Virtual Clustering Analysis for Reproducing Kernel Particle Method with Applications

  • Tang, Shaoqiang (Peking University)
  • Nan, Chenyu (Peking University)

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We propose a reduced-order homogenization framework that extends Virtual Clustering Analysis (VCA) to the meshfree Reproducing Kernel Particle Method (RKPM). The proposed VCA-RKPM approach represents the deformation gradient field using RKPM shape functions and embeds it within the Lippmann-Schwinger equation, from which a new reduced algebraic system is derived. The method follows a two-stage strategy. In the offline stage, a two-field generalized variational principle with deformation gradient and displacement is employed, and deformation gradient particles are clustered to identify regions with similar deformation during direct numerical simulations on representative volume elements (RVEs). In the online stage, a much reduced system is solved, enabling substantial savings in computational cost. Compared to the conventional VCA method, the present framework is naturally compatible with meshfree discretization and can reduce sensitivity to mesh distortion and mesh orientation. Numerical studies demonstrate the validity and efficiency of the method for (i) large-deformation rubber bonding and (ii) quasi-static brittle phase-field fracture with mesh-orientation sensitivity tests.