Keywords: shock waves, anisotropy, damage, finite elements, viscoplasticity, shell theory.

The focus of the present paper is on a material model that is able to predict the anisotropic damage evolution, i.e. the onset of damage, the gradual degradation and final failure, during the dynamic response of structures to impulsive loading conditions. Here, shock wave loadings on circular metal plates which are subjected alternately to impulsive loadings are considered. For this purpose we will review the ductile damage law of Lemaitre [1], which had been originally derived for strain rate independent materials, with the intention to apply it for strain rate dependent material behaviour. The adaptation for impulsive loading conditions of strain rate dependent material is supported by results of uniaxial tension tests, consisting of loading and unloading cycles at different strain rates. These experimental tests have been carried out to investigate the effect of different strain rates on the damage initiation and evolution.

Two damage models are selected. For these models all material parameters in the damage law can be determined by tension tests. The damage growth is observed phenomenologically by the loss of stiffness of the material depending on the plastic strain. The damage evolution can be determined by loading and unloading cycles.

In previous studies it was shown that these aluminium plates exhibit a conical shape of the finally deformed structure after the first impulsive loading. During the second impulsive loading on the other side of the deformed plate a snap-through occurred. As a result, this deformed plate has a shape with two different curvature directions. This leads to intensified accumulated plastic strains in the area of inflexion points between these curvature directions. It was observed that in this area the surface material became very rough. This can be an indication of damage growth in this area. After the third shock wave loading, i.e. the second snap-through, a circular piece of the plate broke out. The hole occured in the zone, where the above mentioned inflexion points of the deformed plate configuration are located. By the experimental procedure described above, a realistic plastic ductile damage accumulation and rupture under dynamic loading conditions is obtained, which can be compared to dynamic damage simulations.

The calculated results of the damaged structure, using isotropic and anisotropic damage evolutions, are very similar to each other. It can be observed that the failure of the plate occurs during the second snap-through, as it was observed in the experiment. But the damage growth is predicted too fast in the isotropic damage simulation.
The prediction in the anisotropic case is in accordance with the experimentally obtained hole after the second snap-through and the observation that in the rest of the plate no damage was visible.

It can be concluded that a suitable mechanical model for the analysis of the transient dynamic response of structures accounting for strain-rate sensitivity as well as anisotropic damage effects was derived.

1

J. Lemaitre, J.L. Chaboche, "Mechanics of Solid Materials", Cambridge University Press, 1994.

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