As far as I see, the plastic hinges in FLAC3D works separately in X and Y directions as if the problem is 2D in both directions. There is no interaction between them. Is that right?

I am sending the figure below showing the yield surface definitions for FLAC3D and expected cases.

Could you please confirm or inform me if it is not correct?

model new
model large-strain off
model title "Laterally loaded pile"
; Create zones
zone create brick size 8 8 8 edge=11
zone face skin ; Label model boundaries
; Assign material model and properties
zone cmodel assign elastic
zone prop bulk=5e9 shear=1e9 density=2000
; Boundary conditions
zone face apply velocity-normal 0 range group 'East' or 'West'
zone face apply velocity-normal 0 range group 'North' or 'South'
zone face apply velocity-normal 0 range group 'Bottom'
; Initial conditions
model gravity 10
zone initialize-stresses ratio 0.6,0.4
model solve ratio-local 1e-4 ; Should be instant
; =======================================================
; Create a pile in the center of the soil block
struct pile create by-line (5.5,5.5,12.0) (5.5,5.5,4.0) segments=8
struct node group 'Top' range position-z 12 ; Tag top node
struct pile property young=8.0e10 poisson=0.30 cross-sectional-area=0.7854 ...
torsion-constant=9.82e-2 moi-y=4.91e-2 moi-z=4.91e-2 ...
perimeter=3.14 ...
plastic-moment-y 3.89e4 ...
plastic-moment-z 3.89e4 ...
coupling-stiffness-shear=1.3e11 coupling-cohesion-shear=1.0e10 ...
coupling-friction-shear=0.0 coupling-stiffness-normal=1.3e09 ...
coupling-cohesion-normal=1.0e04 coupling-friction-normal=0.0 ...
coupling-gap-normal=off ...
direction-y=(1,0,0)
; so that shear force Fy corresponds with diagonal direction
; =======================================================
; Fish function to find lateral displacement of top node
[global topNode = struct.node.near(5.5,5.5,12)]
fish define lateralDisp
local disp = struct.node.disp.global(topNode)
return math.sqrt(disp(1)^2 + disp(2)^2) * math.sgn(disp(1))
end
; =======================================================
struct pile history name='force' force-y component-id 1 ; shear force at top
fish history name='disp' lateralDisp ; lateral displacement
; =======================================================
struct mechanical damping combined-local
struct node fix velocity-y range group 'Top' ; fix velocities in lateral plane,
; top node
struct node fix velocity-z range group 'Top'
; move (+) diag-dir
struct node initialize velocity (0,0.707e-8,0.707e-8) local range group 'Top'
model save 'Initial'
; =======================================================
; Run no-gap case
; =======================================================
model cycle 40000 ; disp of +4e-4
model save 'NoGap-1'
; move (-) diag-dir
struct node initialize velocity (0,-0.707e-8,-0.707e-8) local range group 'Top'
model cycle 80000 ; disp of -8e-4
model save 'NoGap-2'
; move (+) diag-dir
struct node initialize velocity (0,0.707e-8,.707e-8) local range group 'Top'
model cycle 40000 ; disp of +4e-4
model save 'NoGap-Final'
; =======================================================
; Run full-gap case
; =======================================================
model restore 'Initial'
struct pile property coupling-gap-normal on
model cycle 40000 ; disp of +4e-4
model save 'FullGap-1'
; move (-) diag-dir
struct node initialize velocity (0,-0.707e-8,-0.707e-8) local range group 'Top'
model cycle 80000 ; disp of -8e-4
model save 'FullGap-2'
; move (+) diag-dir
struct node initialize velocity (0,0.707e-8,.707e-8) local range group 'Top'
model cycle 40000 ; disp of +4e-4
model save 'FullGap-Final'

Dear cgulenc,
There are two ways to model plastic hinges in FLAC3D beams: (1) specify the plastic capacity for each beam element, or (2) use a plastic material model for the beam. With method 1, the moment at each node is decomposed into the My and Mz (in terms of the beam local coordinate system), and then each one of these is capped at the specified moment capacity. I believe that this means that the yield surface is the square — you should run a test problem to confirm this. With method 1, the yield surface will be the expected yield surface to within the resolution (how many integration points are assigned over the beam cross section).
Cheers,
David Potyondy
Note that I am out of the office from now until Monday afternoon, so I cannot reply immediately to any further questions.

Is there coupling between the plastic hinge elements in two directions?

Unfortunately, these elements are not coupled in two directions. Thus, the plastic hinge element in FLAC3D is actually 1D elastic-perfectly-plastic spring.

Yes, the yield surface I mentioned is square unfortunately. Thus, each plastic hinge is actually 1D spring element in its own direction. Thus, we cannot consider the directional effects on structural response with this model.

It is possible to consider the directional effects on non-linear structural response in Plastic Constitutive Element method. However, this model is not appropriate for RC sections because only one material (a RC section includes three materials, namely, unconfined concrete, confined concrete and reinforcing steel) can be defined in one section in this model. We cannot employ this model for steel sections as well because only circular and rectangular sections can be used to define sections in this model. The steel sections used as pile, column or beam in practice are circular hollow sections, rectangular hollow sections, H or I profiles etc. I believe that this model is a perfect attempt to model the non-linear response of 1D structural elements incorporating the effects in three dimensions. However, it is not applicable, with this currently available version, for both RC and steel elements in real life problems unfortunately. Please tell me if I am wrong. I would be pleased to learn more.

How can I incorporate the directional effects on the non-linear structural response of 1D structural elements in FLAC3D? Is there any other way?

Pardon the delay in my response. I needed to speak with Augusto Lucarelli, one of our Civil Engineering consultants, who is an expert FLAC3D user. He has been modeling the sorts of problems that you describe using three different schemes using the existing FLAC3D logic. The best way for us to explain this to you is to have a meeting wherein he will present the schemes. In order to set this up, I need to send you an email. Please send me your email address so that I can do that.

Have you had a chance to review the results? As shown in the example illustration I provided, when assigning

plastic-moment-y 3.89e4
plastic-moment-z 3.89e4

to the piles and pushing in the direction of (1,1,0), it aligns with the value on the ‘expected yield surface’ in the graph you shared. As can be seen in the graphs from my previous message, the maximum moments generated in both directions are 27.5 kN.m before the pile yields and does not take on any more moment - as expected. If you adjust the dir-y to (1,1,0) in the example I gave, you will find the maximum to be 38.9 kN.m again.

By the way, if I do not assign any plastic hinge capacities, the value rises to 55 kN.m as similar to the graph you shared.

I haven’t tried it for different sections, but for now, these are the results.

I sent you a message @dpotyondy to attend that meeting if possible.

Dear CGulenc and Ozan Bilal, [not sure if this will get to both of you, so sending it twice, once to each]

I need to have both of your email addresses to set up our meeting. I now have the email address of Ozan Bilal but not of CGulenc. Please send me both of these addresses to my email address of: dpotyondy@itascacg.com.

Dear CGulenc and Ozan Bilal, [not sure if this will get to both of you, so sending it twice, once to each]

I need to have both of your email addresses to set up our meeting. I now have the email address of Ozan Bilal but not of CGulenc. Please send me both of these addresses to my email address of: dpotyondy@itascacg.com.

Thank you very much for your participation.
Then new questions arise regarding how does the plastification occur after yielding?
Let’s talk these issue in the meeting.