A multiscale DEM-FEM coupled approach for modelling of collision of particle-filled structures

Beschreibung

With the increase in the number of ships in world fleet, the risk of collision has increased. In the current work, a novel idea for the increase in the crashworthiness of the ships with double hull construction will be investigated. As proposed in SCHÖTTELNDREYER (2015), it involves usage of the granular materials within the cavity of the double hull ship. This strategy provides a medium between the hull, which can absorb the impact energy and transfer it to the inner hull. Therefore, the impact energy is shared, in contrast to the localized impact on the outer hull only. Furthermore, crushing of the particles also contributes to the energy dissipation. For modelling of such a complex problem, several numerical techniques must be considered. It includes usage of the Discrete Element Method (DEM) for modelling granular materials, where material dependant contact laws and parameters are used. In order to use granules as filling material, it is necessary to characterize their constitutive response at different levels and under different loading conditions. At the grain level, the contact formulation of the particles in DEM must correspond to the single particle tests. In addition, an aggregate response of the particles has to be comparable to the laboratory tests. In the current work, expanded glass granules are used as filling material. The fidelity of the model is validated by comparison with the experimental results, for an aggregate response of the particles, with the numerical results for the oedometer and triaxial test. To model the ship structure the Finite Element Method is used, where a gradient enhanced ductile damage model is implemented to account for the degradation of the material. The standard lower order element formulations are susceptible to locking for problems involving nearly incompressible deformation and bending dominated thin structures. In order to circumvent this problem, an enhanced assumed strain based formulation is used. Furthermore, to enforce the contact constraint, a Mortar based contact algorithm, as implemented in WEISSENFELS (2012), is used. For large scale particle problems, numerical modelling of the granules with the realistic size can be computationally expensive. Here, a two-scale model based on the work of WELLMANN (2011) two is used, where areas of significant localizations are modelled with the DEM while elsewhere a continuum model is used. For the interaction of these two regions, the Arlequin method based coupling is used. In the continuum region, modelled with a Mohr-Coulomb material model, material parameters are estimated by the numerical homogenization. Here, with the usage of meshless interpolation functions, particle's displacement and stress are projected onto a background mesh. This allows calculation of the volume averaged stress and strain for the particles within the representative volume elements (RVE) and subsequently material parameters for the continuum model. Finally, the results from this numerical model are compared with the experimental results for the indentation of a particle filled box. This validates both the fidelity of numerical model and the proposed idea to increase the crashworthiness of double hull vessels with the granular materials.

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Mohsin Ali Chaudry

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Crash-worthiness of ships Gradient enhanced ductile damage Mortar contact Particle crushing Two-scale DEM-FEM coupled model

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