A multiscale DEM–FEM coupled approach for the investigation of granules as crash-absorber in ship building

Abstract

This paper covers a numerical analysis of a novel approach to increasing the crashworthiness of double hull ships. As proposed in Schöttelndreyer (Füllstoffe in der Konstruktion: ein Konzept zur Verstärkung vonSchiffsseitenhüllen, Technische Uni-versitt Hamburg, Hamburg, 2015), it involves the usage of granular materials in the cavity of the double hull ship. For the modeling of this problem, the discrete element method (DEM) is used for the granules while the finite element method is used for the ship’s structure. In order to account for the structural damage caused by collision, a gradient-enhanced ductile damage model is implemented. In addition to avoid locking, an enhanced strain-based formulation is used. For large-scale problems such as the one in the current study, modeling of all granules with realistic size can be computationally expensive. A two-scale model based on the work of Wellmann and Wriggers (Comput Methods Appl Mech Eng 205:46–58, 2012) is applied—and the region of significant localization is modeled with the DEM, while a continuum model is used for the other regions. The coupling of both discretization schemes is based on the Arlequin method. Numerical homogenization is used to estimate the material parameters of the continuum region with the granules. This involves the usage of meshless interpolation functions for the projection of particle displacement and stress onto a background mesh. Later, the volume-averaged stress and strain within the representative volume element is used to estimate the material parameters. At the end, the results from the combined numerical model are compared with the results from the experiments given in Woitzik and Düster (Ships Offshore Struct 1–12, 2020). This validates both the accuracy of the numerical model and the proposed idea of increasing the crashworthiness of double hull vessels with the granular materials.