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 www.comsol.com/products/specifications/). Also, the available options depend on the physics interface in which the Linear Elastic Material is used.

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.

Define the Material symmetry and the linear elastic material properties.

Select the Material symmetry — Isotropic, Orthotropic, Anisotropic, or Crystal. Select:

Note: The Orthotropic, Anisotropic, and Crystal options are only available with certain COMSOL products (see www.comsol.com/products/specifications/)

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 an expression for the reference temperature locally.

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.

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.

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, enter three values in the fields for Young’s modulus E, Poisson’s ratio ν, and the Shear modulus G. The latter defines the relationship between engineering shear strain and shear stress. It is applicable only to an orthotropic material and follows the equation

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 the User defined option is selected.

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.

Because of the material symmetry, only certain components of the elasticity matrix need to be specified. The actual components to enter depend on the selected Crystal system — Cubic (3 constants), Hexagonal (5 constants), Trigonal (6 constants), Trigonal (7 constants), Tetragonal (6 constants), Tetragonal (7 constants), or Orthorhombic (9 constants).

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 adds 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. It is also possible to select an Implicit formulation when an assumption of plane stress is used.

Select a Formulation — From study step, 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.

When From study step is selected, a total Lagrangian formulation for large strains is used when the Include geometric nonlinearity checkbox is selected in the study step. If the checkbox 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 checkbox in all study steps.

Select a Strain decomposition — Automatic, Additive, Logarithmic, or Multiplicative to decide how the inelastic deformations are treated. This option is not available when the formulation is set to Geometrically linear.

The Strain decomposition input is only visible for material models that support both additive and multiplicative decomposition of the deformation gradient.

This section is only available with COMSOL products that support geometrically nonlinear analysis (see www.comsol.com/products/specifications/).

Select how to compute the energy dissipated by Creep, Plasticity, Viscoplasticity, or other dissipative processes.

Select how to Store dissipation — From physics interface, Individual contributions, Total, Domain ODEs (legacy), or Off.

Use From physics interface to treat the dissipative processes as specified in the settings of the physics interface, see for instance Energy Dissipation in the Solid Mechanics interface.

Use Individual contributions to treat each dissipative process independently. Selecting this option gives a more flexible implementation for problems where dissipation occurs at different time scales, and you want to distinguish each phenomenon separately.

Use Total to accumulate all the dissipative processes into one common variable.

Use Domain ODEs to accumulate the dissipative processes into ODE variables instead of internal state variables.

Select the Reduced integration checkbox to reduce the number of integration points used for the weak contribution in the material. Reduced integration give faster computations at the element level and help mitigate locking issues. However, reduced integration may also introduce numerical instabilities, which then require an additional stabilization term.

By default, the Reduced integration checkbox is cleared, except in interfaces designed for explicit dynamic analysis, where it is always selected.

Select a method for Hourglass stabilization — Automatic, Energy sampling, Hessian, Flanagan–Belytschko, Manual, or None to be used in combination with the reduced integration scheme.

The Automatic option selects the stabilization method and its properties based on the physics interface, space dimension, shape function type and order of the displacement field, and the study type.

For the Energy sampling, Hessian, and Flanagan–Belytschko methods, the hourglass stiffness can be scaled by specifying a stiffness multiplier fstb. This multiplier can be an expression of any parameter or variable in the model. This multiplier can be expressed as any parameter or variable in the model. However, to maintain computational efficiency, avoid expensive definitions such as nonlocal coupling operators.

For the hourglass stabilization methods, the stiffness is automatically adjusted during the solution process using an internal multiplier. This accounts for the effect of inelastic deformations, such as damage and plasticity. This correction can be disabled by setting Inelastic deformations to Ignore. Ignoring inelastic deformations may be necessary for scenarios like cyclic loading, where the hourglass stiffness could become too small during unloading. Alternatively, adjust the value for the Minimum stiffness multiplier., which acts as a lower bound for the hourglass stiffness, which is applied in addition to any expression entered for fstb.

For the Energy sampling method, the default stabilization uses an isotropic linear elastic potential. Set the Energy Sampling Potential to Hyperelastic for large deformations. When selected, a neo-Hookean potential is used for nonlinear strains, while linear strains use the linear elastic potential.

The Hessian method evaluates a weak contribution using the reduced integration order. For hexahedral mesh elements, this approach may not suppress all hourglass modes. In most cases, non-stabilized modes are suppressed by constraints adjacent to the domain, but if they are not, select Use full integration to increase the integration order of the stabilization equations to suppress all modes. The higher integration order will increase the computational cost of the stabilization method.

Select how the maximum wave speed in the material is determined — Automatic or User defined. For User defined, enter the maximum wave speed, cmax.

Physics tab with Solid Mechanics or Solid Mechanics, Explicit Dynamics selected:

Physics tab with Layered Shell selected:

Physics tab with Multibody Dynamics selected: