Activate a solid mechanics PDE model:

Define a stationary solid mechanics model with a particular material:

Define a model with material values specified:

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:

Visualize the displacement:

Define a symbolic solid mechanics PDE model that considers thermal expansion:

Compute the displacement of a rectangular steel plate held fixed at the left and with a forced displacement on the right. Set up the region, variables and parameters:

Solve the equations:

Visualize the displacement:

Compute a plane stress case as an extended model. This allows for the computation of the out-of-plane strain and verifies that the out-of-plane stress is 0. A rectangular steel plate is held fixed at the left and with a forced displacement on the right. Set up the region, variables and parameters. The variables now include all three directions:

Solve the equations with thee semi-dependent variables:

Note that now there are three output variables in the list of displacements. Visualize the displacement for the main variables:

Compute the strain:

Note, that the strain is a 3 by 3 array. Visualize the out-of-plane strain:

Compute the stress from the strain:

Note, that the stress is a 3 by 3 array. Verify the plane stress condition:

Compute the displacement of a rectangular steel plate held fixed at the left and with a pressure applied at the right end. Set up the region, variables and parameters:

Solve the equations:

Visualize the displacement:

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:

Visualize the normal strain in the direction:

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

Visualize the normal strain in the direction:

Find the shear strain:

Visualize the normal strain in the - direction:

Define a 2D plane strain PDE model:

Define an extended plane strain PDE model:

Compute a plane strain case as an extended model. This allows for the computation of the out-of-plane stress and verifies that the out-of-plane strain is 0. Set up the region, variables and parameters. The variables now include all three directions:

Set up the solid mechanics PDE component:

Set up the PDEs:

Solve the PDE:

Compute the strains from the displacements:

Note that the strain is a 3×3 array. Verify the plane strain condition:

Compute the stress from the strain:

Note that the stress is a 3×3 array. Visualize the out-of-plane stress:

Define a time-dependent solid mechanics model for a particular material:

Simulate a time-dependent force on a beam. Set up a region, variables and a material:

Set up the PDE model:

Create a time dependent force at the right end of the beam:

Fix the beam on the left:

Set up zero initial conditions and the initial velocity condition:

Solve the time-dependent PDE and monitor the progress:

Visualize the -displacement over time at a query point:

Simulate a time-dependent force on a cross section of a spoon considering a Rayleigh damping model. Set up a region, variables and a material:

Set up the PDE and solve while monitoring progress:

Visualize the -displacement over time at a query point:

Visualize the displacement:

Define an eigenmode solid mechanics model for a particular material:

Compute the eigenmodes of an iron bracket. Set up the region, variables and a material:

Compute the eigenvalue and modes:

Visualize the seventh to tenth eigenmode:

Set up the variables and the model parameters for a piece of rubber that is held fixed at the left and a pressure is applied on the right. A neo-Hookean hyperelastic material model is used:

Set up the geometry:

Set up the equation and solve for the displacement:

Visualize the deformed body over the original shape of the body:

Set up the variables and the model parameters for a neo-Hookean hyperelastic material model:

Create the PDE model with boundary conditions:

Show the actual displacement:

Compute the strain:

Compute the stress:

Set up the variables and the model parameters for a fiber-reinforced piece of rubber that is held fixed at the left and a pressure is applied on the right. A neo-Hookean hyperelastic material model is used:

Set up the geometry:

Visualize the fiber reinforcement in the geometry:

Set up the equation and solve for the displacement:

Visualize the deformed body over the original shape of the body:

Compute the strain:

Compute the stress:

Compute the von Mises stress:

Visualize the von Mises stress:

A compliance matrix needs to be specified as a matrix. This is also true for multi-material models. This example shows how to do that. Specify two compliance matrices:

Create a multi-material compliance matrix, where material 1 is to be used for values in the geometry where , and material 2 is used in all other cases:

Note that the compliance matrix now is a matrix:

Look at a specific entry:

Set up the parameters to make use of the multi-material compliance matrix:

Create the solid mechanics PDE component:

For anisotropic elastic material that is not axis aligned, an orientation matrix can be specified to adjust the material to that. This also works with thermal expansion and is shown here. Variables and parameter are set up:

Solve the PDE:

Visualize the displacement:

When modeling soil in geotechnical applications, the Young modulus can change with the depth of the soil. This example explores a position-dependent Young's modulus. We use a rectangular slab of soild that is 100 meters wide and 100 meters deep:

Next, we set up variables and parameters. At this point, we have a symbolic Young modulus :

Set up the PDE:

We have a force in the negative direction acting on part of the top:

On the left- and right-hand side we constrain the movement in the direction; in the direction, the soil is able to move freely. At the bottom, the soil can move in the direction but not in the direction. This models a scenario where the soil is "standing" on a harder ground that does not move:

Set a constant Young modulus:

Solve the PDE on a refined mesh with the Young modulus set to baseYoungModulus:

Visualize the displacement:

Create a helper function to compute the von Mises stress:

Compute the von Mises stress for the constant Young modulus:

Make a contour plot of the von Mises stress:

Now we create a Young modulus depending on the depth :

Visualize the function:

Solve the PDE on a refined mesh with replaced with the variable-depth Young modulus:

Visualize the displacement:

Compute the von Mises stress:

Visualize the von Mises stress:

Plot the difference between the von Mises stress of the two models:

Plot the difference between the von Mises stress of the two models with the full plot range: