Characterizing the complex shear modulus of materials with an iPhone

Abstract

Dynamic mechanical analysis (DMA) is a technique that accurately measures the mechanical properties, such as stiffness and damping, of a material as a function of frequency, temperature, and time. However, DMA is expensive, requires significant training to operate, and must be performed on-site, lending itself impractical for hands-on classroom activities or research during the early stages of a global pandemic. To characterize the complex shear modulus of seagrass during the COVID-19 shelter-in-place order in May 2020, an iPhone XS Max was used as the tail mass of a freely oscillating torsional pendulum. The Vibrations application (Diffraction Limited Design, LLC) acquired the angular velocity of the underdamped system during oscillation, and the damped natural frequency and decay rate were later extracted from the time series. By measuring the cross-section and length of the material under test, the natural frequency and decay rate were used to determine the complex shear modulus. A strip of 1-cm-wide polyethylene film (McMaster Carr #85655K13) was first used to test the measurement technique. iPhone-obtained shear modulus of the strip was within the range of tabulated values, and was in agreement with DMA-obtained shear modulus measured after COVID-19 restrictions were relaxed. Uncertainty analysis and instructional applications will be discussed.