Linear Elastic Material
The Linear Elastic Material node adds the equations for a linear elastic shell 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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Safety
A Shell Local System subnode is always added. In this node you specify the coordinate system in which material orientations and results are interpreted. You can add several Shell Local System nodes in order to control the local directions on different boundaries.
Linear Elastic Material
Select Material symmetry— Isotropic, Orthotropic, or Anisotropic and enter the settings as described for the Linear Elastic Material for the Solid Mechanics interface. Note that:
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For Orthotropic no values for Ez, νyz, or νxz need to be entered due to the shell assumptions. It is also possible to define Transversely isotropic material properties.
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For User defined Anisotropic a 6-by-6 symmetric matrix is displayed. Due to the shell assumptions, you only need to enter values for D11, D12, D22, D14, D24, D55, D66, and D56.
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The material orientation is always interpreted in a local coordinate system aligned with the shell boundary as described in Local Coordinate Systems.
Out-of-Plane Strain
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
If the Solve for out-of-plane strain components check box is selected, extra degrees of freedom will be added for computing the out-of-plane strain components. This formulation is similar to what is used for plane stress in the Solid Mechanics and Membrane interfaces, and it is computationally somewhat more expensive than the standard formulation. In the default formulation, the out-of-plane strain in the shell is explicitly computed from the stress. This may cause circular references of variables if you for example want the constitutive law to be strain-dependent. If you encounter such problems, use the alternative formulation.
Geometric Nonlinearity
The settings in this section control the overall kinematics, the definition of the strain decomposition, and the behavior of inelastic contributions, for the material.
Select a Formulation — From study step (default), 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.
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With the default From study step, a total Lagrangian formulation for large strains is used when the Include geometric nonlinearity check box is selected in the study step. If the check box 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 check box in all study steps.
When inelastic deformations are present, such as for plasticity, the elastic deformation can be obtained in two different ways: using additive decomposition of strains or using multiplicative decomposition of deformation gradients.
Select a Strain decomposition — Automatic (default), Additive, or Multiplicative to decide how the inelastic deformations are treated. This option is not available when the formulation is set to Geometrically linear.
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When Automatic is selected, a multiplicative or additive decomposition is used with a total Lagrangian formulation, depending on the Include geometric nonlinearity check box status in the study step.
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Select Additive to force an additive decomposition of strains.
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Select Multiplicative to force a multiplicative decomposition of deformation gradients. This option is only visible if Formulation is set to Total Lagrangian.
The Strain decomposition input is only visible for material models that support both additive and multiplicative decomposition of deformation gradients.
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There are some cases when a small strain formulation could be useful for a certain domain, even though the study step is geometrically nonlinear. One such case is contact analysis, where the study step is always geometrically nonlinear, but where a geometrically linear formulation is sufficient for the material.
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When a multiplicative decomposition is used, the order of the subnodes matters. The inelastic deformations are assumed to occur in the same order as the subnodes appear in the model tree.
See Lagrangian Formulation, Deformation Measures, and Inelastic Strain Contributions in the Structural Mechanics Theory chapter.
See Modeling Geometric Nonlinearity in the Structural Mechanics Modeling chapter.
See Study Settings in the COMSOL Multiphysics Reference Manual.
Location in User Interface
Context Menus
Shell>Material Models>Linear Elastic Material
Plate>Material Models>Linear Elastic Material
Ribbon
Physics tab with Shell selected:
Boundaries>Material Models>Linear Elastic Material
Physics tab with Plate selected:
Domains>Material Models>Linear Elastic Material