Achieving Damage Tolerance via Inhomogeneity and Nonlocality through Ultra-Cellular Materials

Abstract

Cellular materials find several industrial applications as engineered materials due to their outstanding specific mechanical properties, such as specific stiffness under bending and compressive strength. These features enable the attainment of lightweight structures with several potential benefits in e.g. aerospace, automotive and wind energy production. However, cellular materials and structures are typically quasi-brittle and can suffer from severe failures. As a consequence, increasing the damage tolerance without penalizing the strength and stiffness significantly has been the subject of intensive studies in recent years. The formulation of a general approach to increase the damage tolerance of cellular materials lies at the heart of the present work. To achieve this goal, two concepts are explored in this work: (1) non-locality realized by combining lattices featuring multiple length scales and (2) inhomogeneity which is achieved by combining stretch and bending dominated lattices. This new type of cellular material is called here Ultra-Cellular Material (UCM). It combines two or more representative periodic structures characterized by their topologies along with multiple characteristic length scales. UCMs are designed to improve the fracturing behavior compared to conventional cellular materials while maintaining a good balance between stiffness, strength, and toughness. Towards this goal, a study on 2D regular lattices is conducted first to fully understand the mechanical behavior of different types of lattices and to set a performance benchmark for UCMs. Secondly, since the study focused on the case of a lattice made of quasi-brittle materials, the traction separation law was implemented to determine material properties and to mitigate the sensitivity to element sizes.In addition, finite element models are developed to perform the comprehensive analysis of its mechanical response from linear elastic behavior to ultimate failure. The comparison of damage tolerance between conventional and UCMs are estimated in terms of their force-displacement curve performance, toughness, size effects due to boundary layers, fracture energy and crack sensitivity. To evaluate improvement in damage tolerance, the unloading tests are conducted to obtain the toughness of the lattice; lattice panels are test at different size to examine the free-edge effects on mechanical properties and the type II size effect were applied to evaluate the fracture energy. Since the provided size of lattice panel has not attained the region of linear elastic fracture mechanics (LEFM) yet, the Bazant size effect law is adjusted and implemented to approximate the fracture energy accordingly. The analysis results show that the UCM gained an increase in specific toughness by 23 times with no measurable penalty in specific peak load and only 0.3% drop in specific stiffness compared to the conventional regular triangular lattice. Moreover, the UCM exhibited less sensitivity to the free edges effect and to the central crack compared to its component lattices (triangular and hexagonal lattice).