Linear Elastic Material

The is selected by default. The 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.

To use a mixed formulation by adding the pressure as an extra dependent variable to solve for, select the check box. For a material with a very low compressibility, using only displacements as degrees of freedom may lead to a numerically ill-posed problem.

Define the and the linear elastic material properties.

Solid Model

Select a linear elastic : (the default), , or . Select:

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for a linear elastic material that has the same properties in all directions.

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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.

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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 and options are only available with certain COMSOL products (see http://www.comsol.com/products/specifications/)

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Material Models

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Linear Elastic Material

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Orthotropic and Anisotropic Materials

Density

The default ρ uses values . For enter another value or expression.


	The density is needed for dynamic analysis or when the elastic data is given in terms of wave speed. It is also used when computing mass forces for gravitational or rotating frame loads, and when computing mass properties (Computing Mass Properties).

Specification of Elastic Properties for Isotropic Materials

For an , from the list select a pair of elastic properties for an isotropic material — , , , , or . For each pair of properties, select from the applicable list to use the value or enter a 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.

Table 4-1: Expressions for the elastic moduli.
Description	Variable	D(E,ν)	D(E,G)	D(K,G)	D(λ,μ)
Young’s modulus	E =	E	E
Poisson’s ratio	ν =	ν
Bulk modulus	K =			K
Shear modulus	G =		G	G	μ
Lamé parameter λ	λ =				λ
Lamé parameter μ	μ =		G	G	μ
Pressure- wave speed	cp =
Shear-wave speed	cs =

The individual property parameters are:

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(elastic modulus) E.

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ν.

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λ and μ.

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(longitudinal wave speed) cp.

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(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 is selected from the list, the material properties vary in orthogonal directions only. The can be specified in either or notation. When is selected in 3D, enter three values in the fields for E, ν, and the 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 is selected from the list, the material properties vary in all directions, and the stiffness comes from the symmetric , D The can be specified in either or notation. When is selected, a 6-by-6 symmetric matrix is displayed.

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 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 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/).

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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 in contact analysis, where the study is always geometrically nonlinear, but it is possible that a geometrically linear formulation is sufficient in the material.

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When a multiplicative decomposition is used, the order of the subnodes to matters. The inelastic deformation are assumed to have occurred in the same order as the subnodes appear in the model tree.

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In versions prior to 5.3, only the additive strain decomposition method was available. If you want to revert to the previous behavior, select . If the results then differ significantly, probably the assumption of additivity is questionable, however.

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In models created in a version prior to 4.2a, a check box named 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 window, it is permanently removed and the study step assumes control over the selection of geometric nonlinearity.
When is selected in this section, it automatically also selects the check box in the study window.