Continuum mechanics uses tensors . Students need to acquire a usable
facility with short learning curve. Is there a free open source software (FOSS)
which can be used to gently introduce this subject and demonstrate the advantages
of using continuum mechanics on simple examples?
Hi,
Although I have no idea about a software concerning Quantum Mechanics, I found a few lectures by Donny Lee to be quite interesting. You can have a look.
Best Regards.
http://www.youtube.com/watch?v=S427pzdAvKc&list=PLA37E77BB7D1DCD25
http://www.youtube.com/playlist?list=PLD8062C327B497E74
I guess that the former question was maybe on continuum mechanics, assumed as a part of classical mechanics, not on continuum fields in quantum mechanics (maybe I am wrong... but if not, let us pursue a little bit).
If tensors are an issue, they can be postponed when starting by beam theory (which can be thought as part of continuum classical mechanics). The only drawback is that if you intend to design the beam, and in particular its section, you will need to go back to a reconstructed stress tensor from the beam solution...
Maybe an alternative is then to use at this point a part of the course on traction test (linear elasticity, homogeneous, small perturbations), that may help in defining 1D than 3D strain and stress in simple cases (with Cauchy tetrahedron). This may then help the approximated stress reconstruction from Beam solution.
Finally, one can move to full 3D behavior. Then to plate, to material non-linearities, to large displacements, to large rotations, to large strains... I guess there are some material on wikipedia to get a first glimpse on the developments.
Concerning codes, I think that almost any finite element freeware could be used.
Thank you David Dureisseix and Raktim Haldar . The answers are useful. The question referred to a continuum mechanics course to be introduced where students have a basic knowledge of
Linear algebra but not Tensors. The expectation is that the students will be in
unfamiliar territory wrt Tensors , so how can this be introduced , further
is there a strong motivation in terms of applicability and use of this knowledge
compared to other techniques .
Cheers
Some suggestions for introducing tensors (in the context of continuum mechanics):
- stress tensor can be derived from surface forces using Cauchy tetrahedron, i.e. F = sigma x n (interpretation as a matrix vector product). Seems easy to provide.
- components of strain tensor epsilon can be settled via elementary deformation modes. Question: not sure how to justify easily the gathering of these components into a single thing called "strain tensor"
- some higher order tensors? Maybe from the linear relationship betwen a component of the stress tensor and all the components of the strain tensor, leading to a 4th-order Hooke tensor sigma = H epsilon, or convertly epsilon = H^{-1} sigma
- generalisation: scalar are tensors of order 0, vectors of order 1, matrices (with two entries) of order 2, there are matrices with 4 entries (for instance H_{ijkl}) which are tensors of order 4, that can be symmetric, invertible.... [There exist tensors of order 3, for instance in piezoelastic couplings if I remember correctly; tensors of order 4 for damage... but this rapidly become somehow technical]
Thank you David Dureisseix . It is indeed very helpful especially wrt introduction
of Tensors .
Cheers
For structural analysis code, I would suggest Code_Aster
http://www.code-aster.org/V2/spip.php?rubrique2.
It is open source, well documented, with a lot of examples available with its test case database
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