Linear Elastic Material, Layered
The Linear Elastic Material, Layered node adds the equations for a layered linear elastic membrane.
If the Composite Materials Module analysis is available, this material model can be applied to arbitrary layers in a multilayered membrane. The material properties, orientations, and layer thicknesses are defined using Layered Material node. The offset, and local coordinate system, in which material orientations and results are interpreted, is defined by Layered Material Link or Layered Material Stack node.
Without the Composite Materials Module, only single layer membranes can be modeled. This is still useful, for example for some multiphysics couplings. For single layer materials, an ordinary Material node can be used, as long you include a Shell property group in which, for example, the thickness is given.
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For a general description about layered materials, see Layered Materials in the documentation for the Composite Materials Module.
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See also the discussion in Layered and Nonlayered Membranes.
By adding the following subnodes to the Linear Elastic Material, Layered 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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Inelastic Strain Rate
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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
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Safety
Some of these material models are only available together with the Nonlinear Structural Materials Module (see https://www.comsol.com/products/specifications/).
Shell Properties
For this node, the Shell Properties section is only used for selecting a material model, but not individual layers.
Table 7-1: Layer Selections; Linear Elastic Material.
Selection
Use All Layers
Selection of Individual Layers
Boundary
Default when added
No
For a general description of this section, see Layer and Interface Selections in the documentation for the Composite Materials Module.
Boundary Selection
The boundary selection in this node is similar to the Linear Elastic Material node. It is however only possible to select boundaries which are part of the selection of a layered material defined in Layered Material Link or Layered Material Stack node.
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. If the layers have different types of anisotropy properties, select the one that is most complex.
Note that:
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For Orthotropic no values for Ez, νyz, or νxz need to be entered due to the membrane 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 membrane 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 laminate coordinate system aligned with the membrane boundary together with the orientation of each layer specified on a layered material. The laminate coordinate system is always a Boundary System.
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, Strain formulation, or Implicit 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.
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.
Discretization
If Pressure formulation is used, select the discretization for the Auxiliary pressure — Automatic, Discontinuous Lagrange, Continuous, Linear, or Constant. If Strain formulation is used, select the discretization for the Auxiliary volumetric strain — Automatic, 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 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, and the shear correction factor kstb. The value for Gstb 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
Membrane>Material Models>Linear Elastic Material, Layered
Ribbon
Physics tab with Membrane selected:
Boundaries>Material Models>Linear Elastic Material, Layered