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# Example26Deformation of Cantilevers made of Elasto-Plastic Bilinear Material and Elastic Material

General

• A cantilever made of elasto-plastic bilinear material and the other made of elastic material are analyzed together for comparison..

• The deformation, the displacement and the mechanical stress are solved.

• Unless specified in the list below, the default conditions will be applied.

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### Analysis Space

 Item Settings Analysis Space 3D Model unit m

### Analysis Conditions

 Item Settings Solvers Mechanical Stress Analysis [Galileo] Analysis Type Static analysis Options Select “Acceleration”.

The acceleration tab is set up as follows. The gravity acceleration is 9.8[m/s2] and applied in the negative Z direction.

 Tab Item Settings Acceleration Acceleration X=Y=0.0、Z=-9.8[m/s2]

The nonlinear analysis is set up on the Step/Thermal Load tab as follows.

 Tab Item Settings Step/Thermal Load Step/Reached Temperature Setting Substeps of Step 1 : 1 Options for the Nonlinear Analysis Add unloading step : Select

### Model

Two cantilevers are the same shape. Both are subjected to the gravity in -Z direction.

One is made of elasto-plastic material (body number 2). The other is made of elastic material (body number 3).

All the material properties but the elasticity are the same.

### Body Attributes and Materials

 Body Number/Type Body Attribute Name Material Name 2/Solid BA1 ElastoPlasticMaterial 3/Solid BA1 ElasticMaterial

The material properties are set up as follows:

 Material Name Tab Properties ElasticMaterial Elasticity Material Type: Elastic/Isotropic Young’s modulus: 100×10^9[Pa] Poisson’s ratio: 0.3 Density 500×10^3[Kg/m3] ElastoPlasticMaterial Elasticity Material Type: Elasto-plastic/Bilinear, Isotropic Young’s modulus: 100×10^9[Pa] Poisson’s ratio: 0.3 Strain hardening rate : 20×10^9[Pa] Initial yield stress 200×10^6[Pa] Density 500×10^3[Kg/m3]

### Boundary Conditions

 Boundary Condition Name/Topology Tab Boundary Condition Type Settings FIX/Face Mechanical Displacement Select all X/Y/Z components. UX=0, UY=0, UZ=0

### Results

The deformation at the step 1 is shown below. The contour diagram shows the displacement.

“Same scale” is selected on “Displacement Diagram” tab in “Graphics Setup”.

The cantilever made of the elasto-plastic material (body number 2) has lager displacements than the other (body number 3) made of the elastic material.

“Same scale” is selected on “Displacement Diagram” tab in “Graphics Setup”.

After released from the gravity, the elastic cantilever (body number 3) does not exhibit any displacement, while the elasto-plastic cantilever (body number 2) does due to the plastic strains.

Plastic strain vectors at the step 1 are shown below.

Some plastic strains remain near the fixed end of the elasto-plastic cantilever while no strain remains in the elastic cantilever.

The vectors of the mechanical stress at step 1 and step 2 (unloading step) are shown below.

Step 1