Constitutive Relation for Prolate Pin–Reinforced Transversely Isotropic Media for Additive Manufacturing

Layered composites are found in the natural environment; they have inspired a variety of engineering structures and become critical to lightweight transportation vehicles. Layered composites are strong within layers but often suffer from delamination and failure in tensile loading across layers. Reinforcement of layered composites in the weaker directions is often critical to reduce interlayer failure and improve performance but retain transversely isotropic properties. Material extrusion additive manufacturing, which assembles parts in sequentially stacked layers, suffers from weaker interlayer bonding failures similar to layered composites. In this work, material extrusion produced structures are modeled as transversely isotropic and reinforced with cross-layer pins, assumed to be prolate inclusions. Previous analytical methods have derived bounds on material mixtures of constituents, which can be adjusted and applied to the target structures. This study adapts prior analytical models for reinforced composite constitutive relations using the well-established eigenstrain method to a transversely isotropic matrix with isotropic pin reinforcements aligned in the less stiff direction of the matrix. This is a change in the matrix material from prior models. A parametric variation is performed of the impacts of material choice and pin aspect ratio. The results showed improvement in the reinforcing direction with muted impact on moduli in other directions, which supports the intended design goal. The discovered formulation is numerically perturbed for a variety of material mixtures and inclusion aspect ratios, showing a significant impact of inclusion aspect ratio on the interlayer elastic modulus but a minor impact on shear moduli and in-layer elastic modulus. These findings are useful for the design of reinforcing geometries for additively manufactured parts and composite parts where transversely isotropic matrix materials occur.