# CSM Toolbox

## 1. Models

The solid mechanics model can be selected in json file :

Listing : select solid model
``"Models": { "equations":"Hyper-Elasticity" }``
Table 1. Table of Models for `model` option
Model Name in json

Linear Elasticity

`Elasticity`

Hyper Elasticity

`Hyper-Elasticity`

When materials are closed to incompressibility formulation in displacement/pressure are available.

Table 2. Table of Models for `material_law` with hyper elasticity model
Model Name Volumic law

Saint-Venant-Kirchhoff

`SaintVenantKirchhoff`

classic, simo1985

NeoHookean

`NeoHookean`

classic, simo1985

option: `mechanicalproperties.compressible.volumic_law`

## 2. Materials

The LamÃ© coefficients are deducing from the Young’s modulus $E_s$ and the Poisson’s ratio $\nu_s$ of the material we work on and can be express

$\lambda_s = \frac{E_s\nu_s}{(1+\nu_s)(1-2\nu_s)} \hspace{0.5 cm} , \hspace{0.5 cm} \mu_s = \frac{E_s}{2(1+\nu_s)}$
Materials section
``````"Materials":
{
"<name>":
{
"E":"1.4e6",
"nu":"0.4",
"rho":"1e3"
}
}``````

where `E` stands for the Young’s modulus in Pa, `nu` the Poisson’s ratio ( dimensionless ) and `rho` the density in $kg\cdot m^{-3}$.

## 3. Boundary Conditions

Table 3. Boundary conditions
Name Options Type

Dirichlet

faces, edges and component-wise

"Dirichlet"

Neumann

scalar, vectorial

"Neumann_scalar" or "Neumann_vectorial"

Pressure follower ,

Nonlinear boundary condition set in deformed domain

TODO

Robin

TODO

TODO

## 4. Body forces

Table 4. Volumic forces
Name Options Type

Expression

Vectorial

"VolumicForces"

## 5. Post Process

### 5.1. Exports for visualisation

The fields allowed to be exported in the `Fields` section are:

• displacement

• velocity

• acceleration

• stress or normal-stress

• pressure

• material-properties

• pid

• fsi

• Von-Mises

• Tresca

• principal-stresses

• all

### 5.2. Measures

• Points

• Maximum

• Minimum

• VolumeVariation

#### 5.2.1. Points

Same syntax as FluidMechanics with available Fields :

• displacement

• velocity

• acceleration

• pressure

• principal-stress-0

• principal-stress-1

• principal-stress-2

• sigma_xx, sigma_xy, …​

#### 5.2.2. Maximum/Minimum

The Maximum and minimum can be evaluated and save on .csv file. User need to define (i) <Type> ("Maximum" or "Minimum"), (ii) "<tag>" representing this data in the .csv file, (iii) "<marker>" representing the name of marked entities and (iv) the field where extremum is computed.

``````"<Type>":
{
"<tag>":
{
"markers":"marker>",
"fields":["displacement","velocity"]
}
}``````

#### 5.2.3. VolumeVariation

``"VolumeVariation":<marker>``

## 6. Run simulations

programme avalaible :

• `feelpp_toolbox_solid_2d`

• `feelpp_toolbox_solid_3d`

`mpirun -np 4 feelpp_toolbox_solid_2d --config-file=<myfile.cfg>`