The Linear Elastic Material node adds the equations for a linear elastic solid and an interface for defining the elastic material properties.

By adding the following subnodes to the Linear Elastic Material node you can incorporate many other effects:

Note: Some options are only available with certain COMSOL products (see https://www.comsol.com/products/specifications/). Also, the available options depend on the physics interface in which the Linear Elastic Material is used.

The Global coordinate system is selected by default. The Coordinate system list contains all applicable coordinate systems in the component. The coordinate system is used for interpreting directions of orthotropic and anisotropic material data and when stresses or strains are presented in a local system. The coordinate system must have orthonormal coordinate axes, and be defined in the material frame. Many of the possible subnodes inherit the coordinate system settings.

Define the Material symmetry and the linear elastic material properties.

Select the Material symmetry — Isotropic, Orthotropic, Anisotropic, or Crystal. Select:

Note: The Orthotropic, Anisotropic, and Crystal options are only available with certain COMSOL products (see https://www.comsol.com/products/specifications/)

The default Density ρ uses values From material. For User defined enter another value or expression.

If any material in the model has a temperature dependent mass density, and From material is selected, the Volume reference temperature list will appear in the Model Input section. As a default, the value of Tref is obtained from a Common model input. You can also select User defined to enter a value or expression for the reference temperature locally.

For an Isotropic material, from the Specify list select a pair of elastic properties for an isotropic material — Young’s modulus and Poisson’s ratio, Young’s modulus and shear modulus, Bulk modulus and shear modulus, Lamé parameters, or Pressure-wave and shear-wave speeds. For each pair of properties, select from the applicable list to use the value From material or enter a User defined value or expression.

Each of these pairs define the elastic properties and it is possible to convert from one set of properties to another according to Table 4-1.

When Orthotropic is selected from the Material symmetry list, the material properties are different in orthogonal directions (principal directions) given by the axes of the selected coordinate system. The Material data ordering can be specified in either Standard or Voigt notation. When User defined is selected, enter three values in the fields for Young’s modulus E, Poisson’s ratio ν, and the Shear modulus G. The latter defines the relationship between engineering shear strain and shear stress. It is applicable only to an orthotropic material and follows the equation

You can set an orthotropic material to be Transversely isotropic. Then, one principal direction in the material is different from two others that are equivalent. This special direction is assumed to be the first axis of the selected coordinate system. Because of the symmetry, the following relations hold:

Thus, only five elasticity moduli need to be entered when the User defined option is selected.

When Anisotropic is selected from the Material symmetry list, the material properties vary in all directions. They can be specified using either the Elasticity matrix, D or the Compliance matrix, D-1. Both matrices are symmetric. The Material data ordering can be specified in either Standard or Voigt notation. When User defined is selected, a 6-by-6 symmetric matrix is displayed.

Because of the material symmetry, only certain components of the elasticity matrix need to be specified. The actual components to enter depend on the selected Crystal system — Cubic (3 constants), Hexagonal (5 constants), Trigonal (6 constants), Trigonal (7 constants), Tetragonal (6 constants), Tetragonal (7 constants), or Orthorhombic (9 constants).

For a material with a very low compressibility, using only displacements as degrees of freedom may lead to a numerically ill-posed problem. You can then use a mixed formulation, which adds an extra dependent variable for either the pressure or for the volumetric strain. For details, see the Mixed Formulation section in the Structural Mechanics Theory chapter.

From the Use mixed formulation list, select None, Pressure formulation, or Strain formulation. It is also possible to select an Implicit formulation when an assumption of plane stress is used.

Select a Formulation — From study step, Total Lagrangian, or Geometrically linear to set the kinematics of the deformation and the definition of strain. When From study step is selected, the study step controls the kinematics and the strain definition.

When From study step is selected, a total Lagrangian formulation for large strains is used when the Include geometric nonlinearity checkbox is selected in the study step. If the checkbox is not selected, the formulation is geometrically linear, with a small strain formulation.

To have full control of the formulation, select either Total Lagrangian, or Geometrically linear. When Total Lagrangian is selected, the physics will force the Include geometric nonlinearity checkbox in all study steps.

Select a Strain decomposition — Automatic, Additive, or Multiplicative to decide how the inelastic deformations are treated. This option is not available when the formulation is set to Geometrically linear.

The Strain decomposition input is only visible for material models that support both additive and multiplicative decomposition of the deformation gradient.

This section is only available with COMSOL products that support geometrically nonlinear analysis (see https://www.comsol.com/products/specifications/).

Select the Reduced integration checkbox to reduce the integration points for the weak contribution of the feature. Select a method for Hourglass stabilization — Automatic, Manual, or None to use in combination with the reduced integration scheme. The default Automatic stabilization technique is based on the shape function and shape order of the displacement field.

Control the hourglass stabilization scheme by using the Manual option. Select Shear stabilization (default) or Volumetric stabilization.

When Shear stabilization is selected, enter a stabilization shear modulus, Gstb. The value should be in the order of magnitude of the equivalent shear modulus.

When Volumetric stabilization is selected, enter a stabilization bulk modulus, Kstb. The value should be in the order of magnitude of the equivalent bulk modulus.

Physics tab with Solid Mechanics selected:

Physics tab with Layered Shell selected:

Physics tab with Multibody Dynamics selected: