Parameterized crack modelling based on a localized non-intrusive reduced basis method

Abstract

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.

Figures (13)

• Figure 1: Univariate B-spline basis for two different parameters $\mu_1$ and $\mu_2$ describing the location of the crack.
• Figure 2: Approximation of the map in Eq. \ref{['eq54']} via neural networks.
• Figure 3: Example 5.1: Geometry and parameterization of the plate with edge crack under tension.
• Figure 4: Example 5.1.1: Singular values decay and relative error in $L^{\infty}$ norm vs. maximum number of reduced basis functions $N$ over all the clusters, for different numbers of clusters.
• Figure 5: Example 5.1.1: Singular values decay and relative error in $L^{\infty}$ norm vs. maximum number of reduced basis functions $N$ over all the clusters, for different numbers of clusters.

Theorems & Definitions (3)

• Remark 1
• Remark 2
• Remark 3