Abaqus/Standard may generate inaccurate external work (ALLWK) in static non-linear analyses (finite hyperelasticity)

It should be noted that Abaqus/Standard may generate inaccurate external work (ALLWK) in a static geometrically non-linear analysis (finite hyperelasticity) and, consequently, will cause ETOTAL to be inaccurate.

For example, we assume that a hyperelastic solid is only subjected to body forces. It doesn't matter a linear or non-linear analysis will be, the external work of the body forces can be calculated over reference configuration

$\;\;\;\;\;\;\;W^{ext}=\int_{\Omega_0} \boldsymbol{f}_0(\boldsymbol{X})\cdot \boldsymbol{U} \;dV $

For linear static analysis, we obtain the almost identical values of the external work provided by Abaqus and using custom post-processing calculation. Turning to finite elasticity, the difference may be significant and leads to the erroneous results in the external work estimation.

P.S. Recall that for a static problem a value of external work reported by Abaqus is half of "true" external work.

CAPLET - fast-field electrostatic solvers scaled up by parallelizing

Looking for a new generation of fast-field solvers capable of being scaled up by parallelizing, recently I find the interesting project CAPLET on the same MIT site we can find FASCTAP.

Project CAPLET is a capacitance extraction toolkit that extract capacitance at field-solver accuracy. This is the open-source code under GNU Lesser General Public license aimed for ultra-fast extraction of small-to-medium structures with 5% accuracy of reference solutions and efficiently parallelized.Thought the author claimes the simplified installation procedure, it demands some steps. We did it on Ubuntu 10.04. You can use any virtual machine (VirtualBox, etc.), install Ubuntu 10.04, upgrade the OS and install the following package:


apt-get update; sudo apt-get upgrade
   apt-get install g++
   apt-get install libcr-dev mpich2 mpich2-doc
   apt-get install libblas3gf libblas-doc libblas-dev
   apt-get install liblapack3gf liblapack-doc liblapack-dev
   apt-get install gfortran
   apt-get install openmpi-bin openmpi-doc libopenmpi-dev

To compile QT GUI you can download, for example, Qt Creator 2.4.1 and Qt 4.7.0.

The toolkit has three solvers:

 1. Caplet (based on instantiable basis functions), 

 2. FastCap (additional link to the solver is required), and

 3. Standard BEM solver (piecewise constant basis functions with collocation testing, obviously without any acceleration).

We compared the standard BEM solver verus FASTCAP with -d0 option on the proven configuration (two parallel 100x2000x200 plates). The results are not the same :-0.

Compatibility of constrained displacement field in the case of simply connected body

In nonlinear elasticity we regard the compatibility as a restriction of the motion (of a simple body) in terms of the strain measures: deformation tensor F or right Cauchy-Green deformation tensor C (also left Cauchy-Green deformation tensor b).

Commonly when we talk about the compatibility we consider an inverse problem. Given F (or C) we need to derive the deformation map. To do this certain mathematical restrictions must be placed upon the strain measures in order that the inverse problem have a solution. We call these mathematical restrictions the compatibility conditions or more precisely the integrability conditions, since in general the compatibility is equivalent to path independence of the solution dealing with integrations of the strains. So, the main question to answer is,  given F (or C or b), is there a deformation mapping?


Now we consider the forward problem. Given a deformation mapping (smooth immersion), it is easy to compute the strain measure. And following Truesdell C.A, Toupin R.A., Ericksen J.L, "The Classical Field Theories",

In a problem formulated entirely in terms of the deformation, the conditions of compatibility need not be regarded, since they are satisfied automatically in virtue of the definitions of b and C. 

It's look simple.

Now the question is raised when the deformation mapping itself is constrained. For instance, instead of assuming that here is the deformation mapping from the abstract space R^3 to the Euclidean space E^3, we consider the mapping from R^3 to  R^3 times  R^N times R^M times SO(3). What's going on the compatibility conditions in this case?

2013: Still with FASTCAP. Towards ExaFMM?

Electrostatics. Looking for the parallel fast field solver.

I successfully used the FASTCAP fast field solver long years ago for capacitance calculation and electrostatic charge density and forces derivation. Incorporating this solver into a finite element code, solution of multiphysics coupled problems can be obtained quickly. With staggered scheme of course.
 

Recently coming back  to the electrostatic problem calculation, I tried to find a new generation of the fast field codes. My feeling that here is still no ready open source code except the premium FASTCAP.


The FASTCAP itself is acceptable from the accuracy standpoint, particularly for my problems in the hand. I have compared the BEM results with FEM reference solutions  and found it quite acceptable. Also for the science community it is a common practice to compare new and more efficient solvers versus FASTCAP. The problem is the speed of runs. The code was born in 90's, in the era of single-core computations. Nowadays impressed by "Biomolecular electrostatics using a fast multipole BEM on up to 512 gpus and a billion unknowns" I think to write a custom electrostatic code with ExaFMM library. Obviously it would take a long time and  perhaps I'll go flop. As a result the simple, open source,  parallel performance, electrostatic solver is still looking for.