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Center for Nonlinear Studies |
Meshfree methods such as the Reproducing Kernel Particle Method (RKPM) are well suited for modeling materials and solids undergoing fracture and damage processes, and nodal integration is a natural choice for this class of problems. However, nodal integration suffers from spatial instability, and the excessive material deformation and damage process could also lead to kernel instability in RKPM. This presentation introduces the recent advances in nodal integration for meshfree methods that are stable, accurate, and with optimal convergence. A variationally consistent integration (VCI) is introduced to allow correction of many low order quadrature rules to achieve optimal convergence, and stabilization techniques with implicit gradient are developed for nodal integration. Independent to the quadrature rules, a quasi-linear Reproducing Kernel approximation is constructed to address the kernel instability issue. Several RKPM shock algorithms are also formulated under the variationally consistent nodal integration framework. The application of the new RKPM formulation for fracture to damage multiscale modeling, and their applications to the modeling of extreme events, are demonstrated. The demonstration problems include the modeling of man-made disasters such as fragment-impact processes, penetration, shock and blast events, as well as simulation of natural disasters such as landslide.
Host: Duan Zhang