This contribution presents a model order reduction strategy for fast parametric modelling of problems with cracks formulated on spline discretizations. In the context of damage detection, parametric reduced order models (ROMs) are well suited for fast computations by establishing an efficient offline/online split of the simulation process. The problems of interest focus on geometric parameters that describe the crack configuration and may pose challenges to constructing efficient ROMs. This work proposes a framework based on non-intrusive reduced basis methods and a localization strategy tailored to parametric problems with moving discontinuities. The combined benefits of non-intrusive ROMs and localization enable accurate and efficient reduction with low online cost. We demonstrate the applicability of the ROM approach with benchmark tests on linear elastic problems discretized with splines and the extended isogeometric method (XIGA) for crack modelling. The results we obtain show the accuracy and real-time efficiency of the constructed reduced order models.

翻译：本文提出了一种模型降阶策略，用于在样条离散化基础上快速参数化建模含裂纹问题。在损伤检测的背景下，参数化降阶模型通过建立高效的离线/在线仿真流程分割，非常适合快速计算。所关注的问题聚焦于描述裂纹构型的几何参数，这可能对构建高效降阶模型构成挑战。本研究提出了一个基于非侵入式降阶基方法的框架，以及一种针对具有移动不连续性的参数化问题定制的局部化策略。非侵入式降阶模型与局部化策略的结合优势，使得能够在较低在线成本下实现精确高效的模型降阶。我们通过基于样条离散和扩展等几何分析方法的线弹性裂纹建模基准测试，展示了该降阶模型方法的适用性。所得结果表明，所构建的降阶模型具有精确性和实时高效性。