SS-V: 5040 Residual Deformations in an Axially Loaded Plastic Bar
Test No. VNL05 Find residual deformations in a bar axially loaded beyond plasticity.
Definition

Bar dimensions are 10 x 10 x 200 mm. Strain-stress curve of the bar material is defined by the power law:
Where,
- Strength coefficient.
- Must be in the range [0,1].
- =0
- Material is perfectly plastic.
- =1
- Material is elastic.
The left end of the bar is clamped and the right end is loaded with force F.
The material properties are:Figure 2. Corresponded strain-stress curve

- Properties
- Value
- 530 MPa
- 0.26
- Poisson's Ratio
- 0

Note: Elasticity modulus defined by the first two points of the strain-stress
curve is E=2.67324e+10 Pa.
The study was performed for the following load F values: 20000 N, 25000 N, and 30000 N
Reference Solution
One-dimensional analytical reference solution is described here.
At strain and stress , the residual strain is:
Where,
- Total strain in the bar.
- Elastic component of the total strain.
- Residual strain.
- Bar cross-section area.
Then residual displacement at the right end of the bar.
Results
The bar was modeled as a 3D solid. The left end of the solid was fixed and the right
end loaded with axial force (Figure 3).Figure 3.


The following table summarizes the residual deformations results.
Force F [N] | SOL Reference, Residual Displacement [mm] | SimSolid, Residual Displacement [mm] | % Difference |
---|---|---|---|
20000 | 3.22 | 3.3 | 2.48% |
25000 | 9.16 | 9.23 | 0.76% |
30000 | 19.077 | 20.2 | 5.89% |