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/mm2 and =0.2

• Yield stress: y= 243 N/mm

• Tangent modulus Et= 2171 N/mm2

Problem Definition, material

Problem Definition, material

y

Elastic

plastic

Problem Definition, hardening rules

y

y

Kinematic

Isotropic

E

Et

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.