39. reduced order modeling of fracture
Name: Jonghyuk Baek
Grad Year: 2021
Qizhi He, email@example.com
A framework of projection-based model order reduction (MOR) for fracture mechanics using enriched Reproducing Kernel (RK) approximation based on the integrated singular basis function method (ISBFM) is proposed. By using ISBFM, the near-tip enrichment functions appear only on the boundary terms not containing the crack surfaces, which avoids taking high-order quadrature scheme for domain integration involving singular functions and yields a sparser discrete system allowing effective MOR procedures. Two MOR methods, the uniform reduction method and the decomposed reduction method, are introduced for the enriched RK approximated ISBFM system. The decomposed reduction method, consisting of separate reduced-order projections associated with the smooth and non-smooth approximations, is capable of preserving the near-tip singularity characteristics in the low-dimensional reduced space. But the error analysis reveals that the uniform reduction approach is susceptible to the inappropriate scaling of enrichment functions. A proper scaling is thus introduced to suppress the associated error, letting the scaled uniform reduction method able to capture the near-tip non-smoothness as well as the decomposed reduction method. Moreover, the issue caused by the inhomogeneous Dirichlet boundary conditions is investigated and an effective projection correction method is proposed to recover the representation for those inhomogeneous boundary behaviors in reduced-order models. Numerical examples are given to validate the effectiveness of the proposed MOR methods for fracture problems.
Industry Application Area(s)