# SolidMechanicsStrain SolidMechanicsStrain[vars,pars,displ]

yields solid mechanics strain with variables vars, parameters pars and displacements displ.

# Details  • SolidMechanicsStrain returns the mechanical strain from a given displacement with dependent variables of displacement , and in units of , independent variables in and time variable in units of .
• • Normal strain where is the change in length and the original length.
• Strains are unitless.
• SolidMechanicsStrain uses the same variables vars specification as SolidMechanicsPDEComponent.
• SolidMechanicsStrain uses the same parameter pars specification as SolidMechanicsPDEComponent.
• Typically the displacement displ is the result of solving a partial differential equation generated with SolidMechanicsPDEComponent.
• For each dependent variable , and given as dependent variable vector in vars, a displacement displ needs to be specified.
• SolidMechanicsStrain returns a SymmetrizedArray of engineering strains of the form:
• • The represent the normal strain and represent the shear strains.
• The default strain measure is based on an infinitesimal strain tensor model and assumes small displacements and small rotations.
• The shear strains used are engineering shear strains related to the tensorial strain by .
• SolidMechanicsStrain returns strains including initial or thermal strains.
• SolidMechanicsStress computes stress from SolidMechanicsStrain.

# Examples

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## Basic Examples(1)

Compute strain from a displacement:

Visualize the strain:

## Scope(4)

Compute the strain from the displacement:

Inspect the engineering strain:

Compute the strain tensor:

Verify the relation between the engineering strain and the strain tensor:

The default usage of engineering strain in the linear elastic regime can be turned off:

### Stationary Analysis(1)

Compute the deflection of a spoon held fixed at the end and with a force applied at the top. Set up variables and parameters:

Set up the PDE and the geometry:

Compute the strain from the displacement:

Visualize the strain:

### Stationary Plane Stress Analysis(1)

Compute the displacement of a rectangular steel plate held fixed at the bottom and with pressures applied at the remaining sides. Set up the region, variables and parameters:

Solve the equations:

Visualize the displacement:

Compute the strain:

Verify that the normal strain in the direction is about 0:

Verify that the normal strain in the direction is about 0:

Find the shear strain:

### Stationary Hyperelastic Plane Stress Analysis(1)

Compute the displacement of a rectangular rubber plate held fixed at the left and with force applied at the right-hand side. Set up the region, variables and parameters:

Solve the equations:

Visualize the displacement:

Compute the strain from the displacement:

Visualize the strain:

## Possible Issues(1)

By default, the solid mechanics framework uses engineering strains for the linear elastic regime. This can be switched off.

Set up a helper function with a solid mechanics PDE model:

Create variables and parameters:

Solve the solid mechanics model with engineering strains:

Solve the solid mechanics model with engineering strains off:

Verify at a specific point that the shear strains of the engineering formulation relate to the normal strain formulation by a factor of 2: