Stress Recovery for the Particle-in-cell Finite Element Method

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Haibin Yang, Louis N. Moresi , John Mansour


The interelement stress in the Finite Element Method is not continuous in nature, and stress projections from quadrature points to mesh nodes often causes oscillations. The widely used particle-in-cell method cannot avoid this issue and produces worse results when there are mixing materials of large strength (e.g., viscosity in Stokes problems) contrast in one element. The post-processing methods including (1) distance weighted average from surrounding particles to the centroid mesh node (Post-local), (2) global projection with least square fit (Post-global), and (3) superconvergent point recovery method (SPR), cannot effectively eliminate the stress fluctuations. We propose three pre-processing methods to reduce the interface contrast in mixing elements: (1) global method with harmonic-mean averaging (GHM), (2) unification of properties at mixed-material elements (UnE), and (3) averaging particle properties within a specified distance to gauss quadrature points (AGP). For tests of Q1 elements, the results processed by combining either pre-processing method with the Post-local projection can increase the precision. The GHM pre-processing method is the least computationally expensive application and the easiest to implement, the AGP pre-processing method is the most expensive and the UnE in-between. However, for Q2 elements, the GHM pre-processing method fails in stress recovery, and produces worse results than those without any pre-processing procedures. For general cases (both Q1 and Q2 elements), the AGP pre-processing method is recommended. The optimal sampling radius used in the AGP method is close to that size of one element, beyond which it increases computational time, but does not significantly increases the accuracy of recovered stresses. In terms of the averaging approaches used in the AGP method, the harmonic mean is suitable for simple-shear-dominated processes and the arithmetic mean is better for the pure-shear-dominated models. For complex models, the AGP method of harmonic mean combined with the SPR post-procedure is recommended. The AGP method is found to be able to efficiently reduce stress perturbations in a synthetic model of complex fault geometries like the San Andreas Fault system.



Applied Mathematics, Computer Sciences, Earth Sciences, Geophysics and Seismology, Mathematics, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Physical Sciences and Mathematics, Tectonics and Structure


Finite element method, Numerical geodynamic modelling, Particle-in-cell, Stress fluctuation, Stress smoothing


Published: 2020-05-25 21:02

Last Updated: 2020-12-21 22:53

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