Dear colleagues,

I kindly ask for advice on the following problem:

I simulate the uniaxial compression of a heterogeneous cylinder representing bone. Thus, it is not the visible solid exterior rim of the bone, but represents a porous structure within the bone, so-called trabecular bone, see the figure underneath.

The simulation is done in ABAQUS. The sample contains 164175 elements of type C3D4. The heterogeneous, porous structure makes it impossible to use axisymmmetric elements. The constitutive behavior is ELASTIC.

Dear iMechanica,

suppose you have a beam with a square cross-section, manufactured from an elastic-ideally plastic material.

Now apply a load that rises linearly in time, but is locally constant along the beam length. Upon sagging, the beam will develop a plastic zone beginning in the top and surface regions at mid-length.
This is the "straight" problem solved in Prager, Hodge: Theory of perfectly plastic solids, publisher: Springer

I am curious about the inverse problem: how do I have to load the beam in time and space so as to achieve a circular arc along the length ?