Multiscale Finite-Element-Simulation of the load carrying behaviour of fibre composite structures

本课题的主要目标是在两个尺度上计算复合纤维增强聚合物结构的承载载荷。待开发的模型将通过出现特殊性的实际问题进行检验和评价。这些是结构部件的交叉点，角弧，例如在腹板到法兰的过渡处，在组装范围内重叠，以及开口处的加强。现有的方法无法处理具有这些特性的整个结构。所有使用全局层节点自由度来获得三维应力应变状态的单元公式都是不合适的。这种说法也适用于3d全尺寸计算，因为由于计算工作量，只能处理详细的问题。因此，对于二尺度模型的全局部分的一个基本要求是使用标准的5或6节点壳自由度。在前人研究的基础上，将几何非线性加入到双尺度模型的局部部分。局部模型可以看作是一维代表性体积元（RVE）。与传统的三维rve相比，这大大减少了计算时间。通过扩展，可以得到任意非线性三维物质定律的界面。分层是层合纤维增强聚合物最主要的破坏模式。由于在层边界处使用了局部位移自由度，因此可以扩展当前模型来描述分层。通过引入双节点或所谓的加工层，可以描述不连续位移。应力和切向矩阵由不可逆内聚定律得到。所建立的双尺度壳模型将应用于上述实际问题。对于简单的几何形状，将与现有昂贵的3d模型的结果进行比较和相关评估。

The superior goal of the project is the computation of bearing loads for laminated fiber reinforced polymer structures on two scales. The model which has to be developed will be tested and evaluated by means of practical problems with appearing specialties. These are intersections of structural parts, corner arcs e.g. at a transition of a web to a flange, overlapping in assembling ranges, as well as reinforcements at openings. With existing methods whole structures with these specialties cannot be treated. All element formulations which use global layer wise nodal degrees of freedom to obtain the three dimensional stress and strain state are not suitable. This statement also holds for 3D-full scale computations, since due to the computational effort only detailed problems can be handled. Therefore an essential demand for the global part of the two-scale model is the use of the standard 5 or 6 nodal shell degrees of freedom. Basing on the previous research, geometrical nonlinearity is to be added to the local part of the two-scale model. The local model can be considered as a one-dimensional representative volume element (RVE). This comes with a significant reduction of computing time, compared with conventional three-dimensional RVEs. With the extension an interface to arbitrary nonlinear three-dimensional material laws is available.Delamination is the most important failure mode of laminated fiber reinforced polymers. Since local displacement degrees of freedom are used at the layer boundaries, it is possible to expand the current model to describe delamination. With the introduction of double nodes or so called processing layers discontinuous displacements can be described. Stresses and tangential matrices are obtained through irreversible cohesive laws. The developed two-scale shell model will be applied to above mentioned practical problems. For simple geometries comparisons with the results of existing costly 3D-models and related assessments will be performed.