Abstract Pentamode metamaterials called as PM materials belong to a new kind of artificial materials, and their main characteristics are that the five eigenvalues of the effective modulus matrixes of PM materials are zero, which makes PM materials behave like fluid. As a results, PM materials show big potentialities in the design of acoustic cloaks. However, according to A.N.Norris theory[1], the design method for PM materials is different from others for common acoustic metamaterials, because an nonlinear partial differential equation must be satisfied while using the coordinate transformation method to design PM materials. The paper firstly derives the weak form of the partial differential equation, and then the nonlinear finite element formula for solving the partial differential equation are established by using the full Lagrangian methods for finite element analysis; thirdly, an iterative algorithm to solve the partial differential equation is constructed; finally two numerical examples of the coordinate transformation scheme are offered, and one is for 2D round domain, the other is for 3D sphere domain.
Received: 16 February 2015
Published: 28 August 2015
YI Hui,YU Xiao-Meng,MEI Yu-Lin. Coordinate transformation algorithm for pentamode metamaterial design based on non-linear finite element analysis[J]. , 2015, 36(4): 297-318.
2015, Vol. 36 
