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五零能模式材料是一种新型人工超材料,特征为其弹性模量矩阵的6个特征值中5个为零,可用等效体积模量来描述,表现出类似流体的性质,可被应用于声学隐声斗篷的设计中.然而,根据Norris A N[1]提出的理论,设计五零能模式材料时,与应用变换声学方法设计一般声学人工超材料不同,要求其满足一非线性偏微分方程约束.论文利用非线性有限元的完全拉格朗日方法,推导了这一偏微分方程的弱形式,并给出了相应的非线性有限元计算列式,以及迭代求解的具体算法.最后,给出了五零能摸式材料设计的二维和三维坐标变换数值算例.
Five zero energy mode material is a novel artificial metamaterial characterized by five of the six eigenvalues of its elastic modulus matrix that are zero and are described by equivalent bulk modulus and exhibit fluid-like properties that can be applied However, according to the theory proposed by Norris AN [1], the design of five zero-energy mode material is different from the acoustic technique used in the design of transonic acoustic general metamaterials, which is required to satisfy a nonlinear partial differential Equation constraints.The thesis derives the weak form of this partial differential equation by the complete Lagrange method of nonlinear finite element and gives the corresponding nonlinear finite element calculation formula and the concrete algorithm of iterative solution.Finally, , Gives a numerical example of two-dimensional and three-dimensional coordinate transformation of five zero-energy touch material design.