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 close to incompressibility, formulations 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 Lamé coefficients are deduced from the Young’s modulus \(E_s\) and the Poisson’s ratio \(\nu_s\) of the material we work on and can be expressed as

\[\lambda_s = \frac{E_s\nu_s}{(1+\nu_s)(1-2\nu_s)} \hspace{0.5 cm} , \hspace{0.5 cm} \mu_s = \frac{E_s}{2(1+\nu_s)}\]
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-criterion

  • tresca-criterion

  • principal-stresses

  • all

5.2. Measures

  • Points

  • Maximum

  • Minimum

  • VolumeVariation

5.2.1. Points

Same syntax as Fluid Mechanics 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 saved in a .csv file. The user needs 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 fields where extrema are computed.

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

5.2.3. Volume variation

"VolumeVariation":<marker>

6. Run simulations

Avalaible application :

  • feelpp_toolbox_solid

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