# Strain rate

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The effective strain rate in an element is dependent not only on the rate of loading but also such factors as the shape and dimensions of your speciman. If we assume that the speciman stretches uniformly (no necking/localization) in an uniaxial test such that the strain rate is spatially uniform over the whole specimen, then the following is true:

• change in length = deltaL = r * time
• engineering strain = deltaL/L = r * time/L
• engineering strain rate = strain per time = r/L
• true strain = ln(1+ engineering strain) = ln(1+ r*time/L)
• true (effective) strain rate varies with time = d(true strain)/dt

= [ln(1+r*time2/L) – ln(1+r*time1/L)]/(time2-time1)

Of course, if the strain rate is not spatially uniform over your speciman, then it isn’t quite so simple and you will have a range of strain rates to consider in your analysis. To approximate this range of strain rates, you may have to run a preliminary analysis and write strain data (set STRFLG=1 in *DATABASE_EXTENT_BINARY) at a high resolution for a few characteristic elements. You can use *DATABASE_BINARY_D3THDT and *DATABASE_HISTORY_SHELL for this purpose. (Setting N3THDT=1 in *DATABASE_EXTENT_BINARY is suggested to minimize data written to D3THDT database.)

### There are two ways to plot strain rates.

1. Set STRFLG to 1 using *DATABASE_EXTENT_BINARY so that strains are written directly to the output databases. Write very high resolution output to D3THDT or ELOUT for a few elements of interest. Select these elements using *DATABAE_HISTORY_… . Set N3THDT=1 in *DATABASE_EXTENT_BINARY to minimize output. After you run the job, read d3thdt into LS-Prepost and plot a strain time history. Choose “Oper” in the time history window and select “differentiate” (you may have to toggle off and then back on “differentiate” to get it to activate), and then select “Apply”. This approach allows you to choose a thru-thickness location in shells (lower, middle, upper).
2. Use Fcomp > SRate to produce a fringe plot of strain rate computed from nodal displacements. Next, plot a time history of strain rate using History > Scalar. This strain rate corresponds to the midsurface of the shell. Method 1 must be used to get strain rates at other through-thickness locations.

Using either method, the accuracy of the strain rate is dependent upon the resolution of the output. The units of strain rate are strain per time unit used in the model.

### Strain rates in the local shell element system:

Either of the two methods below will produce a time history of strain rate in the shell element local system as defined by the element connectivity. LS-Prepost doesn’t support output in arbitrary local coordinate systems.

Method 1:

• Toggle local axes on using either the Toggle pull-down menu or the Setting button. Fringe strain rate using the S.Rate button. Plot a time history of strain rate using the Scalar option under History (this is strain rate at the midsurface of the shell; NG for any other thru-thickness location).

Method 2:

• Make sure you set STRFLG in *DATABASE_EXTENT_BINARY to 1. Plot a strain time history using the Element option under History; “Local” must be selected. Use Oper to differentiate the strain history to give an approximate strain rate (accuracy depends on the resolution of the strain time history; works for any thru-thickness location).

If you happen to be using a composite material model, you can use the composite output flag in *DATABASE_EXTENT_BINARY to get the strains output in the local MATERIAL direction. You can then differentiate a strain time history to get an approximate strain rate.