Materials

Use the tool to view, add, and edit the material properties that are used for NLFE bodies.

Create and Edit Materials

From the Model menu, select from the drop-down menu.
The Material Properties dialog opens.
Select an elasticity type from the left-most drop-down menu.
Select a material from the Material list and review its properties.

CAUTION: For your convenience, a set of materials are provided by default. The values of the properties provided are generic in nature, and might not be appropriate for the actual problem or material you intend to use with it. It is advised these materials be used with caution and that you obtain more accurate material properties.
Optional: Edit the material's elastic strain limit by entering a value in the corresponding field.

Note: For NLFE bodies, MotionSolve will provide warning whenever the strain in the body crosses this specified limit. You can also disable a material's elastic strain limit but deactivating the check box next to the field.
Add a new material property.
1. Select the desired elasticity type.
2. Click the Add button to bring up the Add a Material Property dialog.
3. Specify a label for the material property.
4. Specify a variable name for the material property.
5. Select a preexisting material to use as a source for the new material's values or select New.
Tip: Delete any material property that was added by selecting that property and clicking Delete.
Edit the material property.
1. Select the material property type from the Type drop-down menu.
  For linear elastic materials, the available options are Isotropic, Anisotropic, and Orthotropic. For hyper elastic materials, the available options are Neo-Hookean, Incompressible, Mooney-Rivlin, and Yeoh.
2. Enter values for the available properties in each field. For anisotropic material properties, specify the elements of the 6x6 stiffness matrix.
  
  Tip: For linear elastic materials that are used by NLFE bodies of type Beam, activate the Elastic line check box to have the material model consider the beam as an elastic line (curve) passing through the neutral axis. All the deformation, including the axial, bending, shear and torsion are calculated at the neutral axis. The elastic line approach considers effects of cross section deformations averaged and calculated at the neutral axis.
Click Close to exit the dialog.

Hyper Elastic Materials Overview

For hyper elastic materials, different constitutive material models are supported, such as: Neo-Hookean (both compressible and incompressible), Mooney-Rivlin, and Yeoh models that are used to model a hyper elastic NLFE Body.

Hyper elastic materials can undergo large deformations with a non-linear stress strain relationship.

The constitutive models for hyper elastic materials are characterized using the strain energy density function.

The following table lists the constitutive equations for various models:


Type	Equation	Description
Neo-Hookean Compressible	$U = \frac{μ}{2} (I_{1} - 3) - μ \ln J + \frac{λ}{2} {(\ln J)}^{2}$	U - Strain Energy density function μ - Shear modulus $I_{1} - r_{x}^{T} r_{x} + r_{y}^{T} r_{y} + r_{z}^{T} r {}_{z}$ - rx, ry, and rz are the gradients of NLFE grids $λ = \frac{2 μ v}{1 - 2 v}$ , is called the 2nd Lame's constant, v is the Poisson's ratio $J = \det (J) = r_{x}^{T} (r_{y} \times r_{z})$
Neo-Hookean Incompressible	$U = \frac{μ}{2} ({\bar{I}}_{1} - 3) + \frac{k}{2} {(J - 1)}^{2}$	${\bar{I}}_{1} = J^{\frac{- 2}{3}} I_{1}$ $k = \frac{2 μ (1 + v)}{3 (1 - 2 v)}$ , bulk modulus
Mooney-Rivlin	$U = μ_{10} (\bar{I} {}_{1}- 3) + μ_{01} ({\bar{I}}_{2} - 3) + \frac{k}{2} {(J - 1)}^{2}$	μ₀₁ and μ₁₀ are material constants ${\bar{I}}_{2} = J^{\frac{- 4}{3}} I_{2}$ ${\bar{I}}_{2} = \frac{1}{2} ({(t r (C))}^{2} - (t r (C^{2})))$ , where C is the Cauchy-Green deformation tensor $C = J^{T} J$ $J = [r_{x} r_{y} r_{z}]$ $r_{x} r_{y} r_{z}$ are the gradient vectors
Yeoh	$U = C_{10} ({\bar{I}}_{1} - 3) + C_{20} {({\bar{I}}_{1} - 3)}^{2} + C_{30} {({\bar{I}}_{1} - 3)}^{3} + \frac{k}{2} {(J - 1)}^{2}$	C₁₀, C₂₀, and C₃₀ are material constants

The material constants for these models have to be derived through testing, such as: uniaxial, bending, and shear tests.