Mechanical characterization of constrained soft materials via nonlinear vibrations

Soft materials such as gels and elastomers have widespread applications in robotics, biomedical engineering, and the food industry. Traditional mechanical characterization methods such as uniaxial tension/compression and rheometry cannot work in-operando or track the internal stress build-up and geometric changes of the materials due to environmental stimuli. Vibration-based methods with non-contact sensing techniques can achieve high-throughput measuring to monitor the evolution of mechanical properties and internal stresses of soft materials. However, vibration characteristics depend not only on mechanical properties and internal stresses, but also on the geometry of the samples and boundary conditions. This work demonstrates the use of nonlinear vibrations to simultaneously identify the geometry, mechanical properties, and internal stresses of constrained soft structures. This novel mechanical characterization method utilizes nonlinear transient vibrations and the corresponding amplitude-dependent frequency (backbone) curves. The method is demonstrated on clamped PDMS and gelatin disks. Linear and nonlinear vibration tests (frequency sweeps and nonlinear resonance decay) via laser vibrometry are performed on the disks and vibration characteristics are obtained; e.g., modal frequencies and stiffening coefficients due to nonlinear kinematics. These experimental vibration characteristics, when fitted with an FE model, deliver the thicknesses, Young's moduli, and internal stresses of the disks. For experimental fitting, a global surrogate model-based optimization algorithm is used. The proposed method successfully monitors the dehydration-induced changes in internal stresses as well as thicknesses and constitutive properties of the gelatin disks. The use of nonlinear stiffening responses facilitates the unique mechanical characterization of the disks and eliminates the need for independent monitoring of the full sample geometry. Potential applications of the method will be in the continuous high-throughput monitoring of bioactuators, engineered tissues, and products in the biofabrication and food industry.