Entwicklung robuster Interface-Elemente für die Simulation von Delaminations-Prozessen in CFK-Laminaten

分层是复合材料中常见的失效模式。由于刚度变化和厚度方向上缺乏加强，在低载荷下就已经发生分层，并可能导致整个结构倒塌。例如，界面单元被用来模拟薄层之间的树脂层，提供了一个适当的模拟裂纹的萌生和扩展的机会。通常，线性和指数内聚定律用于模拟软化行为。内聚区模型的缺点是需要正确再现裂纹尖端前的应力分布。这意味着由于分层处理区中的高应力梯度和一个元件中的相关部分结合，需要非常细的网格。因此，单元尺寸沿着分层部分由界面单元限定，而不是通常由相邻的壳单元限定。本研究的目的是利用不同的数值技术来提高间断界面单元的稳健性。在研究应用中，总结了过去的工作成果，并提出了未来的工作。在迄今为止所做的研究中，界面单元已被改进的多杂交制剂从胡鹫津双线性和特殊开发的形函数的应力和应变，从而单元的大小可以减少50%。研究了高阶积分和自适应积分格式，以描述一个单元中的总应力分布。最后，双线性元运动学已被增强为二次和偶然性形状函数，以提供一个更好的近似的脱层过程区内的位移。在随后的研究中，Hellinger-Reissner（HR）的一个额外的混合IF公式将被开发并实施到元素算法中。混合HR公式提供自由形状函数的应力，提供了一个很好的近似应力分布的裂纹前沿，可以提高鲁棒性。在增强运动学领域的进一步研究应软化刚度并避免载荷-位移曲线中的振荡。除了在每个节点处的当前节点位移自由度之外，附加的旋转自由度和附加的虚拟元件自由度将在接口公式中实现。之后，额外的自由度将被集成在开发的混合接口。最后，着眼于鲁棒性的提高，将内聚律放大。在当前工作状态下，指数内聚定律基于相对位移。将与德国航天中心和德国亚琛工业大学合作审查接触公式和混合模式问题，包括取决于层间断裂韧性的内聚定律。

Delamination is a commonly observed failure mode in composite materials. Due to stiffness changes and the lack of reinforcement in thickness direction, delamination already occurs by low loads and can yield total structural collapse. For instance, interface elements are used to simulate thin resin layers between lamina, providing the opportunity for an adequate simulation of crack initiation and propagation. Typically, linear and exponential cohesive laws are used to simulate the softening behavior. The drawback of the cohesive zone model is the requirement of a correct reproduction of the stress distribution ahead of the crack tip. This means that very fine meshes, due to high stress gradients in the delamination process zone and the associated partial bonding in one element, are needed. Thus, the element size along the delamination part is defined by the interface elements and not as usual by the adjacent shell elements. The purpose of this research is to improve the robustness of discontinuous interface elements with different numerical techniques. In the application for research the results of the past work is summarized and later on providing prospective works are presented. In the research done so far, the interface element has been improved by a multi hybrid formulation from Hu-Washizu with bilinear and special developed shape functions for stresses and strains whereby the element size could be reduced by 50 percent. High order and adapted integrations schemes were investigated to describe the total stress distribution in one element. Finally the bilinear element kinematic has been enhanced to quadratic and serendipity shape functions to give a better approximation of the displacements within the delamination process zone. In the subsequent research an additional mixed IF-Formulation by Hellinger-Reissner (HR) will be developed and implemented into the element algorithm. Providing free shape functions for stresses, the mixed HR-Formulation offers a good approximation of the stress distribution ahead of the crack front and can advance the robustness. Further investigations in the field of enhanced kinematics shall soften the stiffness and avoid oscillation in the load-displacement curve. Beside the current nodal displacement degrees of freedom at each node, additive rotational degrees of freedom and additive virtual element degrees of freedom are to be implemented in the interface formulation. Afterwards, the additional degrees of freedom will be integrated in the developed hybrid interface. Finally, focusing on the improvement of robustness the cohesive law will be amplified. In the current state of work the exponential cohesive law is based on relative displacements. The contact formulation and the mixed mode problem, including a cohesive law depending on the interlaminar fracture toughness, are to be reviewed in collaboration with the DLR and the RWTH Aachen.