Linear and Nonlinear Mechanics of Lattice Materials : Computational Modelling and Experiments

Abstract: Lattice materials are artificial materials made of repeating unit-cells. The internal architecture of these materials can be engineered for a specific application such as energy absorption, heat transfer, or acoustic damping. The advancements in additive manufacturing have enabled the design and fabrication of lattice materials with complex geometries, but the lack of understanding about their mechanical performance has limited their application. This thesis investigates the mechanics of lattice materials via numerical simulations and mechanical tests. We start with development of a discrete homogenization scheme for the elastic analysis of lattice materials with arbitrary level of complexity. Next, the method is extended to a continuum elastoplastic homogenization and accompanied with the theory of critical distances to assess the low cycle fatigue behaviour of lattice materials. Following that, the model is coupled with continuum damage mechanics to mimic the fracture initiation of the material unit-cell under quasi-static loads. The proposed model is calibrated using tensile tests, leading to a defect-informed numerical model that accommodates the manufacturing imperfections. Following this, an environmentally assisted failure known as hydrogen embrittlement is studied by incorporating hydrogen failure mechanisms into elastoplastic homogenization model. In the next step, numerical simulations and compression tests are employed to analyze the mechanical coupling and elastic anisotropy in the so-called non-regular tetrahedron lattice. The results show a good correspondence but the periodicity assumption in computational homogenization –mimicking an infinite cell number–should be considered when comparing numerical results with the data obtained from real samples. To capture the size effect, as the final step, we develop a homogenization scheme based on strain-gradient elasticity. The model is verified using numerical and experimental three-point bending tests and has shown to be more precise compared to classical elasticity. The methodologies proposed in this thesis are generic and can be used as guidelines for design of micro-architectured materials.