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：本文提出了一种基于样条离散化的裂纹问题快速参数化建模的模型降阶策略。在损伤检测背景下，参数化降阶模型通过建立高效的离线/在线仿真过程分离，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。本工作提出了一种基于非侵入式降阶基方法和针对含移动间断参数问题定制化局部化策略的框架。非侵入式降阶模型与局部化的协同优势使得在低在线计算成本下实现精确高效降阶成为可能。我们通过采用样条离散化和扩展等几何分析法进行裂纹建模的线弹性问题基准测试，验证了降阶模型的适用性。结果表明，所构建的降阶模型具有精度高和实时计算效率好的特性。