The material must have a plasticity material model to cause plastic strain to develop and reduce the stress from getting too high.

To support a plasticity material model, the mesh should have 3 linear elements in each direction in the thin sections. That means 3 elements across the width and 3 elements through the thickness. One way to achieve that is to use the Mesh Pull feature.  That requires you to go into SpaceClaim, select the inner face of the solid and use Copy/Paste to create a surface. Then delete the solid. In Mechanical, mesh that surface with Quad elements, and Pull those elements into Hex elements.