I was just reading about volumetric locking in Dhondt's book (for Thermomechanical analysis) and came across this (funny) question;
Now, we say the physical interpreation about Jacobian is change in volume, now if a material is incompressible Jacobian = 1, now this incompressibility is a material property, right?
Where is a material parameter attached to Jacobian expression of finite elements (1-d,2-d or 3d finite element)?
I have been bugged by this question ever since I studied cauchy's stress theory 10 years ago.
In cauchy's analysis of solids, there two popular geometries.
First one is a unit cube used for deriving equations of equilibrium.
And the second one is a tetraheadon used for deriving Cauchy's stress theorem.
In both the cases limit of force equilibrium as solid geometry shrinks to a point is derived.
My question has been, how come limit of force equilibrium at a point inside a solid depenent on the path taken by limiting process.
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