Limit on macroscopic Poisson's Ratio

Asked by Piotr Klejment on 2019-12-12

Hello!

In a recently defended doctoral dissertation
(available online - https://www.researchgate.net/publication/337533641_New_formulation_of_the_discrete_element_method_with_deformable_particles)
I found an information that the maximum value of Poisson’s ratio that can be obtained with discrete element model
is 0.25 for bonded spherical elements and 0.33 for bonded disc elements:

"(...) Predominantly in discrete element formulation, particles are treated
as rigid and overlap between particles is allowed, assuming it to be equivalent to the particle
deformation at the contact. This approach is known as the soft contact approach.
The particle overlap is used in an appropriate contact model which offers an advantage
of obtaining the desired macroscopic behaviour. However, despite using the soft-contact
approach, assumed particle rigidity makes the accurate representation of macroscopic
properties in DEM a great challenge and even impossible in some cases. For instance,
the maximum value of Poisson’s ratio that can be obtained with discrete element model
is 0.25 for bonded spherical elements and 0.33 for bonded disc elements. (...)"

I am curious if it is a general rule, valid also in ESyS-Particle simulations?
I would like to ask also about variability of microscopic Poisson's ratio. Does it change in range 0-0.5, like macroscopic Poisson's ratio, or maybe higher values are also available?

Best wishes,
Piotr Klejment

Question information

Language:
English Edit question
Status:
Solved
For:
ESyS-Particle Edit question
Assignee:
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Solved by:
Dion Weatherley
Solved:
2019-12-13
Last query:
2019-12-13
Last reply:
2019-12-13
Best Dion Weatherley (d-weatherley) said : #1

Hi Piotr,

This is new to me but I was able to track down the original article pertaining to this assertion. It's a paper by Bathurst and Rothenburg (1988):
https://doi.org/10.1115/1.3173626

I've not carefully read their analysis as yet but it appears that this result may only be applicable for spheres/discs of a narrow size range (almost mono-disperse). For random packings with a broader size range, this restriction may not apply.

Wang and Guo (2016) produced a similar graph of Poisson's ratio versus Kt/Kn and reported ratios up to 0.3 for random packings. Wang and Guo used a branch of ESyS-Particle for their studies.

A preprint version of their paper is here:
https://www.researchgate.net/profile/Yucang_Wang/publication/305553509_Reproducing_the_realistic_compressivetensile_strength_ratio_of_rocks_using_discrete_element_model/links/582e846d08ae102f072dba6e.pdf

Earlier this year, Steffen and I were able to reproduce their result using the current trunk version of ESyS-Particle and BrittleBeamPrms. We varied the beam (microscopic) PoissonsRatio over a very broad range (0.1 to 10 IIRC) and measured macroscopic Poisson's ratio in UCS tests on cylinders. One thing that was concerning however was that the fracture patterns became very diffuse for larger Poisson's ratios, with almost no evidence for fracture localisation for simulations with a macroscopic Poisson's ratio between 0.25 and 0.3. Indeed the cylindrical specimens remained essentially intact post-failure albeit with a large amount of damage distributed throughout the specimen. IMO, this is not realistic as brittle materials with Poisson's ratio in the range 0.25-0.3 clearly produce localised fracture planes and fragment into two or more detached pieces.

I think it is fair to say that there is still work to be done to improve DEM bonded particle models, particularly to achieve realistic Poisson's ratios and compressive:tensile strength ratios, whilst ensuring that the fracture patterns localise into narrow fracture planes. IMO, it is not sufficient to reproduce macroscopic observables such as the stress-strain relations. The model needs to also fail like a brittle material. Maybe the deformable DEM formulation of the thesis you referenced will get there, once it's extended to 3D. Demonstration of localised failure in 2D is not sufficient to presume that the same occurs in 3D...

Cheers,

Dion

Piotr Klejment (glaubiger) said : #2

Thank you very much Dion for your answer!

Piotr Klejment

Piotr Klejment (glaubiger) said : #3

Thanks Dion Weatherley, that solved my question.