PSI - Issue 42

Manuel Sardinha et al. / Procedia Structural Integrity 42 (2022) 1098–1105 Manuel Sardinha / Structural Integrity Procedia 00 (2019) 000 – 000

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2.1. Mechanical behavior of NPTs Relevant research has been carried out towards a better understanding of the mechanical behavior of NPTs [1], [2]. Contrary to PTs, for which damping, and stiffness behavior is deeply related with the air pressure inside the wheel, in NPTs, this will be associated with the internal geometrical structure of the wheels, and more specifically but not exclusively, of its spokes design space and shear ring. These annular sections can be better understood by a type of circular beam, which core is usually composed of a relatively low modulus elastic material or structure. Load-bearing capacity is one of the most important factors in the design of these tires, which can be characterized by the relative displacement between the hub and the tread of the wheel [3]. This characteristic will not only directly affect the rolling resistance of the tire, but also the total energy consumption of the vehicle. The great majority of energy loss from tire rolling resistance comes from repeated changes in the shape of the tires as they roll [4] [5]. Reports in the literature state that, if carefully designed, NPTs grounding pressure and rolling resistance could be one of their main advantages [6]. Additionally, a major searched-for tire characteristic is its life expectancy, commonly evaluated through its fatigue behavior, which is deeply influenced by the three core variables of design theory, i.e., the geometry, the manufacturing process, and the materials it is made of. To characterize the life cycle of NPTs, fatigue and fracture mechanics are not only fundamental but can also assist in the estimation of product reliability and vehicle safety requirements. Even if these are the basic mechanics of tire functional design, the advent of more difficulty-defined load scenarios such as tire-slipping, braking, sudden direction shifts, and tire inclination (notably in two-wheel vehicles), implies that the NPTs design process should be equally concerned with radial, longitudinal, and transverse mechanical response, and the spokes or cellular structures that compose the cores of its rings, with both in and out of-plane behavior [7], [8]. 2.2. Common NPT design characteristics Both the shear ring and the spokes design space have been the major, and almost exclusive, research focus concerning NPTs design proposals. Fig. 2 (a) and (b) show two of the most common types of structure found in the literature. Fig. 2 (c) demonstrates an example of a parallelogram grid with in-phase cellular rings occupying the spokes design space, and a graded cell size from outer to the inner radius.

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Fig. 2. Common unit cell structures found in NPTs research with main design parameters identified. (a) Auxetic structure example; (b) Hexagonal honeycomb structure example; (c) Examples of spokes design space composed by a parallelogram grid of in-phase cellular rings. Adding to classical structural compositions, reports can be found with NPTs containing more intricate cellular structures. Examples of researched structures relevant for NPTs composition are solutions containing triply periodic minimal surfaces (TPMS) [9], functionally compliant [2], [10] or functionally graded-based solutions [11], bio inspired cell designs [12], [13], or even non-phased cellular rings and grid-based designs [14].