Stress recovery for the particle-in-cell finite element method

The particle-in-cell finite element (PIC-FE) method has been widely used in geodynamic numerical modelling due to its efficiency dealing with large deformations without the requirement of remeshing. However, material deformation within a Eulerian mesh frame will mix particles contrasting strength properties (e.g., viscosity Stokes problems) single requiring some form averaging project particle integration points. solutions are thus dependent on way how projected An intra-element property discontinuity may introduce severe stress oscillations along interfaces. In this study, we assess three preprocessing methods smooth contrast one element. For simplified models analytical solutions, accuracy and convergence rate L2 norm systematically studied ensembles. It is found that using higher-order quadrature elements does not improve for either velocity or solution, both close one. Additionally, maximum error, which exists adjacent mixed-material elements, much less than all cases here. Comparing each component tensor, find tensor highest strain gradient across interface produces error. Such errors can be reduced by Gaussian point an inverse-distance-weighted harmonic mean.