# Designing and Calibrating Materials for Additive Manufacturing – Part 2

In Part 1 of this blog post, I explored the procedure to design materials for purpose—from the single molecule design to the part level, in-service performance prediction.

In Part 2, I’ll discuss how to design and optimize materials for lattice structures.

#### Sizing Optimization with Tosca Structure

Topology optimization is the first thing that comes to mind when we start exploring a new design space using the additional design freedoms enabled through additive manufacturing. The optimum results given by topology optimization becomes readily available for the additive manufacturing process. Using the Generative Design Explorer app, CATIA’s geometry creation/reconstruction capability is combined with the finite element solver of Abaqus, effectively enabling the adaption of topology optimization for additive manufacturing.

A unique capability in additive manufacturing is the ability to manufacture hollow structures using small cells known as infill/lattice patterns. Most commonly used infill patterns include:

• Grid
• Honeycomb
• Rectilinear Extrusion Patterns
• Triangular Extrusion Patterns
• 3D Lattice Patterns

We are continuously expanding our solutions for lattice structure designs, and by using Tosca Structure it is possible to increase the stiffness of a sample beam type lattice structure by 40% compared with a topology optimized structure of the same weight.

To design lattice structures, limitations to the above methods exist. With topology optimization we obtain either a solid or a void over our design space and cannot take advantage of intermediate densities of lattice structures. With lattice sizing we are restricted to using beam type structures of fixed lattice sizes and beam angles. To address these limitations and enable intuitive lattice designs and equivalent material behavior calibration, we use a multiscale topology optimization approach.

#### Multiscale Topology Optimization Approach

Let’s first understand equivalent material properties of lattices in the macroscopic sense. For this we have developed an Abaqus micromechanics plugin for material homogenization (Figure 1).

This plugin provides functionalities including linear/nonlinear thermal and mechanical material upscaling/downscaling, periodic/non-periodic boundary conditions, post processing, etc.

We can use the micromechanics plugin for infill homogenization to explore the infill pattern and void ratio, create heat maps, and analyze resultant structure performance under in-service conditions in a multiscale aspect. In addition, based on homogenized material properties for different infill/lattice densities from the micromechanics plugin, we can interpolate lattice behavior and perform topology optimization to generate density distribution over the design space.

Running Shoe Design: Additive Manufacturing for the Sole

Let’s illustrate this idea by using a shoe sole design scenario. Running shoes affect the entire body and are considered the most valuable piece of equipment for runners. Critical factors must be considered in the design of each shoe: shock absorption, flexibility, fit, traction, sole wear, breathability, weight, etc. Today, additive manufactured lattice shoe soles are gaining attention from almost every leading sports shoe manufacturer.

Abaqus/CAE can be used to generate the unit cell Representative Volume Element (RVE) models of any intuitive lattice design (Figure 2). The unit cell RVE models can then be imported into the Abaqus micromechanics plugin. This plugin handles periodic boundary conditions in an automatic manner and solves for homogenized material properties and stiffness matrices.

Homogenization can be performed for various infill densities, and validation can be done on simple geometries such as an enclosed square box with latticed core. The geometric models are then compared with non-geometric models applied with homogenized material properties.

We validate the homogenized structural response of a grid extrusion infill pattern against a geometry based model (Figure 3). Although the geometric model shows more roughness in the stress result due to geometric discontinuity, the magnitude of the stresses corresponds well.

The homogenized material properties for different infill/lattice densities can be used to construct a polynomial function up to the 4th order. Tosca topology optimization is enhanced to support the polynomial for material interpolation. This enables optimum design generations with intermediate lattice density distribution, as shown in Figure 4.

We can apply single or multiple loads to the topology optimization. For example, a mapped pressure load can be used to represent static loading of an average human’s weight and a bending load can be used to represent the resistance to push off. Tosca supports a clustering design condition and is used to generate the same density for a cluster of elements.

In this example, we clustered element groups through the vertical direction/infill extrusion direction. Tosca topology optimization iterates to find the maximized stiffness structure with a reduced weight target. Iteration by iteration, this optimization yields intermediate relative density distributions. It is found that the maximum density region in an optimum design does not always correspond to maximum load location. Therefore, the topology optimization is useful to determine the most effective material to use. The relative density/material stiffness distribution can then be used to reconstruct optimum geometries with matching lattice patterns, as shown in Figure 5.

We have explained how to design and optimize materials for lattice structures. Another key aspect of material calibration for Additive Manufacturing is the printing process. How to characterize and calibrate material properties during the process simulation is essential to capturing the correct part behavior.

Part 3 of this blog post will address the additive manufacturing printing process and how to address key material calibration challenges. Stay tuned!