sfepy/sfepy — Issue #118: Linear elastic anisotropic materials
Author: rc
Created: 2012-01-30 10:26:38+00:00
State: open

We have functions for isotropic materials, can this function be extended to
deal with anisotropy.

Migrated from http://code.google.com/p/sfepy/issues/detail?id=116

earlier comments

robert.cimrman said, at 2010-04-12T13:10:13.000Z:

See dw_lin_elastic, which accepts the material parameters in the general tensor form
- example use is e.g. in examples/biot/biot_npbc.py ...

freevryheid said, at 2010-04-12T14:30:47.000Z:

Please expand - to set the anisotropic material parameters in the 3 dimensions would
you need to do something like this:

out['D'] = nm.tile(stiffness_tensor_lame(dim, lam=1.7, mu=0.3),
(coor.shape[0], 1, 1))
out['D'] = nm.tile(stiffness_tensor_lame(dim, lam=2.7, mu=0.4),
(coor.shape[0], 2, 2))
out['D'] = nm.tile(stiffness_tensor_lame(dim, lam=3.7, mu=0.45),
(coor.shape[0], 3, 3))

A

robert.cimrman said, at 2010-04-12T14:40:17.000Z:

You do not need stiffness_tensor_lame() at all - this function just builds the tensor
using the two Lame constants.

So to have anisotropic material, set the components of D directly. It is a 6x6 tensor
in 3D, 3x3 in 2D, with the order of components described in [1] - it is 11 22 33 12
13 23 in 3D, 11, 22, 12 in 2D. There is also explained the relation of isotropic D to
the Lame constants.

As an example of anisotropic material, an orthotropic material can be defined as
described at [2].

[1] http://docs.sfepy.org/doc-devel/src/sfepy/mechanics/matcoefs.html
[2] http://en.wikipedia.org/wiki/Hooke%27s_law#Orthotropic_materials