Example26 Deformation 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.

If [Add unloading step] is selected, the deformation can be analyzed after the removal of load which was created by the acceleration.

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.

 

Below is the deformation at the step 2, the unloading step.

“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

 

Step 2 (Unloading step)

Some stresses remain in the elasto-plastic cantilever (body number 2) after the load is removed due to the remaining plastic strains.