====Problem Description====
 
'''Homogenization'''
In this example, isotropic matrix and transversely isotropic fiber are considered as constituent materials. The corresponding material properties that we will use are defined in the following table.

||Resin Conductivity, k{{sub}}r{{sub}} ||0.29 W/m/K||
||Fiber Conductivity in Fiber Direction, k_f11||6.83 W/m/K||
||Fiber Conductivity in Transverse to the Fiber Direction, k_f22||2.60 W/m/K||

We will use a hexagonal pack with fiber volume fraction equal to v_f = 0.8320

[[Image(Problem_1.jpg, desc="Homogenization process")]] 


====Software Used==== 
In his tutorial we will use Abaqus CAE with the Abaqus SwiftComp GUI  plug-in. Abaqus CAE will be used to define the material properties and Abaqus SwiftComp GUI to define the different structure genomes (SGs). SwiftComp will run in the background. 

====Solution Procedure==== 
The steps required to carry out the thermal conductivity using Abaqus SwiftComp GUI are as follows. 

''' # Step 1.''' We define the material properties in global coordinate system. In this case, we only need to define thermal conductivity properties in Abaqus CAE clicking on ''Thermal, Conductivity''.
[[Image(Step_1.png, desc="Definition of thermal conductivity as constituent properties")]] 

''' # Step 2.''' From the default the Abaqus SwiftComp GUI SGs, we pick the 2D Structure Genome with Hexagonal pack. 

[[Image(Step_2.png, desc="Definition of the 2D SG hexagonal pack microstructure")]] 

''' # Step 3.''' Now, in order to compute the homogenized thermal conductivity properties, we click on ''Homogenization'' and we select ''Conduction'' in Analysis Type. 

[[Image(Step_3.png, desc="Definition of the homogenization step")]] 

''' # Step 4.''' We click on ''Ok'' to run the homogenization step. SwiftComp on the background will run the homogenization. 

[[Image(Step_4.png, desc="SwiftComp running on the background")]] 

''' # Step 5.'''The results can be found in the ''.sc.k'' file as shown next. Note that the first matrix corresponds to the effective thermal conductivity matrix in the form of K_ij_^*^. The second matrix corresponds to the compliance matrix in the form of (K_ij_^*^ )^-1^.

[[Image(Step_5.png, desc="Results corresponding to the effective thermal conductivities")]] 

====References====
 # Rique, O.; Barocio, E.; Yu, W.: “Experimental and Numerical Determination of the Thermal Conductivity Tensor for Composites Manufacturing Simulation,” ASC 32nd Technical Conference, October 2017, Purdue University.