Computational Solid Mechanics

Welcome to the Computational Solid Mechanics(CSM) toolbox. This chapter explains how to use the Solid Mechanics interface to simulate and analyze applications involving solid mechanics. The interface is used for stress analysis and general solid mechanics simulation but also can be coupled with other types of physics such as the computational fluid dynamics, see here.

1. CSM Toolbox

1.1. 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

1.2. 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 \(kg \cdot m^{-3}\).

1.3. 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

1.4. Body forces

Table 4. Volumic forces
Name	Options	Type
Expression	Vectorial	"VolumicForces"

1.5. Post Process

1.5.1. 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

1.5.2. Measures

Points
Maximum
Minimum
VolumeVariation

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, …

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"]
    }
}

Volume variation

"VolumeVariation":<marker>

1.6. Run simulations

Avalaible application :

feelpp_toolbox_solid

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