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<p>The Mechanics of Structural Genome (MSG) is a unified homogenization theory used to find equivalent constitutive models for beam, plate, and solid structures. It has been proven accurate for periodic structures. However, for certain applications such as non-prismatic wind turbine blades and helicopter flexbeams featuring ply drop-off, where there is no repeating structure and the periodic boundary condition cannot be used, MSG's accuracy is limited. In this work, we aim to extend MSG to find element stiffness matrices directly for aperiodic structures, instead of beam properties or three-dimensional (3D) solid material properties. Two finite elements based on MSG have been developed: Heterogeneous Beam Element (HBE) and Heterogeneous Solid Element (HSE).</p> <p><br></p> <p>For beam modeling, the beam-like structure is homogenized into a series of 3-node Heterogeneous Beam Elements (HBE) with 18×18 effective beam element stiffness matrices. These matrices are used as input for one-dimensional (1D) beam analysis using the Abaqus User Element subroutine (UEL). Using the macroscopic beam analysis results as input, we can also perform dehomogenization to predict the stresses and strains in the original structure. We use three examples (a prismatic composite beam, an isotropic homogeneous tapered beam, and a composite tapered beam) to demonstrate the capability of HBE and show its advantages over the MSG cross-sectional analysis approach. HBE can capture macroscopic behavior and detailed stresses due to non-prismatic geometry.</p> <p><br></p> <p>The Heterogeneous Solid Element (HSE) is developed based on MSG to model a heterogeneous body as an equivalent solid element using an effective element stiffness matrix. HSE modeling includes homogenization, macroscopic global analysis, and dehomogenization to recover local strains/stresses. HSE avoids the local periodicity assumption for traditional multiscale modeling techniques for composite structures that compute effective material properties instead. Abaqus composite solid element and MSG-based traditional multiscale modeling are used to validate the accuracy of HSE. All example results show that HSE is more accurate in predicting global structural behavior and local strains/stresses.</p> <p><br></p> <p>HBE and HSE provide a new concept for modeling aperiodic composite structures by modeling structures into equivalent beam or solid elements instead of beam properties of the reference line in 1D beam analysis or material properties of material points in solid structural analysis.</p>

<p>Extrusion Deposition Additive Manufacturing (EDAM) is a process in which fiber-filled thermoplastic polymers pellets get molten in the extruder and deposited onto a build plate in a layer-by-layer basis. The use of short fiber composite for EDAM has enabled large-scale 3D printing structures and tools for traditional composite manufacturing processes. Successful EDAM production critically depends on the understanding of the process-structure-property relationship. Especially on the bonding between the beads which is of paramount importance in additive manufacturing since it affects primarily the fracture and strength characteristics of the printed part. Bonding is influenced mainly by the temperature history and the contact between the beads. Both of which is dependent on the fiber orientation within the bead induced by the flow deformation that occurs according to the printing parameters. This study aims to investigate and model the complex relationship between the printing conditions and inter-bead bonding in the lateral direction.</p> <p>A framework was developed to facilitate this aim, and it contains a fusion bonding model that couples the time-temperature history and the bead-to-bead contact interface. Four deposition parameters were studied: the nozzle height, ratio of the print velocity to extrudate velocity, bead-to-bead spacing, and layer time. First, a deposition flow model was developed, utilizing the anisotropic viscous flow model and smooth particle hydrodynamic finite element formulation, to predict the fiber orientation state across the deposited bead and the bead-to-bead interface for the given set of deposition parameters. Next, the effect of printing conditions on the temperature history of the bead was discovered by utilizing the heat transfer process simulation in ADDITIVE3D. Third, the experimental characterization procedure for mode I fracture toughness in the lateral direction was developed, and the fracture toughness was characterized using linear elastic fracture mechanics principles. Lastly, the phenomenological model for non-isothermal lateral fusion bonding was characterized using the bead contact interface, temperature history, and fracture toughness properties. This work showed a comprehensive effort in fusion bonding modeling while also presented a valuable process-structure-property-performance relationship in EDAM.  Guidance on the selection of printing conditions and strategy can be made using the developed model to print higher-strength parts.  </p>