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Novel and Fast Peridynamic Models for Large Deformation and Ductile Failure
Predicting ductile failure is vital to many industries and continues to be a challenging and active area of research. The nonlocal reformulation of classical mechanics, “Peridynamics” (PD), introduced by Dr. Silling has attracted broad interest due to its great potential for simulating fracture and damage. While several PD models have been recently introduced for ductile failure, important limitations have been noticed. For example, some such theories are inconsistent with the classical theory, are limited to small strains/small rotations, or suffer from numerical instabilities. The consistent and stable ones are computationally costly, making them unusable in simulating engineering 3D systems. In this dissertation, we first introduce a new elastoplastic 2D ordinary state-based PD model for plane stress/strain conditions that is, in contrast with previous works, consistent with J2 plasticity. A novel strategy for testing the PD formulation’s consistency for elastoplasticity is presented. When applicable, a 2D elastoplastic model offers significant computational savings compared to full 3D models. This model works for large rotations and small strains. It is shown to qualitatively capture shear banding, an essential mechanism in ductile failure. A PD model of ductile failure capable of handling large deformations is needed. We utilize a stabilized PD-correspondence model for that. To overcome high computational cost of existing numerical methods (the meshfree method with direct quadrature - DQ), we formulate a “fast convolution-based method” (FCBM) for the PD-correspondence model for finite plastic deformations and ductile failure. The computational efficiency is improved by orders of magnitude compared with meshfree DQ method. The introduced method allows efficient simulation of elasto-plastic deformations and ductile rupture in large-scale 3D structures. The model is validated against experiments. A user-friendly MATLAB code implementing newly FCBM-PD for dynamic deformation and fracture is provided. Other issues in PD modeling are the “surface effect” and difficulties in imposing local boundary conditions. We extend the “mirror-based” fictitious nodes method to equations of motion. This, unlike prior studies, applies to bodies of arbitrary shape. The method is verified for curved boundaries.
Mousavi, Farzaneh, "Novel and Fast Peridynamic Models for Large Deformation and Ductile Failure" (2022). ETD collection for University of Nebraska - Lincoln. AAI29323137.