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:
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Thermal Expansion (for Materials)
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Hygroscopic Swelling
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Initial Stress and Strain
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External Stress
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Damping
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Viscoelasticity
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Plasticity
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Creep
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Viscoplasticity
Note: Some options are only available with certain COMSOL products (see http://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
To use a mixed formulation by adding the pressure as an extra dependent variable to solve for, select the Nearly incompressible material check box. For a material with a very low compressibility, using only displacements as degrees of freedom may lead to a numerically ill-posed problem.
Define the Solid model and the linear elastic material properties.
Solid Model
To use a mixed formulation by adding the pressure as an extra dependent variable to solve for, select the Nearly incompressible material check box.
Select a linear elastic Solid model — Isotropic (the default), Orthotropic, or Anisotropic. Select:
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Isotropic for a linear elastic material that has the same properties in all directions.
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Orthotropic for a linear elastic material that has different material properties in orthogonal directions, so that its stiffness depends on the properties Ei, νij, and Gij.
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Anisotropic for a linear elastic material that has different material properties in different directions, and the stiffness comes from the symmetric elasticity matrix, D.
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Material Models
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Linear Elastic Material
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Orthotropic and Anisotropic Materials
Density
The default Density ρ uses values From material. For User defined enter another value or expression.
The density is needed for dynamic analysis or when the elastic data is given in terms of wave speed. It is also used when computing mass forces for gravitational or rotating frame loads, and when computing mass properties (Computing Mass Properties).
Specification of Elastic Properties for Isotropic Materials
For an Isotropic Solid model, 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 (see Table 3-1 in the theory chapter).
The individual property parameters are:
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Young’s modulus (elastic modulus) E.
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Poisson’s ratio ν.
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Shear modulus G.
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Bulk modulus K.
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Lamé parameter λ and Lamé parameter μ.
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Pressure-wave speed (longitudinal wave speed) cp.
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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 Solid model list, the material properties vary in orthogonal directions only. 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. This 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.
Specification of Elastic Properties for Anisotropic Materials
When Anisotropic is selected from the Solid model list, the material properties vary in all directions, and the stiffness comes from the symmetric Elasticity matrix, D. 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.
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 Force linear strains check box. When selected, a small strain formulation is always used, independently of the setting in the study step.
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Modeling Geometric Nonlinearity
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Studies and Solvers in the COMSOL Multiphysics Reference Manual
Energy Dissipation
The section is available when you also have the Nonlinear Structural Materials Module. Then, to display this 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.
Location in User Interface
Context Menus
Membrane>Material Models>Linear Elastic Material
Ribbon
Physics tab with Membrane selected:
Boundaries>Material Models>Linear Elastic Material