Topology optimization creates an organic geometry flowing material to where it is needed and eroding where it is not efficient. This technology is ideally suited to the limited manufacturing constraints that 3D printing offers. 3D printed parts by virtue of their layer by layer additive manufacturing approach have complex material properties. These properties are similar to wood where there is a stiff direction (with the grain) and a weak direction (across the grain). To gain the highest performance in 3D printed parts these material properties must be considered in the design process.

Lacrosse Topology Optimization


This post is a continuation of the work presented in Lacrosse Head Topology Optimization. In that post, topology optimization was used to evolve the design of a lacrosse head based on 3 different loading scenarios. This methodology creates an organic geometry which is ideally suited to the limited manufacturing constraints that 3D printing offers. Most 3D printed technology deposits material in 2D slices and then translates in the build direction. The 2D slices may have differing properties in different directions however most printers will stack these directions differently for each layer effectively homogenizing the smeared properties of each layer. In the build direction this is not possible and therefore will have different properties. The analogy to wood breaks down slightly because wood has 1 strong direction and 2 weak where 3D prints have 2 strong and 1 weak.

A great illustration of wood’s strength was presented in the images below from For a 3D print ideally you would have the build direction coming out of the plane on the second image and the majority of the fibers (if it’s FDM) oriented in the diagonal like the first image.

Board Strength 1 Board Strength 2

Another common way to think about this is breaking a board with martial arts. Here is a video of the expert Bruce Lee’s 1 Inch Punch which takes place between 20-21sec into the video. Popular mechanics did an interesting article on the bio-mechanics and neuro-mechanics of this feat.

Now back to designing for 3D printing. For this post I will assume we are talking about Fused deposition modeling (FDM) where a heated filament is laid down in a raster pattern. I like to call these spaghetti printers. Below is a schematic of the printing process where in general each subsequent layer is laid in a crosshatch pattern like people who cut their lawn twice to make it look good. Here the layers are green, blue, green and blue built from the bottom up as indicated by the arrow.

3D Print Stack Direction

Material Properties

3D prints are similar in structure to composite materials which have a long history being modeled with Finite Element Analysis (FEA). The tricky part is to obtain appropriate material properties for the specific materials and printing techniques. With the help of Google, I found anisotropic material properties for 3D printed ABS at a blog where Sergei Sergeenkov referenced Monish Shivappa Mamadapur’s paper CONSTITUTIVE MODELING OF FUSED DEPOSITION MODELING ACRYLONITRILE BUTADIENE STYRENE (ABS), thanks guys! (Note: the paper will be included in a zip file at the end of the post) This work assumes that you can homogenize the material properties of several layers and that the build direction will have a different set of properties. Again, this is standard practice for fibrous composite laminates.

These properties are listed as:

E2 = E1 = 1636 MPa, E3 = 1197 MPa
nu21 = 0.39, nu31 = nu32 = 0.37
G13 = G23 = 645 MPa, G12 = 676 MPa

Abaqus however requires the constants for the nu’s to be in the opposite convention. From efunda a conversion is provided nu12=nu21/E2*E1 which converts to:

nu12= 0.39, nu13=nu32=0.51

These constants were inputted in to the Abaqus model as elastic engineering constants. (Note: in the description I have placed a trail back to the blog it was found in)

Abaqus Isotropic Material Properties


This material was added to a section and applied to the lacrosse head. Now that we have orthotropic material properties lets figure out what orientation we should print the design. 3 different coordinate systems were created to vary the build direction of the 3 models created. By going in to the property module and selecting Assign->Material Orientation where the 3 direction is the weak build direction. Aside from these changes the exact same Abaqus finite element analysis (FEA) and Tosca topology optimizations were performed as before.


The topologically optimized geometry is shown below with the build directions in the X (front), Y (side) and Z (top) respectively.

1Lacrosse Topology Optimization X2Lacrosse Topology Optimization Y3Lacrosse Topology Optimization Z

For comparison here is an image of the original optimized design for injection molding.

0Lacrosse Topology Optimization

The differences can most easily be seen in this animated GIF.

Lacrosse Topology Optimization

Each of these designs were optimized for maximum stiffness with the 3 orthogonal load cases. Because of the similar loading and constraints the designs have similar load paths. The displacement for the loads and designs are presented in graph below.

Stiffness of 3D Printed Parts

Here the injection molded design is stiffer (lower bars are stiffer) than all others. Printing in the X direction provides the stiffest part in all load cases and since this will likely require the least build time and support material it’s likely the best choice.


Topology optimization and 3D printing are a natural fit. Designs evolve organically and the 3D printer can create complex geometries without the usual manufacturing constraints. By optimizing a design for additive manufacturing higher preforming parts can be achieved.

I hope you found this informative please feel free to comment, like, subscribe, contact us or whatever else can be done today! Thank you.

Rob Stupplebeen