2020-02-27T03:59:24.000-0500

Simcenter Testlab

Neuber’s Rule is used to calculate the corresponding elastic-plastic strain time history from an elastic stress time history (

Materials often exhibit both elastic and plastic behavior:

- Elastic: At low load levels, a material acts like an elastic spring. There is a linear relationship (expressed as Young’s Modulus) between stress and strain.
- Plastic: At higher load levels, the material can permanently deform under load, exhibiting plastic behavior.

An object exhibiting elastic-plastic behavior has a combination of both material areas.

This article has the following sections:

2. Simcenter Testlab Neo and Strain Life

2.1 Load Time History

2.2 Stress Time History

2.3 Strain Time History

**1. Why use Neuber’s Rule?**

An elastic-plastic strain time history is needed to calculate fatigue life, but sometimes only an elastic stress time history is available. For example, when using a linear finite element model and applying forces, the predicted stresses are elastic (*Figure 2*).

For each time point in an elastic stress time history, Neuber’s Rule calculates the corresponding elastic-plastic strain by keeping the red areas (plastic) and blue areas (elastic only) equivalent as shown in *Figure 3*.

Neuber’s Rule works as follows:

- For a given elastic stress value taken from a time history, the corresponding point (blue) can be plotted on the Young’s Modulus line (which is used to describe elastic behavior).
- A corresponding point (red) that has equivalent area can then be found on the Ramberg-Osgood line (which describes non-linear plastic behavior). This point equates the equivalent plastic stress and strain based on the original elastic stress and strain.

Neuber’s Rule allows a linear model to predict non-linear behavior!

See the “Strain Life Approach” knowledge article for more information on the Ramberg-Osgood relationship, which is used in the mapping of elastic to plastic behavior.

When using the Strain-Life method of Simcenter Testlab Neo, several different starting inputs are possible. These include load, stress, and strain as shown in

Any input must be converted to elastic-plastic strain in order to perform fatigue life calculations. The “Input Type” field of the Simcenter Testlab Neo Strain Life method (

Either “Load” or “Elastic-plastic strain” can be selected as input type:

- Load: Selected if force or stress is the input time history. These inputs will be converted to elastic-plastic stress using Neuber’s Rule and other settings.
- Elastic-plastic strain: Selected if input time history is measured strain. No conversion is needed.

If starting with an input type of load (force), conversion to stress (force over area) can be done two different ways (

The software has two settings: “Manual” and “Input Base Unit -> Material Base Unit”:

If the load influence is set to Manual, “Influence factors” can be entered to scale a force time history. There is both a stress influence factor and a load influence factor.

For example, consider a Finite Element Model. When a unit load is applied, a critical element has a stress to force sensitivity 5.03983 MPa/N as shown in

If a force time history to be applied at the node is available for analysis in Simcenter Testlab Neo, then the Stress Influence factor should be set to 5.03983 MPa and the Load Influence factor should be set one Newton. This force time history is converted to elastic stress for use with Neuber’s Rule.

When the influence coefficients are not known, the “Input Base Unit -> Material Base Unit” (

If the input time block history is elastic stress (units of MPa) then the input type can be set to Load and Influence to Manual (

The stress used in Simcenter Testlab Neo needs to be in units of MPa to match the material data information used in the Strain-Life method. If the stress time history is in MPa, the two influence factors are set to 1 (with units set to [MPa]).

Neuber’s Rule can then be used to calculate the corresponding elastic-plastic strain from this stress.

If using a directly measured strain time history, the “Input Type” should be set to “Elastic-Plastic Strain”. This can be used directly in the calculation of fatigue life using the Strain Life approach.

Hope this is helpful! Questions? Email peter.schaldenbrand@siemens.com or contact Siemens Support Center.

- Index of Testing Knowledge Articles
- Simcenter SCADAS RS for Testing in Harsh Environments
- History of Fatigue
- Stress and Strain
- Strain Life Approach
- Simcenter Testlab Neo: Strain Life Method
- Calculating Damage with Miner's Rule
- What is a SN-Curve?
- Rainflow Counting
- Mean Stress Corrections and Stress Ratios
- Difference between 'Range-Mean' and 'From-To' Counting
- Power Spectral Density
- Fatigue Damage Spectrum
- Shock Response Spectrum (SRS)
- How to Calculate a Shock Response Spectrum with Testlab?
- Some Thoughts on Accelerated Durability Testing
- Goodman-Haigh Diagram for Infinite Life
- Introduction to Strain Gauges
- Measuring strain gauges in Simcenter Testlab
- Rosette Strain Gauges
- Calculating Damage in Simcenter Tecware Process Builder
- Strain Gauges: Selecting an Excitation Voltage
- Simcenter Testlab SCADAS and Long Strain Cables

Simcenter Testlab Digital Image Correlation
Testlab Environmental
Testlab Acoustics
Testlab Data Management
Testlab Desktop
Testlab Durability
Testlab General Acquisition
Testlab General Processing & Reporting
Testlab Rotating Machinery & Engine
Testlab Sound Designer
Testlab Structural Dynamics
Testlab Turbine