Multi-Layer Solid Model Reference

Workflow

A typical simulation using the Multi-Layer Solids model includes several similar but distinct laminates, for instance several layers on a Printed Circuit Board (PCB) composing a volume region. General steps to using this model are:

1. In the Physics Model Selection dialog for a physics continuum, select the models that you require for the simulation, including the Multi-Layer Solids model.
2. Choose all the solid materials that can appear in any layer within the board that you are modeling:
   1. Select [physics continuum] > Models > Multi-Layer Solid > Solids, right-click, and select Select Mixture Components...
   2. In the Select Mixture Components dialog, select components from the Material Databases to match the materials you require. If specific materials are not available, select arbitrary materials, rename them, and redefine their properties manually.
3. Define a laminate object as a series of layers:
   1. Select Multi-Layer Solid > Laminates, right-click, and select New to create a Laminate node. Rename the node if necessary.
   2. Select the Laminate node, right-click, and select New to create a layer. Rename the Layer n node if necessary.
   3. Create any additional layers for the laminate.
   4. Select each Layer n node in turn. Specify the thickness of the layer as a normalized proportion of the overall thickness of the laminate. Within a laminate, the thickness of all layers must sum to 1.0. Also set the volume fraction of each solid component present in the layer.
4. Repeat the previous step until you have defined all distinct laminates for the simulation.

5. Depending on the geometry you are modeling, assign laminates to regions, or parts within regions. If you have many connected geometry parts in your simulation, assign them to a single region and use the part subgrouping method to assign laminates to specific parts within the region.

   To assign laminates using part subgrouping:

   1. Make sure that the geometry parts are assigned to the target region.
   2. Select the target region and activate Allow Per-Part Values.
   3. Expand the Regions > [region] > Part Subgroupings node. Within the default subgrouping, create as many subgroups as you require. You can associate one laminate object with each subgroup.
   4. Select the subgroups in turn and set their Objects to one or more geometry parts from the set of parts that are assigned to the region.
   5. Select the [region] > Physics Values > Laminate Specification node and activate Specify by Part Subgroup.
   6. Expand the Laminate Specification node, select each subgroup in turn, and set their Laminate property to the appropriate laminate object.
   To assign laminates per region:

   1. Make sure that the geometry parts are assigned to the target region.
   2. Select the [region] > Physics Values > Laminate Specification node and set Laminate to the appropriate laminate object.

   If you are using the Three Dimensional space model, you can assign the laminate to a shell region.

6. Select the Physics Values > Laminate Normal node and specify the normal vector that applies to all laminates in the region.

Laminates

The Laminates manager node has a Laminate sub-node for each laminate in the simulation. In turn, each Laminate sub-node has a Layer sub-node for each layer in the laminate. Right-click on the Laminates manager to create new Laminate nodes; right-click on a Laminate node to create new Layer nodes. Rename Laminate and Layer nodes to suit the simulation.

Layer Node Properties

Thickness

Determines the relative thickness of the layer. Enter the fraction of the laminate thickness that is occupied by the layer. For example, if the layer is 1 mm thick and the whole laminate is 4 mm thick, enter 0.25.

Volume Fraction

Determines the composition of the layer, by volume fraction, based on the materials listed under the Solids node. The composition is expressed as an ordered list, following the order of materials under the Solids node.

Example: The solids listed are, first, Ag (silver) and, second, Au (gold). The entry [0.75, 0.25] indicates that the layer is three quarters silver and one quarter gold, by volume.

Physics Values

When the Multi-Layer Solid model is selected, the following values become available under the Region nodes that are associated with Laminate nodes:

Multi-Layer Solid Formulation

Properties for the laminates in multi-layer solids are calculated from weighted averages of the properties of the constituent layers of the laminates.

In the following equations, $t_i$ is the thickness of the $i$th layer.

Effective Anisotropic Thermal Conductivity

The normal component of the thermal conductivity is:

$$K_{nr}^{ef}=\frac{1}{{\displaystyle \sum _{i=1}^n\frac{t_i}{K_{i,nr}}}}$$

(116)

where:

• $K_{i,nr}={\displaystyle \sum _{j=1}^m{{\alpha }_j\cdot K}_{j,nr}}$ is the normal component of the $i$ th layer of the laminate.
• ${\alpha }_j$ is the volume fraction of the $j$ th component in the $i$ th layer.
• $K_{j,nr}$ is normal thermal conductivity of the $j$ th component.

The planar component of the thermal conductivity is:

$$K_{pl}^{ef}={\displaystyle \sum _{i=1}^n{t}_i\cdot K_{i,pl}}$$

(117)

where:

• $K_{i,pl}={\displaystyle \sum _{j=1}^m{{\alpha }_j\cdot K}_{j,pl}}$ is the planar component of the $i$ th layer of the laminate.
• $K_{j,pl}$ is planar thermal conductivity of the $j$ th component.

Effective thermal conductivity tensor:

$${\mathbf{K}}^{ef}=\left[\begin{array}{ccc}{K}_{nr}^{ef}& 0& 0\\ 0& K_{pl}^{ef}& 0\\ 0& 0& K_{pl}^{ef}\end{array}\right]$$

(118)

Effective Specific Heat

The effective specific heat is:

$$C_{p_{ef}}=\frac{{\displaystyle \sum _{i=1}^n{t}_i{\rho }_i{C}_{p_i}}}{{\displaystyle \sum _{i=1}^n{t}_i{\rho }_i}}$$

(119)

where:

• $C_{p_i}=\frac{{\displaystyle \sum _{i=1}^m{\alpha }_i{\rho }_i{C}_{p_i}}}{{\displaystyle \sum _{i=1}^m{\alpha }_i{\rho }_i}}$ is the specific heat of the $i$ th layer of the laminate.
• $C_{p_j}$ is the specific heat of the $j$ th component.

Effective Density

The effective density is:

$${\rho }^{ef}={\displaystyle \sum _{i=1}^n{t}_i{\rho }_i}$$

(120)

where $i$ is the layer of the laminate, and ${\rho }_i$ is:

$${\rho }_i={\displaystyle \sum _{j=1}^m{\alpha }_j\cdot {\rho }_j}$$

where $j$ denotes the $j$ th component of the $i$ th layer, and $\alpha$ is the volume fraction of that component.