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### Table of Contents

# Pressure and shear

## Materials

Since pressure/shear interactions are boundary conditions interactions (`LoadingInteraction`

), no materials must be associated to the element.

## Element

Therefore, the first step consist in defining an `ElementProperties`

, as

prp = ElementProperties(typeEl) prp.put(param1, value1) prp.depend(param1, fct1, Lock1)) #optional ...

where

`typeEl` | desired element (for example `Traction[2|3]DElement` ) |

`param1` | name of the property associated to the element (for example `PRESSURE` ) |

`value1` | value of the corresponding property |

`fct1` | function which characterizes the dependency of the property (optional: no fct if no dependency) |

`Lock1` | Lock which defines the dependency variable of the property (compulsory if there is a dependency) |

### Traction2DElement, Traction3DElement

Traction/shear element for a mesh made of quadrangles in 2D or hexaedra in 3D.

#### Parameters

Name | Description | Dependency |
---|---|---|

`STIFFMETHOD` | Method used to compute the stiffness matrix = `STIFF_ANALYTIC` : analytic matrix (default)= `STIFF_NUMERIC` : numerical matrix | - |

`PRESSURE` | Pressure on the entity on which the propriety is applied | time |

`SHEAR_KSI` / `SHEAR_ETA` | Shear along $\xi$ or $\eta$ on the entity on which the propriety is applied | time |

`NPG` | Number of integration points (default : 2) | - |

### TriangleTraction3DElement

Traction/shear element for a mesh made of tetrahedra

#### Parameters

Name | Description | Dependency |
---|---|---|

`STIFFMETHOD` | Method used to compute the stiffness matrix\\= `STIFF_ANALYTIC` : analytic matrix (default)= `STIFF_NUMERIC` : numerical matrix Not applicable, only the numerical one exists ! | - |

`PRESSURE` | Pressure on the entity on which the propriety is applied | time |

`SHEAR_KSI` / `SHEAR_ETA` | Shear along $\xi$ or $\eta$ on the entity on which the propriety is applied | time |

`NPG` | Number of integration points (default : 1) | - |

### ContactTraction2DElement, ContactTraction3DElement

Derivations of Traction2DElement and Traction3DElement with the possibility to set the traction/shear force of a node to zero, when this node is in contact within a specified contact interaction.

#### Parameters

Name | Description | Dependency |
---|---|---|

`STIFFMETHOD` | Method used to compute the stiffness matrix = `STIFF_ANALYTIC` : analytic matrix (default)= `STIFF_NUMERIC` : numerical matrix | - |

`PRESSURE` | Pressure on the entity on which the propriety is applied | time |

`SHEAR_KSI` / `SHEAR_ETA` | Shear along $\xi$ or $\eta$ on the entity on which the propriety is applied | time |

`NPG` | Number of integration points (default : 2) | - |

`NBR_CONTACT_INTERACTION` | Number of the contact interaction | - |

## Interaction

The interaction is defined as:

load = LoadingInteraction(no) load.push(gObject1) load.push(gObject2) ... load.addProperty(prp) interactionset.add(load)

where

`no` | number of the `Interaction` |

`gObject1` , `gObject2` | meshed geometric entity where the boundary conditions are applied |

`prp` | Properties of boundary condition elements to generate |

### Remark

Traction, pressure and shear is generated by “traction elements”. Their definition requires a specific `Interaction`

called `LoadingInteraction`

, to which is associated an ElementProperties. These should not be mixed with dead loads. In most cases, traction elements should be chosen over dead loads:

- traction (or pressure/shear) is always defined in local axes, so the direction of the force depends on the orientation of the edge/face on which it is applied.
- traction is divided properly over all edges/faces on which the
`Interaction`

is applied. Consequently, the resultant force does not depend on the mesh.

Traction element is used backwards in 3D, so a positive value must be applied to generate a pressure. !!