#### Command list

• Input handling
• Solution control and techniques
• Output
• Mesh commands
• Nodes and connectivity
• Material properties
• Initial conditions
• Boundary conditions
• Contact and tied interfaces
• Rigid bodies
• Connectors
• Parameters and functions
• Geometries
• Sets
• Coordinate system
• Particle
• SPH

### OUTPUT_J_INTEGRAL

###### Output
Attention: This command is in the beta stage and the format may change over time.
*OUTPUT_J_INTEGRAL
"Optional title"
coid, entype, enid, csysid, $R$, $b$

#### Parameter definition

VariableDescription
coid Command ID
entype Entity type
options: P, PS, ALL
enid Entity ID
csysid Local coordinate system ID
$R$ Integral path radius
$b$ Crack width
default: local component thickness

#### Description

This command is used to calculate J-integrals at crack tips. The local coordinate system should be positioned with its origin at the tip of the crack. The local x-axis defines the assumed crack propagation direction.

The crack width $b$ only needs to be specified if it does not extend through the complete thickness of the component (see figure below). $b$ is used in the relationship between virtual crack growth $\mathrm{d}a$ and virtual increase in crack area $\mathrm{d}A$:

$\displaystyle{\mathrm{d}A = b \cdot \mathrm{d}a}$

$J$ is defined as:

$\displaystyle{J = \frac{1}{b} \int_{\Omega} \left( w n_x - \mathbf{t} \cdot \frac{\mathrm{d}\mathbf{u}}{\mathrm{d}x} \right) \mathrm{d}\Omega}$

Here $w$ is the specific strain energy (energy per unit volume), $\mathbf{u}$ is the local displacement and $\mathbf{t}=\mathbf{\sigma}\mathbf{n}$ is the surface traction.

Time history data is written to the file J_integral.out. It contains the calculated J-value (energy per unit area of cracking) and the total area of the integral surface.