Linear Elastic Material
The Linear Elastic Material node adds the equations for a linear elastic membrane 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/)
Coordinate System Selection
The built in Boundary System 1 is selected by default. The Coordinate system list contains any additional boundary coordinate systems that the model includes. 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. Many of the possible subnodes inherit the coordinate system settings.
Linear Elastic Material
Define the material symmetry and the linear elastic material properties.
Material Symmetry
Select Material symmetryIsotropic (the default), Orthotropic, or Anisotropic. Select:
Isotropic for a linear elastic material that has the same properties in all directions.
Orthotropic for a linear elastic material that has different material properties in orthogonal directions. It is also possible to define Transversely isotropic material properties.
Anisotropic for a linear elastic material that has different material properties in different directions.
Density
The default Density ρ uses values From material. For User defined enter another value or expression.
Specification of Elastic Properties for Isotropic Materials
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.
The individual property parameters are:
Young’s modulus (elastic modulus) E.
Lamé parameter λ and Lamé parameter μ.
Pressure-wave speed (longitudinal wave speed) cp.
Shear-wave speed (transverse wave speed) cs. This is the wave speed for a solid continuum. In plane stress, for example, the actual speed with which a longitudinal wave travels is lower than the value given.
Specification of Elastic Properties for Orthotropic Materials
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 in 3D, enter three values in the fields for Young’s modulus E, Poisson’s ratio ν, and the Shear modulus G. The latter defines defines the relationship between engineering shear strain and shear stress. It is applicable only to an orthotropic material and follows the equation
νij is defined differently depending on the application field. It is easy to transform among definitions, but check which one the material uses.
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 User defined option is selected.
Specification of Elastic Properties for Anisotropic Materials
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.
Mixed Formulation
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 add 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.
Geometric Nonlinearity
If a study step is geometrically nonlinear, the default behavior is to use a large strain formulation in all boundaries. There are, however, some rare cases when the use of a small strain formulation for a certain boundary is needed.
In such cases, select the Geometrically linear formulation check box. When selected, a small strain formulation is always used, independently of the setting in the study step.
Studies and Solvers in the COMSOL Multiphysics Reference Manual
Energy Dissipation
The section is available when you also have the Nonlinear Structural Materials Module. To display the section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
Select the Calculate dissipated energy check box as needed to compute the energy dissipated by Creep, Plasticity, Viscoplasticity, or Viscoelasticity.
Discretization
If Pressure formulation is used, select the discretization for the Auxiliary pressureAutomatic, Discontinuous Lagrange, Continuous, Linear, or Constant. If Strain formulation is used, select the discretization for the Auxiliary volumetric strainAutomatic, Discontinuous Lagrange, Continuous, Linear, or Constant.
The Discretization section is available when Pressure formulation or Strain formulation is selected from the Use mixed formulation list. To display the section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
Quadrature Settings
Select the Reduced integration check box to reduce the integration points for the weak contribution of the feature. Select a method for Hourglass stabilizationAutomatic, 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.
Location in User Interface
Context Menus
Ribbon
Physics tab with Membrane selected: