
From:  Konstantinos Poulios 
Subject:  Re: [Getfemusers] Hyperelastic law Benchmark 
Date:  Wed, 14 Jun 2017 16:57:56 +0200 
the first use the symmetry of the GreenLagrange strain tensor to simplify the strain energy functionThere are 3 problems, for now i am working on the first one that is to say the deformation of a 3D rectangular beam clamped on one side and with a pressure applied to the bottom face.Dear Getfem users,i am trying to implement a new hyperelastic law and, in order to validate my results, i am using the following Benchmark
http://rspa.royalsocietypublishing.org/ content/471/2184/20150641#sec 15
While the deformed configuration given by Getfem is relatively close to the reference(s) solution(s) provided by the benchmark, a visible difference between them still remains and i don't understand where it comes from.The material is governed by a transversely isotropic constitutive law with an incompressibility constraint, often used in cardiac modelling, where the strain energy function is a function of the components of the Green–Lagrange strain tensor E.I tried 2 differents implementations of this law:The second does not (ergo it is necessary to write the 9 components of the second piola Kirchhoff stress tensor and the 81 components of the fourth order tensor)
Please find enclosed
the comparison in the first case: Results.png
the comparison in the second case: Results_nosym.png (slightly better results but 15 times as slow as the first version)
the python program used to compute the derivative and second derivative of the strain energy function in the first case.the implementation of the laws in getfem_nonlinear_elasticity.cc and getfem_nonlinear_elasticity.hThe program Guccione.cc and Guccione.param used to produce these very pictures
in both pictures, the reference solution is in grey.
The computation uses Q2/Q1 elements (displacement/lagrange multiplier), since there is no restrictions regarding these aspects.
I have tried with a quasiincompressibility condition instead of the Lagrangian multiplier: same result (which was to be expected).I have also tried with other meshes (more or less refined) used by other teams but in vain.
Could someone have a look and provide some advices regarding this case/tell me what i am doing wrong?Thanks a lot.Yours sincerely,David.
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