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A mixed-dimensional CutFEM methodology for the simulation of fibre-reinforced composites
Advanced Modeling and Simulation in Engineering Sciences Pub Date : 2020-04-08 , DOI: 10.1186/s40323-020-00154-5 P. Kerfriden , S. Claus , I. Mihai
Advanced Modeling and Simulation in Engineering Sciences Pub Date : 2020-04-08 , DOI: 10.1186/s40323-020-00154-5 P. Kerfriden , S. Claus , I. Mihai
We develop a novel unfitted finite element solver for composite materials with quasi-1D fibrous reinforcements. The method belongs to the class of mixed-dimensional non-conforming finite element solvers. The fibres are treated as 1D structural elements that may intersect the mesh of the embedding structure in an arbitrary manner. No meshing of the unidimensional elements is required. Instead, fibre solution fields are described using the trace of the background mesh. A regularised “cut” finite element formulation is carefully designed to ensure that analyses using such non-conforming finite element descriptions are stable. We also design a dedicated primal/dual operator splitting scheme to resolve the coupling between structure and fibrous reinforcements efficiently. The novel computational strategy is applied to the solution of stiff computational models whereby fibrous reinforcements may lose their bond to the embedding material above a certain level of stress. It is shown that the primal-dual 1D/3D CutFEM scheme is convergent and well-behaved in variety of scenarios involving such highly nonlinear structural computations.
中文翻译:
一种用于模拟纤维增强复合材料的多维CutFEM方法
我们为具有准一维纤维增强材料的复合材料开发了一种新型的有限元求解器。该方法属于混合维非协调有限元求解器类别。纤维被视为一维结构元素,可以以任意方式与嵌入结构的网格相交。不需要对一维元素进行网格划分。取而代之的是,使用背景网格的轨迹描述纤维溶液场。精心设计了正规化的“切割”有限元公式,以确保使用此类不合格有限元描述进行的分析是稳定的。我们还设计了专用的原始/双重算子拆分方案,以有效解决结构与纤维增强物之间的耦合问题。该新颖的计算策略被应用于刚性计算模型的解,由此,在一定的应力水平以上,纤维增强材料可能会失去与嵌入材料的结合。结果表明,在涉及这种高度非线性结构计算的各种情况下,原始对偶1D / 3D CutFEM方案是收敛的且行为良好。
更新日期:2020-04-08
中文翻译:
一种用于模拟纤维增强复合材料的多维CutFEM方法
我们为具有准一维纤维增强材料的复合材料开发了一种新型的有限元求解器。该方法属于混合维非协调有限元求解器类别。纤维被视为一维结构元素,可以以任意方式与嵌入结构的网格相交。不需要对一维元素进行网格划分。取而代之的是,使用背景网格的轨迹描述纤维溶液场。精心设计了正规化的“切割”有限元公式,以确保使用此类不合格有限元描述进行的分析是稳定的。我们还设计了专用的原始/双重算子拆分方案,以有效解决结构与纤维增强物之间的耦合问题。该新颖的计算策略被应用于刚性计算模型的解,由此,在一定的应力水平以上,纤维增强材料可能会失去与嵌入材料的结合。结果表明,在涉及这种高度非线性结构计算的各种情况下,原始对偶1D / 3D CutFEM方案是收敛的且行为良好。