# Tensor coordinate transforms for linear elasticity

**URL:** <https://discourse.julialang.org/t/tensor-coordinate-transforms-for-linear-elasticity/70326>\
**Category:** Modelling & Simulations\
**Tags:** fem, tensors, coordinate-transform\
**Created:** [October 25, 2021, 11:19am UTC](https://discourse.julialang.org/t/tensor-coordinate-transforms-for-linear-elasticity/70326 "2021-10-25T11:19:05Z")\
**Posts on this page:** 5\
**Page:** 1

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**Author:** ![feanor12](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/feanor12/32/8212_2.png) [@feanor12](https://discourse.julialang.org/u/feanor12)\
**Post date:** [October 25, 2021, 11:19am UTC](https://discourse.julialang.org/t/tensor-coordinate-transforms-for-linear-elasticity/70326/1 "2021-10-25T11:19:05Z")

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I have a linear elasticity problem in 2D (plane stress) with anisotropic material properties.  
I can easily calculate the displacement in the (100) plane, but I have difficulty understanding how to get the correct initial conditions and material properties for the (110) plane.  
Basically I want to transform Hook’s law into the new orientation, but tensor coordinate transforms are a bit tricky for me. I think to change from (100) to (110) is just a rotation of 45 deg around the z axis.

Are there any good packages for coordinate transforms of second order(strain, stress) and fourth order(stiffness) tensors?

A good book/article would also help.

Thank you  
Michael

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**Author:** ![fredrikekre](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fredrikekre/32/1688_2.png) [@fredrikekre](https://discourse.julialang.org/u/fredrikekre)\
**Post date:** [October 25, 2021, 11:44am UTC](https://discourse.julialang.org/t/tensor-coordinate-transforms-for-linear-elasticity/70326/2 "2021-10-25T11:44:37Z")

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Could dust off this old PR: [https://github.com/Ferrite-FEM/Tensors.jl/pull/82](https://github.com/Ferrite-FEM/Tensors.jl/pull/82)

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**Author:** ![fredrikekre](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/fredrikekre/32/1688_2.png) [@fredrikekre](https://discourse.julialang.org/u/fredrikekre)\
**Post date:** [October 25, 2021, 2:57pm UTC](https://discourse.julialang.org/t/tensor-coordinate-transforms-for-linear-elasticity/70326/3 "2021-10-25T14:57:53Z")

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I did, and it is in Tensors 1.7.0.

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<div class="post-metadata">

**Author:** ![feanor12](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/feanor12/32/8212_2.png) [@feanor12](https://discourse.julialang.org/u/feanor12)\
**Post date:** [October 25, 2021, 3:02pm UTC](https://discourse.julialang.org/t/tensor-coordinate-transforms-for-linear-elasticity/70326/4 "2021-10-25T15:02:43Z")

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That sounds great! I’ll take a look at it.

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**Author:** ![rafael.guerra](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/rafael.guerra/32/216610_2.png) [@rafael.guerra](https://discourse.julialang.org/u/rafael.guerra)\
**Post date:** [October 26, 2021, 3:08pm UTC](https://discourse.julialang.org/t/tensor-coordinate-transforms-for-linear-elasticity/70326/5 "2021-10-26T15:08:36Z")

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> [@feanor12](#):
>
> A good book/article would also help

[_Bonet, J. and Wood, R. [2008] Nonlinear Continuum Mechanics for Finite Element Analysis. 2nd Edition. Cambridge University Press._](https://www.cambridge.org/core/books/nonlinear-continuum-mechanics-for-finite-element-analysis/67AD6DBAAB77E755C09E7FB82565DA0B)

Experts seem to recommend this book. An introduction to tensor algebra is provided, the mathematical notation used looks clear and the book layout and illustrations very pleasant. Some Fortran code is provided.

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