Multiscale mechanics and structural design of periodic cellular materials.

摘要

A periodic cellular material, also known as lattice material, is a periodic, reticulated micro-truss structure made up of a large number of elements; it is generated by tessellating a unit cell, composed of a small number of elements, in an infinite periodicity. Lattice materials are used to expand the properties of the solid material from which they are constructed to ranges of properties that depend on the lattice cell topology, besides the relative density, rho The development of lattice materials results in expanding the materials selection design space, thereby providing tailored materials for advanced engineering applications.;The work reported in this thesis aims at improving the current multiscale mechanics models as well as the structural analysis tools for the design of lattice materials.;Recent progress on this new family of materials has led to a classification which categorizes lattice materials into two groups, namely, bending dominated and stretching dominated. The former contains lattice materials that collapse by the local bending of their microscopic constituents, generating mechanical properties that are far from optimal. The latter includes lattice cell topologies that collapse by the stretching of their cell elements, giving a much higher stiffness and strength per unit mass. Despite this recent research advance in the understanding of the failure mechanics of lattice materials, important challenges need to be addressed. i) To date, the current approaches for modeling infinite periodic lattice structures are applicable to certain lattice topologies only. A robust, automated, analytical procedure to characterize the mechanical properties of a lattice material with an arbitrary microscopic topology is missing. ii) The strategy followed in literature to shape the cross-sections of slender cell elements into circular shapes, results in a local buckling failure of the lattice elements. To avoid this collapse, researchers have proposed to increase the cross-section size of the microscopic elements; this resistance increase, however, occurs at the expense of the material weight. iii) A stretching dominated lattice material offers mechanical properties that are remarkably better than a bending dominated material. Its structure consisting of fully triangulated topologies might yet contain several redundant members that bring about undesired extra weight as well as non-conformal and non-morphing structural behavior.