#### 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

### MAT_CABLE

###### Material properties
*MAT_CABLE
"Optional title"
mid, $\rho$, $E$, $\nu$
$E_{t1}$, $E_{t2}$, $E_{tm}$, $\epsilon_{tf}$, $\sigma_{ty}$

#### Parameter definition

VariableDescription
mid Unique material identification number
$\rho$ Density
$E$ Young's modulus
$\nu$ Poisson's ratio
$E_{t1}$ Tensile stiffness (lienar term)
$E_{t2}$ Tensile stiffness (quadratic term)
default: not used
$E_{tm}$ Tensile stiffness (maximum)
default: not used
$\epsilon_{tf}$ Tensile fiber failure strain
default: no failure
$\sigma_{ty}$ Tensile fiber yield stress
default: no plasticty

#### Description

This material model is used to model ropes or steel wires.

The stress is defined as:

$\displaystyle{ \mathbf{\sigma} = K \mathrm{tr}(\mathbf{\epsilon}) \mathbf{I} + 2G \mathbf{\epsilon}_d + \sum_{i=1}^3 \mathrm{min} \left( \sigma_{ty}, \sigma(\epsilon_i) \right) \mathbf{v}_i \otimes \mathbf{v}_i }$

where $\mathbf{\epsilon}$ is the total strain, $\mathbf{\epsilon}_d$ is the deviatoric strain tensor, $\epsilon_i$ is a principal strain and $\mathbf{v}_i$ is its corresponding eigenvector. Note that $K=E/(3(1-2\nu))$ and $G=E/(2(1+\nu))$.

The tensile (fiber) stress $\sigma(\epsilon_i)$ is defined as:

$\displaystyle{ \sigma(\epsilon_i) = \left\{ \begin{array}{lcl} 0 & : & \epsilon_i \leq 0 \\ E_{t1} \epsilon_i + E_{t2} \epsilon_i^2 & : & \epsilon_i \leq \epsilon_{tm} \\ E_{t1} \epsilon_{tm} + E_{t2} \epsilon_{tm}^2 + E_{tm} (\epsilon_i - \epsilon_{tm}) & : & \epsilon_i \gt \epsilon_{tm} \end{array} \right. }$

$\epsilon_{tm}$ is the strain where the full tensile stiffness $E_{tm}$ has been reached:

$\displaystyle{ \epsilon_{tm} = \frac{E_{tm} - E_{t1}}{2E_{t2}} }$

$\epsilon_{tf}$ is an optional tensile failure strain and $\sigma_{ty}$ is an optional tensile yield stress.