Abstract
Non-singular transformation is developed to achieve approximate acoustic and elastic cloaking. In the literature, perfect cloaking is realized under the condition of mapping cloak inner boundary to a single point, which gives rise to the development of unconventional metamaterials. Such cloaks introduce serious challenges in terms of materials design and fabrication. This paper studies the transformation functions that map the inner boundary of a 2D acoustic or elastic cloak (in physical space) to a region with small but finite dimension (in mathematical space). The goal is to find an optimized transformation that considers the limitations on mass density anisotropy, and elastic anisotropy of realizable metamaterials. It should be noted that the proposed cloak is not perfect and scatters minimal portion of the incident wave. However, it provides a realistic path towards the design and fabrication of an acoustic cloak for pressure waves, and elastic cloak for general stress waves.
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