A Coupled Peridynamic-Finite-Element-Simulation for the Damage Analysis of Fibre Reinforced Composits

对于与安全相关的轻质结构的设计、评估和批准，损伤容限评估范围内的损伤行为和剩余强度的预测是决定性的。对于纤维增强塑料(FRP)来说，仍然缺乏足够精确和健壮的方法来评估渐进损伤。因此，通常采用损伤起始来确定结构的承载能力，这导致了设计的保守性。与金属材料相比，FRPS分析的关键挑战在于材料的异质性，这导致了复杂的失效机制。强度评估的模拟方法既要考虑损伤的起始过程，又要考虑损伤的发展过程，包括所有的损伤机制及其相互作用。该项目提案的目的是开发一种改进的FRPS损失评估方法。提出的解决方案是一种新的自适应方法，包括结构潜在损伤部分的动力分析方法和未损伤区域的有限元方法的相互联系。该方法的目的是显著提高结构承载能力的预测精度，从而有助于开发出更坚固、更安全、更节约资源的结构。周期动力学理论是分析均质和非均质材料损伤的一种很有前途的方法。但是，对未受破坏的区域应用动态方法需要付出不必要的高努力才能获得足够准确的结果。相比之下，有限元作为一种经典的基于连续介质力学的方法是非常有效的，如果可以假设应力分布是连续的，并且采用具有较高形函数的有限元(p元)。考虑到申请者的观点，基于周期动力学的模拟方法与有限元相结合，将产生一种稳健而有效的方法来预测特定(关键)区域的损伤起始和损伤进展。该方法还允许将损伤区域对结构未损伤区域的反馈建模。在所提出的项目中，周期动力学将被扩展到基于能量的损伤方法来模拟各向异性FPR材料中的损伤，以及与高阶形状函数的有限元的适当耦合方法。根据DFG关于研究软件可持续性的目标，在DFG方案“电子研究技术”的背景下，在拟议项目中开发的软件工具将作为开源软件免费提供给其他研究人员。

For the design, evaluation and approval of safety-relevant lightweight structures, the prediction of damage behavior and residual strength within the scope of a damage tolerance assessment is decisive. Sufficiently precise and robust methods for the evaluation of a progressive damage are still missing for fiber reinforced plastics (FRP). Therefore, the damage initiation is usually utilized to determine the load-bearing capacity, which results in a conservative design. The key challenge of the analysis of FRPs in comparison to metallic materials consists in the heteroge-neity of the material which results in complex failure mechanisms. A simulation method for the strength assessment has to take into account the damage initiation as well as the damage pro-gression including all involved mechanisms and their interactions. The aim of the project proposal is the development of an improved damage assessment method for FRPs. The proposed solution is a new adaptive approach consisting of an interlink of the peridynamic methodology for potentially damaged parts of a structure with a FEM approach for undamaged regions. The objective of the approach is a significant improvement of the prediction accuracy of the load-bearing capacity of a structure which helps to develop more robust, safer and resource-conserving structures. The peridynamic theory is a promising method for analyzing the damage of homogeneous and heterogeneous materials. But, the application of the peridynamic approach for undamaged regions requires an unnecessary high effort for receiving sufficient accurate results. In contrast, the FEM as a classical continuum mechanics based approach is very efficient, if continuous stress distributions can be assumed and finite elements with higher shape functions (p-elements) are applied. In view of the applicants a coupling of a peridynamic based simulation method with the FEM will result in a robust and efficient methodology to predict the damage initiation and the damage progress in specified (critical) regions. This approach also allows the modeling of the feedback of a damage region to the un-damaged area of a structure.In the proposed project the peridynamic will be extended to model damages in anisotropic FPR materials on an energy based damage approach, and to an appropriate coupling method with finite elements of higher order shape functions, respectively. The software tools, developed in the proposed project will be freely-available as open-source software for other researchers in accordance with the DFG objectives of sustainability of research software in the context of the DFG program “e-Research Technologies”.