Test 11: 3D – triaxial load, primary creep

This problem provides evidence that Abaqus can reproduce the result from the benchmark defined by NAFEMS and cited as the reference solution.

This page discusses:

Elements tested
Problem description
Reference solution
Results and discussion
Remarks
Input files

ProductsAbaqus/Standard

Elements tested

C3D20R

Problem description

Material:

Young's modulus = 200 × 10³ N/mm², Poisson's ratio = 0.3, Creep law: $ε$ = A $σ^{n} t^{m}$ , A = 3.125 × 10⁻¹⁴ per hour ( $σ$ in N/mm²), n = 5, m = 0.5.

Boundary conditions:

$u_{x} = 0$ on face ADEH, $u_{y} = 0$ on face ABFE and $u_{z} = 0$ on face ABCD.

Loading:

Prescribed tensile stress $σ_{1}$ = 300 N/mm² on face BCGF, $σ_{2}$ = 200 N/mm² on face CDHG, and $σ_{3}$ = 100 N/mm² on face EFGH.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 11 from NAFEMS Publication Ref: R0027, “NAFEMS Fundamental Tests of Creep Behaviour,” June 1993.

\begin{matrix} ε_{x x}^{c} & = - ε_{z z}^{c} = 0.004218 \sqrt{t} \\ ε_{e f f}^{c} & ​ = 0.004871 \sqrt{t} \\ ε_{y y}^{c} & ​ = 0.0 \end{matrix}

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.


Abaqus Results
t	$ε_{x x}^{c}$	$ε_{e f f}^{c}$
0.00	0.0000 (0.00%)	0.0000 (0.00%)
8.39	0.0122 (−0.02%)	0.0141 (−0.03%)
67.11	0.0346 (0.01%)	0.0399 (0.00%)
134.22	0.0489 (0.01%)	0.0564 (0.00%)
536.87	0.0977 (0.01%)	0.1129 (0.01%)
805.31	0.1197 (0.02%)	0.1382 (0.01%)

Remarks

The total creep time for this test is 1000 hours. The times listed in the above table are the times calculated by the Abaqus automatic time stepping algorithm with CETOL = 5. × 10⁻⁷.

Input files

ncrbxrkx.inp: C3D20R elements.