Simulation of anisotropic behaviour in additively manufactured structures using a curvilinear coordinate based finite element formulation

Abstract

The advent of additive manufacturing has profoundly transformed component production. However, anisotropic structural behaviour is frequently observed in additively manufactured components, despite the isotropic nature of the constituent materials. This behaviour can be attributed to the manufacturing process, which involves the extrusion and deposition of individual material paths or the powder-based melting of such paths. For example, fused deposition modelling is a common technique employed in the production of polymer components. Technological advancements have enabled the use of fibre reinforcement, which can further amplify anisotropic material behaviour.

Several computational models and approaches have been proposed for simulating and optimising additively manufactured components treated as an anisotropic continuum. Current methods rely on a finite element discretisation of the continuum, where the print paths are assumed to be linear within a finite element. However, since the print paths are essentially arbitrary curves, a fine discretisation is necessary to achieve realistic simulations.

In this work, we propose a curvilinear local approach, where the print paths at the element level are considered to be curvilinear. The fineness of the mesh used in this concept depends solely on the stress gradients that need to be resolved. Furthermore, curvilinear print paths represent the coordinate lines used to describe anisotropy. As a result, the solution to the balance of linear momentum occurs within the local curvilinear coordinate system. This paper presents the implementation of this approach within the finite element method, using an exemplary boundary value problem.