# GlobalStiffnessTimeStepper viscEl background

Hi all!

How does it calculate the timestep in case of elasctic and viscoelastic (viscEl=True) cases? I can see the sourcecode, but is there any paper which describes the mathematical background of the minimum eigen-period for the viscous contribution and which can be referenced? I have not found much in the Yade manual.

Thanks,
D

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2020-01-13
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2020-01-13
 Robert Caulk (rcaulk) said on 2020-01-12: #1

Hello,

>> case of elasctic and viscoelastic (viscEl=True)

Can you please link to the materials/constitutive laws/parameters you are referring to? We have a class reference for this very purpose [1].

>> I can see the sourcecode

See "Stability Considerations" of the Yade manual [2] which also points to Abul Hosn et al. 2017 [3].

Cheers,

Robert

 drasszkusz (drasszkusz) said on 2020-01-12: #2

Dear Robet,

>> Can you please link to the materials/constitutive laws/parameters you are referring to? We have a class reference for this very purpose [1].

I understand the minimum eigen-period for elastic contribution (spring only), but with viscEl=True in globalstiffnesstimestepper [1], the viscous contribution is also considered (dashpot part) when calculating minimum (critical) timestep for Law2_ScGeom_ViscElPhys_Basic [2].

The source code can be found here [3].

>> See "Stability Considerations" of the Yade manual [2] which also points to Abul Hosn et al. 2017 [3].

As I can see, there are no dashpots used in that study [4], so there is nothing about viscous stability cosiderations there. Also I could not find anything in Yade manual about critical timestep considering mass-spring-viscous dampers (only mass-spring).

Cheers,
D

 Jérôme Duriez (jduriez) said on 2020-01-13: #3

Maybe you can try starting from Raphael's PhD Thesis, § 2.1.3 of [Maurin2015PhD, *]...

 Robert Caulk (rcaulk) said on 2020-01-13: #4

>>I understand the minimum eigen-period for elastic contribution

The timestep associated with viscoelastic dampers-case is estimated using identical logic to the stiffness-only case. GlobalStiffnessTimestepper computes both and uses the smallest one. This is apparent by working backwards from [1], and is confirmed by Jérôme's link on page 18.

 drasszkusz (drasszkusz) said on 2020-01-13: #5

Dear Jérôme and Robert,

>> Maybe you can try starting from Raphael's PhD Thesis, § 2.1.3 of [Maurin2015PhD, *]...

Yes, it confirms the same as it is in the GlobalStiffnessTimestepper manual. The references in that study were also a dead end.

>> The timestep associated with viscoelastic dampers-case is estimated using identical logic to the stiffness-only case. GlobalStiffnessTimestepper computes both and uses the smallest one. This is apparent by working backwards from [1], and is confirmed by Jérôme's link on page 18.

In that case I have to reengineer the formula of the viscous part from the source code or search the internet for other studies. Because the references you provided only describe the elastic parts and just mention the viscous critical time step. Only the elastic formula can be found written down.

Cheers,
D