# For boundary conditions combining roller boundary and enforced displacement

**URL:** <https://community.freefem.org/t/for-boundary-conditions-combining-roller-boundary-and-enforced-displacement/3698>\
**Category:** General Discussion\
**Created:** [January 21, 2025, 6:01am UTC](https://community.freefem.org/t/for-boundary-conditions-combining-roller-boundary-and-enforced-displacement/3698 "2025-01-21T06:01:05Z")\
**Posts on this page:** 1\
**Showing post:** 4

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**Author:** ![fb77](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/fb77/32/3796_2.png) [@fb77](https://community.freefem.org/u/fb77)\
**Post date:** [January 28, 2025, 9:18am UTC](https://community.freefem.org/t/for-boundary-conditions-combining-roller-boundary-and-enforced-displacement/3698/4 "2025-01-28T09:18:53Z")

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Dear Ayataka,  
In my statements, u is the velocity field, not the displacement. I was considering an imposed velocity 1 in the direction of W, u\cdot W=1. I realize that it is not what you asked for, you stated an imposed displacement. Thus it has to be modified.  
Anyway to complete the equations we need some constitutive relations, characterizing the material. In general it could be elasto-visco-plastic, compressible or not. If elasticity is dominant (like steel), considering equations on the displacement is mandatory. The equations can be simple if you consider small deformations, or complicate if you want to consider large deformations. Are you thinking of Hooke’s law for elastic small deformations?  
There is an example here [Normal boundary condition - #12 by k-matsushima-19](https://community.freefem.org/t/normal-boundary-condition/341/12)

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