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.

Experimental testing and numerical simulation of granules as crash absorber for double hull structures

“…Using a continuous approach for numerical modelling, the FEM will be introduced in more detail, followed by a very brief overview of the DEM. Further details on the coupling with DEM can be found in [110,111,112].…”

“…Additionally, a model for rolling resistance has to be chosen and crushing and damping has to be considered. The governing equations are integrated in the time domain using an explicit time integration method, with a global-local framework to increase the computational efficiency [111].…”

“…In the concurrent work by the project partner, a DEM framework based on the work of [74] is used. For more details regarding the DEM implementation, please refer to [116,111,112].…”

“…The numerical simulations of the experiments shown in this section are presented in detail in [116]. Next follow the abilities developed throughout the project, including the results for a simplified side hull structure filled with particles [111].…”

“…In order to be able to model this, several tasks have been performed, which will be briefly shown here. For more details, see the publications related to this project considering the particle parameters [124,121,116] as well as the numerical implementation [131,110,111].…”