The question as formulated is quite broad. It would be hard to elaborate a good answer. It depends on the scope of your work and your experience with numerical methods. In general terms mpm might look easier to use for people familiar with fem. The background in general terms is rather similar. As drawback, mpm is "younger" than sph; thus, there are several numerical caveats to be solved. In the other hand sph might present a stiffer learning curve but the method is more mature. In general terms you might say it's slower. But that also depends on the capabilities of the programmer and the computational resources available. When it comes to "post-failure" analysis. At some point you would need to handle with contact algorithms. Both mpm and sph have issues there. There are several strategies, but again it depends on the scope of your work. Finally, the liquefaction part... It depends on the constitutive framework. Not the numerical method itself. In theory both methods should be able to solve it. But the topic it's a whole new question with different alternatives as an answer. Good luck

Dear Mr.Liano

Many thanks for reaviling your ideas about this Topic.

Regards

Hello Nooshin Hadidian Moghaddam

This is quite an interesting question.

You should use the MPM method for liquefaction and post-failure analyses in 2D slopes. The reasons follow below.

SPH (Smoothed particle hydrodynamics)

The SPH method was developed by Lucy (1977); Gingold and Monaghan (1977)

SPH is suitable for problems where the object under consideration is not a continuum. The SPH method employs particles to represent material and form the computational frame. There is no need for predefined connectivity between these particles. All one needs is the initial particle distribution.

The conventional SPH method was originally developed for astrophysical interaction problems.

The early SPH algorithms were derived from the probability theory, and statistical mechanics are extensively used for numerical estimation. These algorithms did not conserve linear and angular momentum. However, they can give reasonably good results for many astrophysical phenomena.

For the simulations of fluid and solid mechanics problems, there are challenges to reproduce faithfully

the partial differential equations governing the corresponding fluid and solid dynamics. These challenges involve accuracy and stability of the numerical schemes in implementing the SPH methods.

Swegle et al. (1995) identified the tensile instability problem that can be important for materials with strength . Morris (1996) noted the particle inconsistency problem that can lead to poor accuracy in the SPH solution.

Many researchers have conducted investigations on the SPH method on the numerical aspects in accuracy, stability, convergence and efficiency. Different variants or modifications have been proposed to improve the original SPH method. For example, Batra and Zhang (2004) concurrently developed a similar idea to Finite particle method (FPM) and named it modified SPH (MSPH) with applications mainly in solid mechanics. Fang et al.(2006) further improved this idea for simulating free surface flows.

MPM (Material point method)

MPM was developed for solid mechanics from the particle in cell (PIC) method by Sulsky and co workers (1995). Particle in cell (PIC) method was developed for fluid mechanics problems by Harlow (1963; 1964)

MPM discretizes the continuum using the material points or particles and discretizes the space

using an Eulerian background fixed mesh on which the equations of motion are solved. This mesh should cover the whole space where the material may go during the simulation process. Material points are the integration points which can move during the simulation and using this property Particles carry all the physical information (e.g. stresses, strain, etc.) during the simulation process and no permanent data are stored on the mesh.

MPM is able to analyze large deformations of the material and material/kinematics discontinuity. MPMs are better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than FEMs.

References

Batra RC, Zhang GM (2004) Analysis of adiabatic shear bands in elasto-thermo-viscoplastic materials by modified smoothedparticle hydrodynamics (MSPH) method. J Comput Phys 201(1):172–190

Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astron J 82(12):1013–1024

Fang JN, Owens RG, Tacher L, Parriaux A (2006) A numerical study of the SPH method for simulating transient viscoelastic free surface flows. J Non-Newton Fluid 139(1–2):68–84

Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics—theory and application to non-spherical stars. Mon Not R Astron Soc 181:375–389

Gingold RA, Monaghan JJ (1982) Kernel estimates as a basis for general particle method in hydrodynamics. J Comput Phys 46:429–453

Harlow, F.H. (1963) The Particle-in-Cell Method for Numerical Solution of Problems in Fluid Dynamics. Proceedings of Symposium in Applied Mathematics, vol.15,No.10, p.269.

Harlow, F.H. (1964)The Particle-in-Cell Computing Method for Fluid Dynamics. Methods in Computational Physics, 3, 319-343.

Morris JP (1996) Analysis of Smoothed Particle Hydrodynamics with Applications. Monash University

Sulsky D and Schreyer H L (1996) Axisymmetric form of the material point method with applications to upsetting and Taylor impact problems J. Comput. Method. Appl. M. 139 409–29

Sulsky D, Zhou S J and Schreyer H L (1995) Application of a particle-in-cell method to solid

mechanics Comput. Phys. Commun. 87. 236–52

Swegle JW, Hicks DL, Attaway SW (1995) Smoothed particle hydrodynamics stability analysis. J Comput Phys 116(1):123–134

Dear Mr.Amaechi J. Anyaegbunam

Many thanks for your nice attention and comprehensive answer. Here I try to gather several ideas and compare them with my achievement.

I wish the all success in all of your scientific activities in the life.

Regards

Nooshin Haddian

Your question is quite broad. For hypervelocity impact problems, see Ma, S., Zhang, X., and Qiu, X. M. (2009a). “Comparison study of MPM and SPH in modeling hypervelocity impact problems”. In: International Journal of Impact Engineering 36.2, pp. 272–282, for a comparative study. It was shown that MPM is much faster than SPH and FEM. that is in-house mpm is faster than ls-dyna fem. that is interesting as everyone says that mpm is slow.

Our experiences, with Alban de Vaucorbeil, showed it is indeed the case. About accuracy, i am not sure.

for fluid mechanics, see this Sun, Z., Li, H., Gan, Y., Liu, H., Huang, Z., and He, L. (2018). “Material point method and smoothed particle hydrodynamics simulations of fluid flow problems: a comparative study”. In: Progress in Computational Fluid Dynamics, An International Journal (PCFD) 18.1, pp. 1–18.

Many thanks for your answer..

Firstly, we need to know whether it is currently possible to use these methods to model "properly" liquefaction-induced slope post-failure. I haven't seen one to my understanding. :) I have been working on MPM for a while and I know it is still challenging but I believe MPM has strong potential to do that.

More specifically, apart from challenges in the constitutive soil models, fully-coupled hydro-mechanical MPM becomes unstable when effective stress approaches zero due to ringing/nullspace instability in MPM.

Thanks for sharing your ideas.