## Introduction

**In this tutorial I will show how to use MCalibration to calibrate the rate-dependent Abaqus Johnson-Cook plasticity model with damage initiation and damage evolution to experimental data.** In the YouTube video below, I will also show how you can use the calibrated material model in an Abaqus Explicit FE simulation with element deletion.

The yield stress for the Johnson-Cook model is given by the equation:

\( \sigma_y = \displaystyle \left[ A + B \varepsilon_p^n \right] \cdot \left[ 1 + C \cdot \text{ln} \left( \frac{\dot{\varepsilon}_p} {\dot{\varepsilon}_0} \right) \right] \cdot \left[ 1 – \theta^m \right], \)

where *A*, *B*, *C*, \( \dot{\varepsilon}_0 \), *n*, *m* are material parameters, \( \varepsilon_p \) is the plastic strain, and \( \theta \) the temperature.

In this example I will use the experimental data shown in the figure to the right. I studied this set of experimental data in detail in the following post.

**The first step is to calibrate the stress-strain part of the Abaqus Johnson-Cook material model.**

The results from the final stress-strain calibration are shown in the following figure.

The next step is to setup the calibration of the damage initiation and damage evolution parameters. This is a multi-step procedure, the first of which is to export the initially calibrated version of the Johnson-Cook material model.

After that we need to setup an material model template in MCalibration. This figure shows the template definition.

Before running the final material model calibration it is useful to deactivate all load cases that were not run to failure, and to turn on Failure Time from the load case dialog box. This will add additional zero-stress failure data at the end of the experimental data file. This makes it easier to find the material model parameters.

Here are the final calibration results. The model can tune a bit more, but the results already capture the strain-rate dependence of the failure response.

The final material model is listed below.

` ````
```*Material, name=Mat
** Units: [length]=millimeter, [force]=Newton, [time]=seconds, [temperature]=Kelvin
*Density
1e-09
*Elastic
** E, nu
53.1556584454, 0.4
*Plastic, hardening=Johnson Cook
** A, B, n, m, ThetaMelt, ThetaTrans
1.10531318429, 23.203093989, 0.576311807976, 1, 2000, 1000
*Rate Dependent, type=Johnson Cook
** C, epsDot0
0.0749390218307, 1.06412678755
*Damage initiation, criterion=ductile
**[plast strain], [triax], [strain rate]
0.6, , 0.001
0.805, , 0.1
*Damage Evolution, type=displacement, softening=linear
** [plastic displacement]
0.02