Topological and Structural Design of Optimized Lattice Models for Mechanical Simulation and Applications in Mechanobiology

Numerical simulations represent a powerful tool for supporting scientific research by adopting the best knowledge from engineering disciplines such as computer science, numerical analysis, and computer graphics. The current computational technologies enable the development of interactive and collaborative design workflows, based on the simulation of multiple scenarios (what-if approach), and the possibility of implementing iterative optimization cycles in acceptable response times with affordable costs. Mechanical simulation for engineering applications is principally founded on mesh-based approaches as Finite Element Methods, for studying the behavior of deformable solids, and Computational Fluid Dynamics for analyses on fluid domains. An interesting research field is currently represented by the simulation methods based on discrete elements approaches, and in particular by Lattice Models, which typically demonstrate a high potential when dealing with large deformations and topological changes as plasticity or fracture. The principal focus of this Ph.D. thesis is the investigation of the possibility to employ lattice modelling approaches to study the mechanical responses at mesoscale of highly deformable elastic objects. This choice was made to exploit the main advantages offered by this class of methods, i.e. a fast and stable formulation capable of providing approximate solutions in reasonable times (and often near real-time) with a pre-defined level of accuracy. These features are ideal for analyzing parallel design configurations at a glance or to implement advanced optimization algorithms in which the fundamental parameters of the simulations are continuously perturbed until reaching a specific goal. The main idea behind this thesis work is to create and test novel simulation frameworks based on discrete lattice models, to be adopted in early design stages for the conceptualization of a particular embodiment or for the preliminary screening of multiple solutions, in order to filter and identify suitable design configurations to be further validated, in a subsequent phase, into rigorous FEM environments or by experimental testing procedures. The general principles of discrete lattice models were deeply analyzed, and different strategies to generate homogeneous, isotropic, and conformal topologies for optimized networks of elastic elements to model deformable surfaces and volumetric objects, were proposed and discussed, thus contributing to the minimization of the variability associated to mesh-dependent mechanical responses. In parallel, a set of topological metrics to assess the overall quality of a specific deformable lattice was defined, along with a series of design guidelines for optimal lattice models generation. Moreover, a series of trials for implementing complete lattice model frameworks into CAD environments were performed, with the aim of creating interactive design workflows. The proposed frameworks were tested and validated on a set of relevant case studies, in the fields of advanced biomedicine and mechanobiology. In detail, lattice spring models were employed to contribute in the understanding of the relationships linking external mechanical stimuli and adaptive biophysical responses of living cells, by extracting the elastic constants of subcellular components in mesenchymal stem cells adhered to a flat substrate. This work started from a series of experimental campaigns conducted in collaboration with researchers from Max Planck Institute for Medical Research, Heidelberg, and from CNRS, Grenoble. In another case study, wireframe-based lattice beam models were adopted to conceive a complete interactive workflow for the modelling and the mechanical simulation of customized biomimetic porous implants to be employed in the field of regenerative medicine. At last, a series of support activities for experimental procedures were carried out. The design and the nanofabrication of a set of rigid substrates presenting variable curvatures, with the aim of assessing the response of adhered mesenchymal stem cells in terms of differentiation to a specific phenotype, were carried out. Moreover, the design of an electro-mechanic cyclic loading device necessary for assessing the response of adhered mesenchymal stem cells to specific mechanical stimuli, in terms of maximization of newly formed bone tissue, was performed. From the present thesis work emerged that lattice models should be considered as a class of powerful methods, characterized by a simple numerical implementation and a fast and stable response, to be effectively adopted in preliminary design phases, or within numerical optimization algorithms, or for the interactive study of highly deformable materials and porous lattices, often present in advanced biomedical applications. The principal results of the research reported in this Ph.D. thesis were published in scientific journals and presented in international conferences.