uneconomical and may induce to give up this formulation, particularly in fast-transient dynamics where explicit algorithms are usually employed. Here, several applications are presented to show that if adequate stress updating techniques are implemented, the ALE formulation could be much more competitive than classical Lagrangian computations when large deformations are present. Moreover, if the ALE technique is interpreted as a simple interpolation enrichment, adequate-in opposition to distorted or locally coarse -meshes are employed. Notice also that impossible computations (or at least very involved numerically) with a Lagrangian code are easily implementable in an ALE analysis. Finally, it is important to observe that the numerical examples shown range from a purely academic test to real engineering simulations. They show the effective applicability of this formulation to non-linear solid mechanics and, in particular, to impact, coining or forming analysis. KEY WORDS Arbitrary Lagrangian-Eulerian formula t ion Finite elemen t s Non-linear continuum mechanics Time integration schemes Large boundary mo t ion Applications

The dynamic response of blast-loaded steel plates is studied both experimentally and numerically. The blast loading was generated using a shock tube facility. This is an alternative to explosive detonations where the blast intensity is easily controlled through the initial conditions in each experiment. Massive and deformable steel plates where located at the tube end during testing, where the massive-plate tests served as a basis for comparison with respect to fluid-structure interaction (FSI) effects. Special focus was placed on the influence of pre-formed holes on the dynamic response and failure characteristics of the deformable plates. The plates had an exposed area of 0 0.3 m .3 m  and the tests covered a wide range of structural responses from large inelastic deformations to complete tearing along the diagonals of the plates. Numerical simulations were performed in the finite element code EUROPLEXUS, where the plate was uniformly loaded by the pressure measurements from the massive-plate tests. The plate deformation and the observed crack propagation were successfully recreated by using element erosion and adaptive mesh refinement in the plate, driven by the damage parameter in the material model. As expected, the simulations overestimated the plate deformations due to the underlying assumption that the blast pressure was uncoupled from the deformation (i.e., neglecting FSI). It was also found that the modelling of the realistic boundary conditions with clamping frames, contact and friction was essential to predict the experimental results.

The inelastic response of thin aluminium and steel plates subjected to airblast loading is studied numerically and validated against experimental data. Special focus is placed on the influence of elastic effects and negative phase on the structural response. The blast loading was varied by detonating spherical charges of plastic explosives at various stand-off distances relative to the centre point of the plates. The numerical results obtained with the finite element code EUROPLEXUS were in good agreement with the experiments and predicted the entire range of structural response from complete tearing at the supports to a more counter-intuitive behaviour (CIB) where the final configuration of the plate was in the opposite direction to the incident blast wave due to reversed snap buckling (RSB). RSB attracted special attention since this is an unstable configuration sensitive to small changes in the loading and in structural characteristics. The negative phase of the blast pressure is usually neglected in blast-resistant design. However, the numerical simulations showed that the negative overpressure dominated the structural response and led to RSB at some loading and structural conditions. Two distinctive types of CIB were identified and both were found to depend on the timing and magnitude of the peak negative overpressure relative to the dynamic response of the plates. The study also revealed that CIB may occur in thin plates when the negative impulse is of the same order of magnitude as the positive impulse. The partial and complete failure along the boundaries observed in some of the tests was also successfully recreated in the simulations by using an energy-based failure criterion and element erosion.