I guess you may try to define the springs (six DOF) between the top and bottom ref points in stead of bush elements. Based on my experience, the connector elements (like bush) with too many DOF free sometimes is hard to converge for static problems.
IF you are looking to create a material constitutive model to describe the concrete behavior under high repetition of forces, you'd better go and look UMAT subroutine. Abaqus manual has explanation and examples.
In Abaqus/CAE, you can partition the beam and create vertices, and assign the springs at each point.
Or if you are familiar with keywords, can use keywords to define the springs like this:
*Spring, elset=springs
1
2.322e+06
*Element, type=springs
1, Spool-1.5
2, Spool-1.6
