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# Periodic Boundary Conditions for uniaxial compression

Dear All,

I am trying to simulate mechanical behaviour of a concrete unit cell for uniaxial compression laoding. I have apllied periodic bounadary conditions on both lateral edges using linear equation option available in ABAQUS where as on top and bottom edges load is apllied. Deformed structure shows there is no lateral deformation and unit cell behaves as if it is confined laterally on both sides. I am confused about my boundary conditions whether they are correct or not.

Equation used to aplly periodic bounadary condition are

** Constraint: Constraint-18

*Equation

2

R17, 1, 1.

L17, 1, -1.

where R17 and L17 are nodes on the right and left of the unit cell.

Can any body suggest what exactly I should use for my unit cell. Unit cell is a plane square with a circular inclusion at the centre.

Regards

Gouse

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## Comments

## In this case, you should

In this case, you should first add a reference node, e.g. called RefNode, and using the following.

*Equation

3

R17, 1, 1., L17, 1, -1., ReNode, 1, 1.0

2

R17, 2, 1., L17, 2, -1.

2

R17, 3, 1., L17, 3, -1.

Here, RefNode represents the relative U1 displacement of your left and right boundaries.

## Periodic Boundary Conditions for uniaxial compression

Hi,

Thank you for your reply. I am not much familiar with using equation constrain and I didn't understand how to define the RefNode, is it a dummy node. Should I have to give the coeficeint of RefNode (dummy node) equal to relative displacement of nodes on the left and right sides. Than I dont know the relative displacement of left and right node apriori.

Thank you

Regards

Gouse

## necessiscity of periodic boundary conditions for uniaxial loadin

Hi,

With your above suggestions, I could able to implement periodic boundary conditions for my problem.

I observed that with periodic boundary conditions, when uniaxial load is applied structure behaves as if it is constrained to move in lateral direction, when shear or other traction laoding is applied it has displacement compatible behavior i.e, parallel edges has periodic deformation behavior. With these above behavior can I conclude that for uniaxial loading I need not apply periodic BCs and simply applying roller is sufficient on lateral edges or there is no need to apply and periodic BCs for uniaxial loading.

With refernce to my above comment whether to use Periodic BCs for uniaxial loading, I found a supporting paper which says for uniaxial loading periodic BCs are not required. Reference paper is -

V. Kouznetsova, W.A.M. Brekelmans, and F.P.T.

Baaijens, An approach to micro-macro modeling of heterogeneous materials,

Computational. Mechanics,27, 37-48, 2001However still I am confused whether to use Periodic BCs or not, can any body clarify about this.

Thank you

Regards

Gouse

## can u tell me how exactly

can u tell me how exactly it has to be done ? im working on thesame.

Thanks,

Aditya