Instead of applying a pressure, you could create a cylindrical surface (tube) around the wire structure, and add frictional contact between the surface and the wire.  You would delete the Fixed Support on the wire structure. You could apply a radial displacement to the nodes on the tube that would shrink the diameter of the tube. You could apply a Thermal Condition to the elements on the tube that would shrink the tube. If you apply an Orthotropic Secant Coefficient of Thermal Expansion so that it only shrinks in one direction, which would be the tangential direction in a cylindrical coordinate system. You would need to apply this coordinate system to the elements on the tube.