Model: Elasto-Plastic Plate

Introduction This model treats the elastic-plastic material behavour of a plate with a centered hole. The development of the plastic regions with increasing load are studied as well as residul stress and deformations when the plate is totally unloaded.

Problem Definition The plate is thin and loaded in the plane, that is, plane stress conditions can be assumed. Due to the double symmetry, only one quarter of the plate needs to be analyzed.

Problem Definition, constraints and loads. The displacements in the normal directions are constrained at the two symmetry cuts The right edge is subjected to a load which increases from zero to a maximum value and then released again. The maximum load value is selected so that the mean stress over the section through the hole is 10% above the yield stress.

The von Mises stress is used as yield criterion. The model uses a isotropic hardening rule for the description of the plastic history dependent yield criterion. Elastic properties: E=70000 N/mm 2 and =0.2 Yield stress:  y = 243 N/mm Tangent modulus E t = 2171 N/mm 2 Problem Definition, material

yy   Elastic plastic

Problem Definition, hardening rules  yy    y  Kinematic Isotropic E EtEt

Results The plastic regions (red) at peak load level where the material has exceeded the yield stress. For a material without strain hardening, the structure would have collapsed before reaching the peak load level.

Results The left figure shows the deformations and von Mises stress levels at peak load. The right figure shows the residual deformations and the residual von Mises stress when the model is totally unloaded.