Linear Elastic Material
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 http://www.comsol.com/products/specifications/). Also, the available options depend on the physics interface in which the Linear Elastic Material is used.
Layer Selection
This section is only present in the in the Layered Shell interface, where it is described in the documentation for the Linear Elastic Material node. The way the Linear Elastic Material node interacts with material definitions differ significantly between the Layered Shell interface and the other physics interfaces.
Coordinate System Selection
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.
Linear Elastic Material
Define the Solid model and the linear elastic material properties.
Solid Model
Select a linear elastic Solid model: Isotropic (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, so that its stiffness depends on the properties Ei, νij, and Gij.
Anisotropic for a linear elastic material that has different material properties in different directions, and the stiffness comes from the symmetric elasticity matrix, D.
Note: The Orthotropic and Anisotropic options are only available with certain COMSOL products (see http://www.comsol.com/products/specifications/)
In the Layered Shell interface, the chosen solid model applies to all selected layers, irrespective of whether the material data is entered explicitly as User defined in the Linear Elastic Material node, or is obtained from a Layered Material node using the default From material option.
Density
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.
When using Common model input, you can see or modify the value of the volume reference temperature by clicking the Go To Source button (). This will move you to the Common Model Inputs node under Global Definitions in the Model Builder. The default value is room temperature; 293.15 K.
If you want to create a model input value which is local to your current selection, click the Create Model Input button . This will create a new Model Input node under Definitions in the current component, having the same selection as in the current node.
Common Model Inputs and Model Input in the COMSOL Multiphysics Reference Guide.
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 according to Table 4-1.
D(E,ν)
D(E,G)
D(K,G)
D(λ,μ)
E =
ν =
K =
G =
μ
λ =
μ =
cp =
cs =
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 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.
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, 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
The settings in this section affect the behavior of the selected domains in a geometrically nonlinear analysis.
If a study step is geometrically nonlinear, the default behavior is to use a large strain formulation in all domains. Select the Force linear strains check box to always use a small strain formulation, irrespective of the setting in the study step.
When a geometrically nonlinear formulation is used, the elastic deformations used for computing the stresses can be obtained in two different ways if inelastic deformations are present: additive decomposition and multiplicative decomposition. The default is to use multiplicative decomposition. Select Additive strain decomposition to change to an assumption of additivity.
Note: This section is only available with COMSOL products that support geometrically nonlinear analysis (see http://www.comsol.com/products/specifications/).
When a multiplicative decomposition is used, the order of the subnodes to Linear Elastic Material matters. The inelastic deformation are assumed to have occurred in the same order as the subnodes appear in the model tree.
In versions prior to 5.3, only the additive strain decomposition method was available. If you want to revert to the previous behavior, select Additive strain decomposition. If the results then differ significantly, probably the assumption of additivity is questionable, however.
In models created in a version prior to 4.2a, a check box named Include geometric nonlinearity may be visible in this section. It is displayed only if geometric nonlinearity was originally used for the selected domains. Once the check box is cleared in this Settings window, it is permanently removed and the study step assumes control over the selection of geometric nonlinearity.
When Include geometric nonlinearity is selected in this section, it automatically also selects the Include geometric nonlinearity check box in the study Settings window.
Studies and Solvers in the COMSOL Multiphysics Reference Manual
Energy Dissipation
You can select to compute and store various energy dissipation variables in a time dependent analysis. Doing so will add extra degrees of freedom to the model.
To display this section, click the Show button () and select Advanced Physics Options.
Select the Calculate dissipated energy check box as needed to compute the energy dissipated by for example creep, plasticity, viscoplasticity, viscoelasticity, or damping.
Location in User Interface
Context Menus
Solid Mechanics>Material Models>Linear Elastic Material
Layered Shell>Material Models>Linear Elastic Material
Multibody Dynamics>Linear Elastic Material
Ribbon
Physics tab with Solid Mechanics selected:
Domains>Material Models>Linear Elastic Material
Physics tab with Layered Shell selected:
Boundaries>Material Models>Linear Elastic Material
Physics tab with Multibody Dynamics selected:
Domains>Multibody Dynamics>Linear Elastic Material