Analysis of crack interactions in laminates by means of the scaled boundary finite element method

本项目的目标是将尺度边界有限元方法推广应用于单向纤维增强单层叠层板中裂纹相互作用的结构情况。纤维增强层合板中的裂缝通常是纤维平行的基质裂缝，例如由于养护收缩、热收缩或外部机械载荷造成的，单向纤维增强对这些裂缝的承载能力不是很大。在大多数情况下，这种基质裂纹直接沿层压板的厚度方向延伸，这穿过整个单层，但有时也沿倾斜方向穿过该层，以便在与相邻层的交界处停止。如果在直接相邻的层中有类似的裂纹产生，则相应的基质裂纹可以在界面处相遇，这是因为通常只在具有相应裂纹相互作用的单个点上有不同的裂纹方向。然而，对于界面内的分层裂纹，裂纹相互作用也可能发生。裂纹的相互作用应在预定的工程中，在线弹性理论的框架内作为一个相应的三维边值问题来研究，由于涉及到各向异性的单层连续介质，这是非常具有挑战性的。特别令人感兴趣的是在所涉及的裂纹的相互作用点上出现的应力奇异性以及伴随而来的渐近应力和应变场。在这种情况下，一种合适的分析方法是相应地制定和实施的比例边界有限元方法。这种新方法的有效性和效率也将通过有限元参考计算进行评估。

Goal of the intended project is the extension and application of the scaled boundary finite element method for the structural situation von interacting cracks in laminates made of unidirectionally fibre-reinforced single layers. Cracks in fibre-reinforced laminate layers typically occur as fibre-parallel matrix cracks, for instance from curing shrinkage, from thermal shrinkage or from external mechanical loading, for which the unidirectional fibre reinforcement has not much load carrying capability. In most cases such matrix cracks run directly in thickness direction of the laminate and this through a complete single layer, but sometimes also in a slant direction through the layer in order to be stopped at the interfaces to the neighbouring layers. If there is an analogous crack generation in a direct neighbouring layer then the respective matrix cracks can meet at the interface, and this due to the in general different crack orientations only at one single point with a corresponding crack interaction. Crack interaction can however also happen with delamination cracks within an interface. The crack interaction shall be investigated within the intended project within the framework of linear elasticity theory as a respective three-dimensional boundary value problem, which due to the involved anisotropic single layer continua is very challenging. Of particular interest are the occurring stress singularities in the interaction points of the involved cracks as well as the accompanying asymptotic stress and strain fields. In this situation an appropriate analysis approach is a scaled boundary finite element method that is correspondingly to formulate and to implement. The usefullness and efficiency of this new approach will be assessed by means of also intended finite element reference calculations.