The finite volume method for solid mechanics in OpenFOAM Philip Cardiff
28th, 29th May 2018
OpenFOAM 2nd Iberian Meeting Santiago de Compostela Spain
The finite volume method for solid mechanics in OpenFOAM Philip Cardiff
[email protected] H. Jasak I. Demirdžić P. de Jaeger A. Karač J. Nagy A. Ivanković Ž. Tuković
School of Mechanical & Materials Engineering University College Dublin ! ! ! !
http://www.ucd.ie/universityrelations/about-ucd/photogallery/hires/16-lake-2163_077D.jpg
Background
OpenFOAM is not just an excellent tool for Computational Fluid Dynamics OpenFOAM also provides a suitable framework for the simulation of multi-physics problems, including fluid-solid interaction The finite volume method offers an interesting alternative to the finite element method for solid mechanics 4
Solids vs Fluids
Consider the governing equations for solids and fluids: Newtonian fluid
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@⇢v + r · [(v @t
v )v] = r ·
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@⇢ + r · [(v @t
v )⇢] = 0
@⇢ + r · [(v @t
v )⇢] = 0
Hookean solid
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@⇢v + r · [(v @t
v )v] = r ·
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… they are the same http://www.ucd.ie/universityrelations/about-ucd/photogallery/hires/16-lake-2163_077D.jpg
6
Consider the governing equations for solids and fluids: Newtonian fluid and Hookean solid
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@⇢v + r · [(v @t
Fluid vs Solid
v )v] = r ·
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@⇢ + r · [(v @t
6= Eulerian vs Lagrangian 6=
v )⇢] = 0
FV vs FE
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@⇢v + r · [(v @t
v )v] = r · v=v 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
http://www.ucd.ie/universityrelations/about-ucd/photogallery/hires/16-lake-2163_077D.jpg
+ fb
Lagrangian: no convection 7
Consider the constitutive laws for solids and fluids: Newtonian fluid
= 2µ dev[D]
1 T D= rv + rv 2
pI
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Hookean solid
velocity displacement
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