Continuum Elastic and Fracture Response of Low-Frequency Resonant Microstructured Media to Impact Loading

Metamaterials are defined as microstructured media, which demonstrate overall properties that are not normally observed in nature. Novel metamaterial designs can break the limitations of conventional materials, e.g., difficulty of being simultaneously wave attenuating and stiff. We analyze the time domain response of a low-frequency resonant ceramic metamaterial design to high strain loading conditions. The asynchronous spacetime discontinuous Galerkin (aSDG) method is used for continuum solutions. We compare the response of metamaterial with monolithic slabs and other microstructured designs (e.g. hollow unit cells) in terms of stress wave mitigation, peak load retardation, and suitable energy transfer metrics. The advantages of the metamaterial design will be demonstrated for different geometry (number of cells) and loading. Furthermore, we extend the comparison beyond linear regime by considering material failure as high amplitude stress wave passes through the slab. Continuum damage and phase field models are used to computationally represent material failure. Overall, metamaterial slabs show better response in delaying and reducing the peak of stress wave compared to other designs considered. We observe a distributed failure response, as opposed to spall fracture reported for monolithic designs. Furthermore, the stress wave amplitude decreases even further for the metamaterial design when material failure is considered. Finally, the uses of this accurate but computationally expensive continuum model for fine-tuning the parameters of a very reduced order model (ROM), based on discrete representation of a grid of metamaterial cells will be briefly discussed.