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Elasticity equation

Electrostatic equation

FEM

Description

This equation describes the nonlinear elastic deformation of solid bodies.

For info about the math of the equation, see the Elmer models manual, section Finite Elasticity.

Usage

1. Add an Elmer solver.
2. Select it in the Tree view.
3. There are several ways to invoke the command:
   • Press the Deformation equation button.
   • Select the Solve → Mechanical equations → Deformation equation option from the menu.
4. Change the equation's solver settings or the general solver settings if necessary.

Solver Settings

For the general solver settings, see the Elmer solver settings.

The deformation equation provides these special settings:

• DataCalculate Pangle: If the principal angles should be calculated.
• DataCalculate Principal: If all stresses should be calculated.
• DataCalculate Strains: If strains will be calculated. This will also calculate the stresses, even if DataCalculate Principal or DataCalculate Stresses is false.
• DataCalculate Stresses: If stresses should be calculated. Compared to DataCalculate Principal the Tresca yield criterion and the principal stress will not be calculated.
• DataInitialize State Variables: See the Elmer manual for more info.
• DataMixed Formulation: See the Elmer manual for more info.
• DataNeo Hookean Model: Uses the neo-Hookean material model.
• DataVariable: The variable for the deformation equation. Change there the 3 to 2 if you have a 2D geometry. For the special case that you have DataMixed Formulation and DataNeo Hookean Model set to true, the variable number must be geometry dimensions + 1, so for 3D geometry the 3 must be changed to 4.

Equation:

• DataPlane Stress: Computes solution according to the plane stress situation. Applies only for 2D geometry.

Analysis Feature Information

The deformation equation takes the following analysis features into account if they are set:

• Fixed boundary condition
• Displacement boundary condition
• Force load
• Initial temperature condition
• Pressure load
• Gravity load
• Spring

Note

• Except for calculations in 2D, for all the above analysis features it is important that they act on a face. Features in 3D set to lines or vertices are not recognized by the Elmer solver.

Results

The available results depend on the solver settings. If none of the DataCalculate * settings was set to true, only the displacement is calculated. Otherwise also the corresponding results will be available.

Elasticity equation

Electrostatic equation

FEM