Simulations techniques for lattice structure design

Lattice structures are widely used in nowadays industries in combination with additive manufacturing technology to obtain components with a limited weight and tuneable mechanical properties. However, industries still find challenging a complete implementation of these metamaterials in the product development due to the complexity given by an accurate prediction of the mechanical and fatigue properties. To overcome this limitation, analytical and numerical techniques are developed, to help designers to achieve the desired performances. Finite Element simulations are a common tool utilized in this sense, where solid models can provide accurate results. Nevertheless, the implementation of this technique requires high computational costs, often not compatible with an iterative design process where versions of the component are constantly updated considering the feedback provided by actors having different backgrounds and product interactions. Accurate and computationally efficient simulations strategies are thus required. The proposed thesis investigates three possible simulations ideas able to describe the mechanical properties of the lattice-based components. Two main properties are studied: the lattice structure elastic behaviour, which is important to determine the in-service behaviour of the designed component and the fatigue resistance, which defines the component service duration. Homogenization technique is the first numerical method analysed and it is pivoted on the idea of substituting the intricate lattice geometries with a solid fictitious material displaying the same elastic properties. In this framework, a case study is analysed, where the design process of a total hip replacement prosthetic device is developed. The workflow starts with a preliminary experimental campaign on lattice specimens with the aim of determining the printing quality, the mechanical properties, and the biological characteristics. In this phase, a verification of the homogenization predictions is performed. On this base, the best specimens’ configurations are selected to design and manufacture the prosthetic device. The second simulation technique leverages on the observation of the onedimensional nature of the strut-based lattice structures. Lattice structures’ behaviour can thus be simulated through the usage of truss and beam elements, depending on the stretching or bending dominated nature of the lattice topologies. Based on this observation, two different paths are followed, the first one aiming to improve the fatigue life of lattice components by acting of their orientation in the printing chamber. It is known that printing orientation influences the surface quality of the components and, in lattice struts this effect can be directly linked to a variation in the fatigue life. An optimization algorithm is thus developed, aiming to optimize the fatigue resistance of the manufactured components. Following this idea, a control and an optimized lattice batch are printed and an improvement in the fatigue resistance is found, even if not as large as expected by the simulations. Improvements in the predictions can be observed if the as-build geometry of the struts is considered. The second path is devoted to the computation of the corrective coefficients able to properly describe the elastic properties of bending dominated lattice structures. One-dimensional simulations are normally too severe for bending dominated lattice topologies, and a compensation has to be provided to match the elastic properties calculated trough computational efficient beam models and lattice ones. To address this problem, an optimization routine is developed, where the compensation factors are computed comparing the elastic properties of the beam models and a homogenised solid model taken as reference. A benchmark testing between the beam model, - built with the so computed compensation coefficients - a homogenised, and a solid model is developed. Compensated beam models are found to be able to improve the predictions of lattice structures elastic properties if compared to the homogenization techniques, showing a comparable computational time. Nevertheless, a reduced accuracy is found in presence of dense lattice structures, where the hypothesis of one-dimensional is weaker. The third analysed simulation method aims to obtain a precise fatigue life estimation at the expense of computational time. Starting from an as-build geometry reconstructed trough CT-scan analysis, a finite element simulation built with solid elements is performed. To reduce the computational cost, an innovative finite element theory is adopted, the Finite Cell Method. A two-step simulation is performed, and thanks to the usage of the average strain energy density method, the fatigue life estimation can be obtained. An excellent agreement is found; however, a complete validation is required for this method before its safe implementation in the design process.