Optimization-based design of an elastostatic cloaking device

Abstract

We present a new method for the design of devices to manipulate the displacement field in Elastic materials. It consists of solving a nonlinear optimization problem where the objective function defines the error in matching a desired displacement field, and the design variables determine the required material distribution within the device. In order to facilitate fabrication, the material at a given point of the device is chosen from a set of predefined materials, giving raise to a discrete optimization problem that is converted into a continuous one using the Discrete Material Optimization technique. The candidate materials maybe simple, isotropic materials, but the device made of them behaves as a whole as a metamaterial, enabling the manipulation of the displacement field in ways that are inconceivable in nature. As an example of application, a device for elastostatic cloaking or unfeelability is designed.