# OS-V: 0270 Torsional Creep of Circular Shaft

This benchmark illustrates the structural response of a power law creeping material in a geometrical configuration subjected to pure torsion. OptiStruct examines strain at the edge of the shaft.

- Relaxation at constant twist
- Forward creep at steady twist rate

## Relaxation at Constant Twist

### Benchmark Model

- X, Y displacements given at all nodes of front face using cylindrical system: 0.002 mm
- Rotation is given at mid-side nodes: 0.001 radians

Uniform twist of 0.01 radians/unit length is held constant in time from 0 to 100s.

**Material Properties****Value**- Young's modulus
- 10 GPa
- Poisson's ratio
- 0.3
- Creep law equation
- $${\dot{\epsilon}}_{eq}=1000\text{}{\sigma}^{5}{}_{eq}$$

- $${\dot{\epsilon}}_{eq}$$
- Equivalent creep strain rate
- $${\sigma}_{eq}$$
- Equivalent stress (Mises)

### Nonlinear Static Analysis Results

OptiStruct | NAFEMS | Normalized Target Value | |
---|---|---|---|

Total Strain (*10^{-3}) |
5.46 | 5.77 | 0.95 |

Creep Strain (*10^{-3}) |
4.85 | 4.77 | 1.01 |

### Model Files

The model file used in this example includes:

<install_directory>/hwsolvers/demos/optistruct/verification/Torsional_Creep_Relaxation_at_constant_twist.fem

## Forward Creep at Steady Twist Rate

A steadily increasing twist is applied at constant rate to the shaft.

The stresses increase from zero to steady value. The loads, which cause this steady-state behavior are referred as “primary” loads.

### Benchmark Model

- X, Y displacements given at all nodes of front face using cylindrical system: 0.004 mm/unit time
- Rotation is given at mid-side nodes: 0.002 radians/unit time

**Material Properties****Value**- Young's modulus
- 10 GPa
- Poisson's ratio
- 0.3
- Creep law equation
- $${\dot{\epsilon}}_{eq}=1000\text{}{\sigma}^{5}{}_{eq}$$

- $${\dot{\epsilon}}_{eq}$$
- Equivalent creep strain rate
- $${\sigma}_{eq}$$
- Equivalent stress (Mises)

### Nonlinear Static Analysis Results

OptiStruct | NAFEMS | Normalized Target Value | |
---|---|---|---|

Total Strain (*10^{-2}) |
1.62 | 1.7321 | 0.94 |

Creep Strain (*10^{-2}) |
1.27 | 1.1693 | 1.094 |

### Model Files

The model file used in this example includes:

<install_directory>/hwsolvers/demos/optistruct/verification/Torsional_forward_creep_at_steady_twist_rate.fem

### Reference

NAFEMS, Selected Benchmarks for Material Non-Linearity, Vol 1. Case NL1A and NL1B