Test 12A: 2D plane stress – uniaxial load, primary-secondary 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

CPS8R

Problem description

Material:

Young's modulus = 200 × 10³ N/mm², Poisson's ratio = 0.3, Creep law: $ε$ = A $_{1}$ $σ^{n 1} t +$ A $_{2}$ $σ^{n 2} t^{m}$ , A $_{1}$ = 10⁻¹⁶, A $_{2}$ = 10⁻¹⁴, $n 1 = n 2$ = 5.0, and m = 0.5.

Boundary conditions:

$u_{x} = 0$ on line AD and $u_{y} = 0$ at mid-point of line AD.

Loading:

Prescribed tensile stress $σ_{1}$ = 200 N/mm² on line BC.

Reference solution

This is a test recommended by the National Agency for Finite Element Methods and Standards (U.K.): Test 12(a) from NAFEMS Publication Ref: R0027, “NAFEMS Fundamental Tests of Creep Behaviour,” June 1993.

\begin{matrix} ε_{x x}^{c} & ​ = 0.0001 (0.01 t + \sqrt{t}) \\ ε_{y y}^{c} & ​ = - \frac{1}{2} ε_{x x}^{c} \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	$ε_{x x}^{c}$	$ε_{y y}^{c}$
0.00	0.000 (0.00%)	0.000 (0.00%)
6.41	0.000222 (−14.35%)	−0.000111 (−14.35%)
70.41	0.000845 (−7.09%)	−0.000423 (−7.09%)
382.73	0.002260 (−3.78%)	−0.001130 (−3.78%)
536.33	0.002770 (−2.87%)	−0.001385 (−2.87%)
823.05	0.003606 (−2.32%)	−0.001803 (−2.32%)
1000.00	0.00408 (−2.02%)	−0.002038 (−2.02%)

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 = 1. × 10⁻⁵. The creep law is defined via user subroutine CREEP.

Input files

ncrcar8x.inp: CPS8R elements.
ncrcar8x.f: User subroutine CREEP used in ncrcar8x.inp.