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


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



classic, simo1985



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

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


faces, edges and component-wise



scalar, vectorial

"Neumann_scalar" or "Neumann_vectorial"

Pressure follower ,

Nonlinear boundary condition set in deformed domain





1.4. Body forces

Table 4. Volumic forces
Name Options Type




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


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, …​


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.

Volume variation

1.6. Run simulations

Avalaible application :

  • feelpp_toolbox_solid

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