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 subnode to the Linear Elastic Material node you can incorporate damping effects; see Damping.
Coordinate System Selection
The Global coordinate system is selected by default. The Coordinate system list contains any additional coordinate systems that the model includes (except boundary coordinate systems). 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
The Solid model is always Isotropic for a linear elastic material that has the same properties in all directions.
Density
The default Density ρ uses values From material. For User defined enter another value or expression.
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.
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.
About Isotropic Material and Elastic Moduli
The elasticity matrix is
Different pairs of elastic moduli can be used, and as long as two moduli are defined. The others can be computed according to Table 15-1.
D(E,ν)
D(K,G)
D(λ,μ)
ν
μ
λ
μ
cp
cs
According to Table 15-1, the elasticity matrix D for isotropic materials is written in terms of Lamé parameters λ and μ,
or in terms of the bulk modulus K and shear modulus G:
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 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.
Energy Dissipation
You can select to compute and store 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 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 damping.
Discretization
If Pressure formulation is used, select the discretization for the Auxiliary pressureAutomatic, 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 stabilizationAutomatic, 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. The value 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
Ribbon
Physics Tab with Solid Mechanics selected: