4.6.3 NL3: Hardening with two variables under load control

Product: ABAQUS/Standard

Element tested

T2D2

Problem description

Model:

AE = 5.0 × 10⁷, L = 2500, L = 25, K₁= 1.5, K₂ = AE/L(1 + )^1/2 = 19999.0, K₃ = 2.0.

Boundary conditions:

0 at node 1, 0 at node 9.

Loading:

A load is applied to node 1 in the x-direction.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test NL3 from NAFEMS Publication NNB, Rev. 1, “NAFEMS Non-Linear Benchmarks,” October 1989.

Step	P		v
1	1100	0.1803	10.37
2	2200	0.7160	35.45
3	3300	8.515	180.7
4	4400	1339	2189
5	5500	3468	2280
6	6600	4986	236.3

Results and discussion

The results are shown in the following table. The values enclosed in parentheses are percentage differences with respect to the reference solution.

Step	P		v
1	1100	0.1802 (–0.06%)	10.37 (0.0%)
2	2200	0.7157 (–0.0%)	35.44 (–0.03%)
3	3300	8.564 (+0.58%)	181.3 (+0.33%)
4	4400	1339 (0.0%)	2189 (0.0%)
5	5500	3469 (+0.03%)	2280 (0.0%)
6	6600	4985 (–0.02%)	244.7 (+3.55%)

Input file

nnl3xf2x.inp

T2D2 elements.