iMechanica - Material Point Method - Comments

MPM

Nguyen Chau Linh — Tue, 18 Mar 2008 23:33:17 -0400

Prof. Nain and his co-worker are research on Material Point Method, you can search on Google with keywords: Nairn, MPM, crack propagation...

Fun,

MPM + rockfall

pedroso — Tue, 18 Mar 2008 19:54:29 -0400

Hi, that's interesting. We, including Dr. Anna Giacomini, are also planning to run some simulations of rockfalls using the (Generalized)MPM.

MPM

Michael G. Sakellariou — Tue, 18 Mar 2008 07:19:00 -0400

We are developing a 3-D rockfall simulation in a GIS environment and we think the MPM could be very powerful method in simulating the impact phenomenon.

how MPM can model material interface?

vinh phu nguyen — Fri, 11 Jan 2008 20:31:22 -0500

Hello everyone,

From your discussing, it seems to me that MPM has been used succesfully in modeling microstructures. I do not see how this is done with MPM where a solid domain is discretised by a background grid and a set of Lagrangian particles. How material is set to a given particle?

I would like to model fracture at the mesoscale of concrete where it is considered to be a three-phase material: matrix, aggregates and ITZ. This microsctructure is an output of a DEM packing simulation. As you know, the mesh generation step for this mesoscale specimen is time-consuming. So, I am looking for novel numerical methods for this kind of problem.

I am very grateful to any suggestions from you.

Thank you in advance.

Rolls-Royce project

Henry Tan — Thu, 13 Dec 2007 08:00:44 -0500

Waqas,

Can you put some of your results on this web, with pictures and physical explanations?

Henry.

Industrial Placement

Waqas Ahmad — Wed, 21 Nov 2007 19:17:42 -0500

Industrial Placement

‘Optimising Superplastic Forming Die Shape and Platens for Next Generation Aero Engine Production’

Background

The design of hot forming dies was optimised in the 1980s for the engine types at the time, the knowledge bank has remained constant ever since. The current high by-pass ratio engines are larger and therefore require larger hot forming dies. The increase in size of dies and presses along with the increase in mass of material and thermal efficiency means the cooling time has increased significantly.

The dies are regularly changed for routine maintenance, this includes die surface cleaning or re-cut. However, the current cooling rates are approximately 37°C per hour, this takes 3 to 4 days and consequently has an adverse impact on productivity. The actual die model has been simplified to fit into the scope of the project. The die is manufactured from cronite (HR4), a nickle based alloy. This project is of interest to Rolls-Royce, as the research done will be used by the company to conduct their own investigations on the hot forming process and improve the entire manufacturing process for fan blades.

Aims and Objectives

The project has aim of the project is:

1. To reduce the thermal cycling time during die change over/maintenance through optimised die and platen design.

These aims have been broken down into the following objectives

1. Model current die and platen thermal stress during thermal cycling,

2. Model current die and platen stress during forming,

3. Consider ways of redesigning die to speeding up the cooling press,

4. Define minimum working surface thickness before distortion occurs in normal surface,

5. Develop designs to optimise die shape and to achieve maximum cooling rates

Current Progress

The material used in the die is specially made for Rolls-Royce, as the material must perform at a temperature of 900°C and pressure in the region of 30bars this and the fact that Cronite has a high nickel content makes the material far too expensive therefore, it was beyond the scope of this project to conduct actual experiments on the material. Finite element analysis has been recognised as the best method of analysing the problem.

The finite element package Ansys was chosen to model the current die and platen stresses so far the progress has been reasonable. Several designs have been analysed and the best design will be taken to the next stage and studied in greater detail. The designs will be analysed structurally to determine the effect of the design change on the cooling time and to make sure the die can withstand the working conditions.

Henry has some good slides

Nitin P. Daphalapurkar — Wed, 20 Jun 2007 17:33:08 -0400

Henry has some good slides on MPM, at http://imechanica.org/node/1102

Ajit, you are right, since the contact between materials is handled naturally, modeling of interlocking fibers can be possible.

If the deformations are small then MPM can handle the problem, with hardly numerical noise. We spent some time in comparing MPM solution with FEM for elastic-plastic material model (http://wwwlib.umi.com/dissertations/fullcit/1425010).

Re: Material Point Method

Biswajit Banerjee — Wed, 20 Jun 2007 13:15:55 -0400

There are a few points I'd like to bring to our attention:

One has to be careful when using the term "deformation". I don't know why this terms was chosen by early continuum mechanicists. It is confusing it also includes rigid body motions which are not really deformations in the colloquial sense of the word.
When I say Sulsky MPM works for small deformations, I also mean that any rigid body motions have to be small enough that particles do not cross cells. This is clearly not the case in many of the examples that she gives in her papers where she simulates bouncing balls and such. The convergence behavior of such simulations with Sulsky MPM is often less than first order if they at all converge.
The main "purported" advantage of MPM is that it can deal with large deformations and large motions. We would also like to see that we get more and more accurate results as we refine and at least first order convergence in both time and space. Large deformations are made possible by the background grid and Largrangian particles. However, if you use the delta function weights of the Sulsky method then convergence is not guaranteed unless an extra volume contribution is included in the grid basis function. GIMP generalizes the weights so that any appropriate weighting function can be used - linear, quadratic, cubic spline etc. We have found that cubic splines do very well though some boundary condition issues are yet to be resolved - including correct and fast contact in three dimensions. Mike Steffan is probably going to publish some of that stuff in the near future.
One also has to be careful when talking about Eulerian/Lagrangian formulations. MPM is purely Lagrangian. The grid is not a true Eulerian grid - it's just a scratch pad for calculations. Hence the statement "contact between materials is handled by the Eulerian formulation" is not accurate even though the balance of forces at grid points is what's used for doing contact in MPM.
Friction between interlocking fibers is not trivial in MPM. You will need an extremely fine grid to get it right. Finite elements will probably do the job better unless the fibers are being stretched significantly.

Small deformation and MPM...

Ajit R. Jadhav — Wed, 20 Jun 2007 04:52:46 -0400

Thanks for the clarification on GIMP and MPM. ... You basically confirm that the original MPM approach does work alright for small deformations in SM and that the issue of numerical instability arises only when the deformation is large... Incidentally, this circumstance is remarkably like that for FDM!! ... So, that reminds me about posting a reply in another thread, FDM in SM. The discussion there, too, involves the aspect of Lagrangian and Eulerian viewpoints.

Re: MPM and frictional contact

Biswajit Banerjee — Tue, 19 Jun 2007 02:07:19 -0400

The original version of MPM (developed and used by Sulsky and her group) runs into serious instability problems when particles cross cell boundaries. If the motions/deformations are small then particles remain within cells and everything is hunky dory. However, for large motions, you have to use alternative approaches such as GIMP (Bardenhagen and Kober) to get reasonable behavior. That point was again made by Scott Bardenhagen and several other people who work with MPM in this year's 3rd MPM Workshop at Sandia.

Sulsky continues to use the old formulation and I'm not sure that I can trust her results for some of the things she does. John Nairn has probably moved to GIMP by now but I'm not sure. Unless I see convergence/completeness studies in their work, their results will at best be qualitative. Please let me know if you find any convergence studies other than those coming out of Jim Guilkey/Mike Kirby/Martin Berzins' groups.

Getting frictional contact correct in GIMP turns out to be nontrivial whereas it's easy in Sulsky MPM. Scott Bardenhagen and others published a paper on that in CMES a few years ago. Frictional contact in general GIMP will be a good MS project for anyone interested in MPM.

MPM applications: Some loud thinking...

Ajit R. Jadhav — Mon, 18 Jun 2007 14:18:45 -0400

OK, thanks. Browsed MPM on the 'net for an hour or so, and then thought of dropping a note here in passing ... For whatever it is worth....

In MPM, Nairn has been researching woods as composites. Sulksy can already address granular materials fairly effectively because MPM makes it easy to include in the factor of contact-friction among individual grains. ...

Now, putting two and two together, I think, it should be very easy for the MPM researchers to model the problem of interlocking of fibers in composite materials. The interlocking can occur both within the uncracked portion and near the crack-separated surfaces. The broken fibers (or other forms of reinforcements) come out protruding from the crack-surfaces behind the crack-tip, and may serve to impede further crack opening, thereby possibly enhancing toughness. ... As far as I remember, the modifications in deflection and stress fields due to reinforcement-interlocking has been well acknowledged as a factor in the composites literature. But I can't tell how serious is its contribution to the overall fracture toughness. And the overall impression that I carry (and it could be wrong) is that it has been difficult to address these kind of factors in numerical simulations using FEM. FEM analyses typically ignore the fiber-to-fiber friction and interlocking. The tendency in FEM analysis is to factor in all such factors right into the homogenization schemes, at least that for the zone near the crack-tip.

But, now, it looks like the problem could be attacked in a very *direct* manner using MPM.

Quantifying interlocking and friction may have other uses too, e.g., in making better particle-boards for acoustic applications. So, apart from rheological applications, MPM seems ideal for particle-boards.

I would appreciate knowing if any of my loud thinking above has been going wrong somewhere.

... And, yes, I still wish simplified slides/tutorials on MPM, suitable for independent reading by the UG students, were already available, ready-made, on the 'net. (I am lazy!)

Ajit: There are a lot of

Nitin P. Daphalapurkar — Sun, 17 Jun 2007 01:30:08 -0400

Ajit:

There are a lot of publications available online (if searched from google and sciencedirect.com) which give intro and algorithms on MPM (also refer Sulsky et al. 1995). The algorithm is not very complex. Just like any other continuum numerical method, computational limitations can be overcome by using parallel computations, upto some extent. MPM can be easy to work with while dealing with certain problems, like simulating real microstructures as in foam.

MPM in SM...

Ajit R. Jadhav — Wed, 13 Jun 2007 11:00:04 -0400

Hi Nitin,

1. I will appreciate pointers to introductory or tutorial articles on MPM in SM (solid mechanics). Ideally, those that are written for a non-PIC non-MPM expert. Will appreciate presentation slides too. Could you please post any such material as attachment(s) here? (Also, similar articles on PIC.)

2. What is the computational complexity (or space and time costs) of the MPM technique? How sensitive is the complexity to the no. of Lagrangian particles? To the size of the background Eulerian mesh?

3. It seems that even after effecting any algorithmic reformulations for efficiency, the basic technique itself would be computationally very expensive. In what kind of applications is the "extra" cost justified? Are there any guidelines available regarding application areas? Or is it too early to tell?

Thanks in advance.

Simulation of foam compression

Nitin P. Daphalapurkar — Tue, 12 Jun 2007 13:39:29 -0400