Assessment of the suitability of the cell-smoothed radial point interpolation method for modeling 2d elastoplastic behavior with focus on geomechanics applications - Sargado, Juan Michael U.V
In the last two decades, considerable amount of research has gone to the development of meshfree methods as alternative to the Finite Element Method for use in a wide variety of problems. One of the most recently developed is the Cell-Smoothed radial Point Interpolation Method, based on the so-called Weakened Weak (W²) formulation. Previous studies dealing mostly with homogeneous, linear-elastic problems have shown CS-RPIM to be very promising. In this study, we assess the suitability of the method for modeling problems which involve small-strain elastoplastic behavior, material incompressibility and material heterogeneity. A code implementing CS-RPIM with the capability to handle the aforementioned conditions was written using the Metlab language, and was then used to analyze several benchmark problems. Our results show that the standard formulation of CS-RPIM augmented with the complete linear basis is inadequate for modelling near-incompressible elastoplastic materials as it exhibits severe volumetric locking in the plastic range, resulting in failure to achieve collapse.We have discovered that the amount of locking can be significantly lessened by using the complete quadratic polynomial basis, leading to reasonably accurate predictions of collapse loads. Furthermore, the quadratic variant showed superior performance for almost all the problems we studied. We also found that oscillatory behavior occurs at the vicinity of material interfaces when no special treatment is implemented for handling heterogeneity at the interface. Lastly, we examined the evolution of material instability in bearing capacity and slope stability problems by calculating minimum eigenvalues of the acoustic tensor for each smoothing cell. A checkerboarding pattern was observed in the case of slope simulations, in which stable cells were interspersed with cells in which loss of ellipticity has occurred. From our results, we conclude that CS-RPIM is adequate for conducting 2D elastoplastic analysis within a continuum context when augmented with the complete quadratic polynomial basis. Since the computational cost of using the full quadratic basis is almost the same as that of using the full linear basis, a significant performance improvement is gained at very little added cost. It is our belief that the method can be further improved by the inclusion of a rigorous method for proper treatment of material interfaces, as a well as an optimal means of imposing essential boundary conditions suited to higher order polynomials. Additional research also needs to be conducted to study the causes of the checkerboarding effect seen in materially unstable regions as this can lead to unrealistic and undesirable behavior when CS-RPIM is coupled partition-of-unity methods for modeling of strong discontinuities.