Homogenization of material properties in additively manufactured structures

• A two-stage approach estimates effective elastic properties in additive manufacturing.
• Implicit geometric model is combined with measured material property information.
• Mesoscale geometry–material model is computationally homogenized at macroscale.
• Efficient homogenization relies on integral equation formulated using Green function.
• Conjugate gradient is used to solve the symmetric and positive definite linear system.

Additive manufacturing transforms material into three-dimensional parts incrementally, layer by layer or path by path. Subject to the build direction and machine resolution, an additively manufactured part deviates from its design model in terms of both geometry and mechanical performance. In particular, the material inside the fabricated part often exhibits spatially varying material distribution (heterogeneity) and direction dependent behavior (anisotropy), indicating that the design model is no longer a suitable surrogate to consistently estimate the mechanical performance of the printed component.We propose a new two-stage approach to modeling and estimating effective elastic properties of parts fabricated by fused deposition modeling (FDM) process. First, we construct an implicit representation of an effective mesoscale geometry–material model of the printed structure that captures the details of the particular process and published material information. This representation of mesoscale geometry and material of the printed structure is then homogenized at macro scale through a solution of an integral equation formulated using Green’s function. We show that the integral equation can be converted into a system of linear equations that is symmetric and positive definite and can be solved efficiently using conjugate gradient method and Fourier transform. The computed homogenized properties are validated by both finite element method and experiment results. The proposed two-stage approach can be used to estimate other effective material properties in a variety of additive manufacturing processes, whenever a similar effective mesoscale geometry–material model can be constructed.