Global-LocAl two-level Multi-scale optimisation strategy accOUnting for pRocess-induced Singularities to design Variable Stiffness Composites – GLAMOUR-VSC

Variable stiffness composites (VSCs) from additive manufacturing (AM) process are fundamental for applications requiring lightness and high performances. VSCs are obtained by placing fibres along curvilinear paths within a given topology. However, general design strategies integrating the physical responses involved at the different VSC scales and the AM process requirements are still lacking in the literature. In particular, the available design methodologies rely on many simplifying hypotheses on both the VSC stacking sequence and the fibres-path within each ply to get target macroscopic properties, which are difficult to be correctly formalised. Moreover, to get manufacturable solutions, a time-consuming post-processing phase is required to adjust plies fibres-path to satisfy the technological restrictions related to the AM process. This project proposes a new paradigm in the multi-scale modelling and design of VSC structures. The idea is to formulate the design problem in the most general sense, without introducing simplifying hypotheses neither on the VSC laminate stacking sequence nor on the fibres-path shape within each lamina. Therefore, the goal is to develop a general theoretical framework and a pertinent multiscale modelling strategy, which will be integrated into a design methodology aiming at optimising, concurrently, the topology and the anisotropy field descriptors of the VSC structure, and capable of accounting for the main manufacturing requirements and process-induced imperfections.
To achieve this goal, the proposed methodology relies on:
1.The polar formalism extended to higher-order equivalent single-layer (HOESL) theories; in this context, the polar parameters (PPs) are used to describe the macroscopic anisotropic behaviour of the VSC;
2.The global-local multi-scale two-level optimisation strategy (GL-MS2LOS), based on PPs to describe both global and local design requirements (DRs);
3.The non-uniform rational basis spline (NURBS) entities to describe the topology, the PPs fields of the VSC structure and the fibres-path within each ply;
4.The solid isotropic material with penalisation (SIMP) approach based on NURBS entities (NURBS-based SIMP method) to perform the topology optimisation (TO) of the VSC;
5.The layer-wise (LW) kinematical model to predict the failure modes occurring at the VSC mesoscopic scale.
In the context of the GL-MS2LOS, the design of the VSC structure is split in two sub-problems. The first-level problem (FLP) aims to determine the optimum distribution of the variables describing the anisotropy and the topology of the VSC at the macroscopic scale. At this level, the VSC is modelled as an equivalent homogeneous anisotropic continuum whose behaviour is described in terms of PPs in the framework of HOESL theories. Both the topology and the PPs fields are represented through NURBS entities and the AM process requirements are formalised as equivalent constraints on the PPs fields and on the topological variable. Local DRs of the VSC structure are introduced in the problem formulation through a suitable GL modelling strategy. The second level problem (SLP) aims to determine an optimum lay-up (in terms of fibres-path in each lamina) matching the FLP results. The generic ply fibres-path is described through a NURBS surface. The SLP formulation is coupled with a GL modelling strategy, based on LW theories to assess, for the most critical regions of the structure, local failure mechanisms, which cannot be described during the FLP. Modelling activities are complemented with experimental and fabrication tests whose aim is twofold: to investigate the influence of the process parameters on the singularities and defects; to identify the main failure mechanisms of the VSC structure and to validate the proposed design approach. The main outcome of the project is the development of a new family of structural solutions (VSCs obtained by AM) characterised by a significant mass reduction and reduced costs.