Modelling of sparse lightweight composite structures using a geometrically discontinuous approach

Carbon fibre reinforced polymers (CFRPs) enable lightweight, high-performance, sparse designs. The sparsity of these composite structures amplifies their complex behaviour, creating a challenging mechanical response landscape. We present a model for an additively manufactured, wound CFRP truss structure composed of connection points ("anchors") and one-dimensional members ("strings"). Anchors are attached to an external surface undergoing assumed deformation. Given the high stiffness contrast, anchors are treated as rigid volumes connected by one-dimensional strings. For the material model of the strings, we rely on a geometrically nonlinear (finite deformation), bimodular elastic formulation. Connectivity information, between strings and anchor volume, translates to a mesh layout consisting of topologically one-dimensional cells, with facets representing the anchor volume's centre points. Additionally, offsets of start- and end points of the strings from the centres are incorporated. Those are superimposed via discontinuous parameters, allowing for the freedom to model multiple strings on a single (topological) anchor point, while allowing each (geometrical) end point to be placed individually.
The analytical description results in a continuous formulation of the strain energy, derived by Tangential Differential Calculus (TDC) , with both displacement and rotational degrees of freedom. In conjunction with symbolic automatic differentiation, this facilitates the seamless integration of higher-order approximations and complex geometrically and/or materially nonlinear behaviour. We discuss the handling of discontinuous geometry and non-standard mesh layouts, followed by numerical tests using the open-source FEM framework, FEniCSx.