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This paper presents an elastodynamic analysis of two-dimensional time-harmonic elastic wave propagation in periodically multilayered elastic composites, which are also frequently referred to as one-dimensional phononic crystals, with a periodic array of strip-like interior or interface cracks. The transfer matrix method and the boundary integral equation method in conjunction with the Bloch-Floquet theorem are applied to compute the elastic wave fields in the layered periodic composites. The effects of the crack size, spacing, and location, as well as the incidence angle and the type of incident elastic waves on the wave propagation characteristics in the composite structure are investigated in details. In particular, the band-gaps, the localization and the resonances of elastic waves are revealed by numerical examples. In order to understand better the wave propagation phenomena in layered phononic crystals with distributed cracks, the energy flow vector of Umov and the corresponding energy streamlines are visualized and analyzed. The numerical results demonstrate that large energy vortices obstruct elastic wave propagation in layered phononic crystals at resonance frequencies. They occur before the cracks reflecting most of the energy transmitted by the incoming wave and disappear when the problem parameters are shifted from the resonant ones.
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Cracks in the System: Twenty Years of the Unjust Federal Crack Cocaine Law(2006): In the 20 years following passage of the Anti-Drug Abuse Act of 2006, many of the myths surrounding crack cocaine were dispelled, making it clear that there was no scientific or penological justification for the 100:1 sentencing ratio.
Whiplash typically occurs when your head is forcefully and quickly thrown backward and then forward. This motion can injure bones in the spine, disks between the bones, ligaments, muscles, nerves and other tissues of the neck.
Rarely, cracking your back causes a slipped disc, or upsets an existing one by irritating it or moving it in the wrong direction. You should exercise caution when cracking your back if you have an existing disc or vertebral injury as it could exacerbate your symptoms.
Urges to crack your back often could be the sign of an underlying cause that may require treatment. Cracking your back may give you temporary relief, but you should figure out the underlying cause and how you can treat it.
Cracking your back is similar to cracking joints such as your neck, shoulder, and fingers. The sound of your back cracking or popping may be due to air bubbles in the synovial fluid surrounding and lubricating your joints.
Measurements of physiological parameters such as pulse rate, voice, and motion for precise health care monitoring requires highly sensitive sensors. Flexible strain gauges are useful sensors that can be used in human health care devices. In this study, we propose a crack-based strain gauge fabricated by fused deposition modeling (FDM)-based three-dimensional (3D)-printing. The strain gauge combined a 3D-printed thermoplastic polyurethane layer and a platinum layer as the flexible substrate and conductive layer, respectively. Through a layer-by-layer deposition process, self-aligned crack arrays were easily formed along the groove patterns resulting from stress concentration during stretching motions. Strain gauges with a 200-µm printing thickness exhibited the most sensitive performance (442% increase in gauge factor compared with that of a flat sensor) and the fastest recovery time (99% decrease in recovery time compared with that of a flat sensor). In addition, 500 cycling tests were conducted to demonstrate the reliability of the sensor. Finally, various applications of the strain gauge as wearable devices used to monitor human health and motion were demonstrated. These results support the facile fabrication of sensitive strain gauges for the development of smart devices by additive manufacturing.
As the importance of smart industrial fields (e.g., human monitoring, the Internet of Things, and soft robotics) has increased in recent times, several state-of-the-art systems have been studied extensively to enhance their efficiency. Strain gauges have been widely used to detect human motion during exercise1,2 or talking3,4, as well as physiological parameters5,6,7, such as pulse rate, blood pressure, and respiration. Among various strain gauges featuring capacitive monitoring8,9,10, crack-based resistive layers1,3,5, and interlocking construction11,12, crack-based sensors containing resistive and flexible membranes have attracted significant attention owing to their facile sensing method and simple structure13,14.
The gauge factor (GF) of strain sensors, which can be calculated based on resistance changes and mechanical strain, is generally used to represent sensitivity4,34. Mechanical deformations caused by external stress open cracks on the metal surface, resulting in an increase in the electrical resistance19,35. In particular, to detect subtle signals such as pulse motion, low pressure (
Therefore, in this study, a highly sensitive crack-based strain gauge was fabricated through FDM-based 3D printing and metal sputtering technologies by generating a high density of self-aligned crack arrays with small strain. Figure 1 depicts the schematic concept of the proposed FDM-based strain gauge (FSG). For the flexible layer, thermoplastic polyurethane (TPU), which is known as a biocompatible material38, was prepared through 3D printing. In addition, a platinum (Pt) layer was deposited onto the substrate as a conductive layer, and then a prestretching process was used to induce initial crack propagation in advance. Because of the FDM printing method, metal membranes exhibited identical specific groove profiles on their surfaces. Therefore, due to stress concentration, a dense array of cracks was easily formed along the patterns by applying a small strain, which led to a high GF. The fabricated bilayer composite enabled sensitive strain detection through highly aligned cracks. The sensitivity of the flexible FSG was compared for different printing thicknesses, and the characteristics of the cracks generated were also compared. In addition, sensing reliability was demonstrated through structural analysis and transient cycling tests. The 3D printing technology-based manufacturing process is easily applied to prepare various wearable devices that contain strain gauges by simply depositing a metal layer onto the dominant bending area. The findings of this study will facilitate facile fabrication of highly sensitive strain gauges that can be applied to wearable devices for health monitoring and motion detection.
Because the GF and recovery time improved as the printing resolution (thickness) decreased, FSGs printed with a resolution below 200 μm showed enhanced GF and recovery time. To investigate the minimum printable resolution, a TPU substrate was printed with 100-μm resolution and compared with other substrates, as shown in Fig. 5b. Compared to the uniform and regular groove patterns seen on substrates printed with 200, 300, and 400-μm resolution, the TPU substrate with 100-μm resolution showed an irregular surface profile. In addition, a comparison of top-view images for the 100-, 200-, 300-, and 400-μm TPU substrates showed incomplete features on the 100-μm TPU substrate (see Figure S1(a) in Supplementary Information), which indicated unstable printing resolution in the FDM printing method used to generate crack-based FSGs. Although the digital light processing (DLP) printing method was used to manufacture a substrate with a smaller printing resolution (25 μm), the substrate was not flexible and showed a relatively smooth surface without groove patterns due to the characteristics of the DLP method, as shown in Figure S1(b); hence, DLP was not appropriate for creating FSGs. Therefore, the minimum printable resolution of 200 μm was selected as the optimal condition for sensitive strain sensors and further analysis, including application examples.
a top and b tilted view of 2-FSGs and enlarged views; d top and e tilted views of a crack along a groove pattern; c top view of the flat-type strain gauge and an enlarged view f
a direct 3D printing of a customized finger glove substrate; b structural details of the double-ring-shaped band; c plasma treatment and Pt sputtering for cleaning and metal deposition processes, respectively; and d wire connection and detection of various finger motions by simply wearing the device
Table 1 shows a comparison of device characteristics, including materials, fabrication method, recovery time, GF, and corresponding strain range, applicable to the present work and previous studies. Compared to chemical synthesis3,4,13 and photolithography16,17, the formation of self-aligned cracks on a flexible substrate was more easily realized using a 3D printing method without complicated manufacturing processes. In addition, the use of 3D printing technology has the advantage of directly printing customized 3D-shaped substrates, which can be used for finger gloves, wrist bands, and masks where curved surfaces are required, rather than simple rectangular and planar substrates2,7,15,20. Although a high GF (2000) in a small strain range was achieved through advanced prestretching3, it was noteworthy that the crack-based strain gauges developed in this study exhibited sufficiently high GFs with faster recovery times compared to other devices1,5,16, thus supporting real-time monitoring applications.
In 2015 and 2016, Apple Inc. received and objected to or challenged at least 11 orders issued by United States district courts under the All Writs Act of 1789. Most of these seek to compel Apple "to use its existing capabilities to extract data like contacts, photos and calls from locked iPhones running on operating systems iOS 7 and older" in order to assist in criminal investigations and prosecutions. A few requests, however, involve phones with more extensive security protections, which Apple has no current ability to break. These orders would compel Apple to write new software that would let the government bypass these devices' security and unlock the phones.[3]
