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# Isotropic and Orthotropic Materials

## Isotropic Materials

A material is isotropic if its mechanical and thermal properties are the same in all directions. Isotropic materials can have a homogeneous or non-homogeneous microscopic structures. For example, steel demonstrates isotropic behavior, although its microscopic structure is non-homogeneous.

## Orthotropic Materials

A material is orthotropic if its mechanical or thermal properties are unique and independent in three mutually perpendicular directions. Examples of orthotropic materials are wood, many crystals, and rolled metals.

For example, the mechanical properties of wood at a point are described in the longitudinal, radial, and tangential directions. The longitudinal axis (1) is parallel to the grain (fiber) direction; the radial axis (2) is normal to the growth rings; and the tangential axis (3) is tangent to the growth rings.

## Defining Orthotropic Properties For Solids

The orthotropic material directions throughout a component are defined based on the reference geometry selected. If a part is manufactured such that this is not true, then you should model it as different parts in order to define orthotropic directions properly. For example, consider the part shown in the figure:

You need to model this part as two parts; the cylinder and the planar sheet. You can then use a plane as the reference geometry for defining the orthotropic material directions for the planar sheet and the axis of the cylinder as the reference geometry for the cylinder.

 The X, Y, and Z directions for an orthotropic material when a plane is used as a reference geometry. The radial (X), tangential (Y), and axial directions (Z) for an orthotropic material when an axis is used as a reference geometry.

## Defining Orthotropic Properties For Shells

For a planar shell, select a plane that is parallel to the shell as the reference geometry. The X and Y axes lie in the plane and the Z-axis is normal to the plane. For a cylindrical shell, select the axis of the cylinder as the reference geometry. The Y-axis is parallel to the axis of the cylinder and the X-axis is tangential.

 The X, Y, and Z directions of an orthotropic material for a planar shell. The X and Y directions of an orthotropic material for a cylindrical shell.

For composite shells, the X, Y and Z directions for orthotropic material  definition are defined differently for each ply depending on ply angle. Reference geometry is not considered for orthotropic material definition.

In general, the software modifies the reference geometry as follows:

• The software transforms the coordinate system defined by the reference geometry such that the Z-axis becomes normal to the plane of the shell. The plane of the shell is defined by the 3 corner nodes.

• If the angle between the X-axis of the selected reference geometry and the normal to the shell plane is larger than 45o, the program projects the X-axis of the reference geometry on the shell plane to define the modified X-axis.

• If the angle between the X-axis of the selected reference geometry and the normal to the shell plane is less than 45o, the program projects the Y-axis of the reference geometry on the shell plane to define the modified X-axis.

• The Y-axis of the modified reference geometry is then defined to complete a right-hand Cartesian coordinate system.

To define orthotropic material:

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