Additive Manufacturing (AM) is used to build models, prototypes, tooling, and produce parts in plastic, metal, ceramic, and composite materials. Its advantages are derived from the additional design freedoms gained that allow novel complex geometries to be realized at little additional manufacturing costs and reduced product weight. The dimension of typical additive manufactured parts may be on the order of hundreds of millimeters. Yet there are lattice structures designed at micrometer scale and important physical transformations that occur at nanometer scale. To address the dilemma of scales, multiscale approaches are essential to capture accurate material behaviors.
With an entire new universe of design possibilities free of conventional manufacturing constraints such as forging, casting and stamping, computer aided design and optimization become efficient tools for product designers. Topology optimization, which is a mathematical approach to optimize material layout within a given space, is well established and well suited for designing AM parts. The optimum results given by a topology optimization becomes readily usable for an additive manufacturing process. The Generative Design Explorer app that combines the geometry creation/reconstruction capability of CATIA with the finite element solver of Abaqus was developed which enables effective adaption of topology optimization for additive manufacture.
Manufacturing Hollow Structures
A unique capability of additive manufacturing is the ability to manufacture hollow structures using small cells known as infill/lattice patterns. Commonly used infill patterns include grid, honeycomb, rectilinear and triangular extrusion patterns, as well as 3D lattice patterns. Tosca lattice sizing optimization generates optimum lattice structures with much higher stiffness compared to topology optimized structures with the same weight. Models of initial lattice structure designs can be created using an Abaqus plugin that generates lattice structure models using beam elements from a solid mesh, or alternatively can be created from lattice software such as nTopology Element, translated into Abaqus format with a python script. Tosca sizing optimization optimizes the radii of the beams and the optimum result can be converted back to nTopology Element for manufacturable geometry reconstruction. In order to further design and explore a more complete library of lattice microstructures that may be not representable by beam structures and address limitations of lattice sizing for lattice sizes and angles, the Tosca topology optimization is enhanced to design for intermediate densities in a multiscale approach. We explain the steps to realize topology optimization for intermediate densities.
The first step is to understand equivalent material properties of lattices in the macroscopic sense. The Abaqus micromechanics plugin was developed for material homogenization (Figure 1). The plugin provides functionalities including linear/nonlinear thermal mechanical material upscaling/downscaling, periodic/non-periodic boundary conditions, post processing, ABD matrix generation for shell like structures and etc. The micromechanics plugin can be used 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. Moreover, based on homogenized material properties for different infill/lattice densities from the micromechanics plugin, we can then interpolate lattice behavior and enable topology optimization to optimize material layout for intermediate density.
Let’s illustrate the idea on a shoe sole design problem. The sports shoe industry has undergone dramatic growth in recent years. For instance, running shoes affect the entire body, and consequently are considered the most valuable piece of equipment for runners. Efforts to meet this concern are further multiplied by the critical factors to be considered in the design of each shoe: shock absorption, flexibility, fit, traction, sole wear, breathability, weight, etc. Additive manufactured lattice shoe soles are gaining attention from almost all of the leading sports shoe manufacturers today.
Abaqus/CAE can be used to generate the unit cell RVE models of any lattice designs. Figure 2 shows CAE models of some of the extrusion lattice patterns that cannot be represented using beam elements. The unit cell RVE models can be imported into the Abaqus micromechanics plugin. The plugin handles periodic boundary conditions in an automatic manner for consistent and inconsistent mesh on opposite faces. It then solves for homogenized material properties and stiffness matrices.
The 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 can be compared with non-geometric models applied with homogenized material properties. We validate the homogenized structural response of a grid extrusion infill pattern against geometry based models (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 of up to 4th order. Tosca topology optimization is updated to support the polynomial for material interpolation. This enables optimum material layout designs with intermediate lattice density distribution.
Apply Single or Multiple Loadings
We can apply single or multiple loadings to the topology optimization. For example, mapped pressure load can be used to represent static loading of an average human’s weight and bending load can be used to represent the resistance to push off. Clustering design condition is also supported by Tosca and can be used in order to generate the same density for a cluster of elements. This is not a necessary constraint but may be desired for certain designs. In this example, we clustered element groups through the vertical direction/infill extrusion direction. Tosca topology optimization iterates to find maximized stiffness structures with a reduced weight target. The optimization yields intermediate relative density distributions, iteration by iteration. It is found that the maximum density region in an optimum design does not always correspond to maximum load location. The topology optimization is useful to determine the most effective way of material use. The relative density/material stiffness distribution can be used to reconstruct optimum geometries with matching lattice patterns.
We can also use Tosca topology optimization to help us design the lattice microstructure/unit cell. We start with a complete filled unit cell model applying periodic boundary conditions using the micromechanics plugin and typical in-service loadings by prescribing far field strains. In order to prevent homogeneous stress fields, we create a globally inhomogeneous density map (Cycle 0 in Figure 4).
We can use weighting factors or maximize the minimum of energy stiffness measures or strain energy to account for multiple loading cases. Design constraints can be applied, such as minimum member size and volumetric constraint. The whole process is illustrated in Figure 4. In this example, convergence is reached after 96 cycles. This procedure can then be combined with the previously explained optimization to obtain optimum density distribution.
At the same time, the mean-field homogenization method in Abaqus/Standard is also developed for multi-scale material modeling. Mean-field homogenization is based on a semianalytical model and, therefore, is computationally more efficient compared to the RVE approach in which the RVE is modeled with a finite element model. This approach has been used in the form of a user subroutine, and by incorporating this approach directly inside the Abaqus software, we provide the opportunities for users to adopt this approach without implementing the basic material model for each constituent on their own. Because of this, users are also able to scale
their model with high performance parallel computing, which enables large scale models to be analyzed with concurrent multiscale. With mean-field homogenization, we open opportunities for modeling chopped fiber reinforced polymers accounting for fiber orientation distribution during filament material extrusion process.
What to learn more about Dassault Systèmes’ simulation solutions for additive manufacturing? Visit: go.3ds.com/Print2Perform
