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.

本文涵盖了一种新型方法的数值分析，该方法可提高双壳船的耐撞性。正如Schöttelndreyer的建议（德国汉堡市的Füllstoffe：ein Konzept zurVerstärkungvonSchiffsseitenhüllen，汉堡工业大学，汉堡，2015年）中所涉及的，是在双层船体的腔体中使用粒状材料。对于此问题的建模，将离散元素方法（DEM）用于颗粒，而将有限元方法用于船舶结构。为了解决碰撞引起的结构损伤，实施了梯度增强的延性损伤模型。除了避免锁定之外，还使用了基于应变的增强配方。对于当前研究中的大规模问题，对具有实际大小的所有颗粒进行建模可能在计算上昂贵。应用了基于Wellmann和Wriggers的工作的两尺度模型（Comput Methods Appl Mech Eng 205：46-58，2012），并且使用DEM对重要的本地化区域进行了建模，而对于其他地区。两种离散化方案的耦合均基于Arlequin方法。数值均质化用于估计具有颗粒的连续区域的材料参数。这涉及使用无网格插值函数将粒子位移和应力投影到背景网格上。随后，将具有代表性的体积元素内的体积平均应力和应变用于估算材料参数。在末尾，将组合数值模型的结果与Woitzik和Düster（船舶近海结构1–12，2020年）中给出的实验结果进行比较。这既验证了数值模型的准确性，又验证了使用粒状材料提高双壳船的耐撞性的建议思想。