To simulate the contact nonlinearity in 2D solid problems, a contact analysis approach is formulated using incremental form of the subdomain parametric variational principle (SPVP). The formulation is based on a linearly conforming radial point interpolation method (LC-RPIM) using nodal integration technique. Contact interface equations are also presented using a modified Coulomb frictional contact model and discretized by contact point-pairs. In the present approach, the global discretized system equations are transformed into a standard linear complementarity problem (LCP) that can be solved readily using the Lemke method. The present approach can simulate various contact behaviors including bonding/debonding, contacting/departing, and sticking/slipping. An intensive numerical study is performed to validate the proposed method via comparison with the ABAQUS ® and to investigate the effects of the various parameters used in computations. These parameters include normal and tangential adhesions, frictional coefficient, nodal density, the dimension of local nodal support domain, nodal irregularity, shape parameters used in the radial basis function and the external load. The numerical results have demonstrated that the present approach is accurate and stable for contact analysis of 2D solids.

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We design a 3D acoustic metamaterial having a coiling resonant structure with high symmetry. Eigenstate analysis reveals that such a 3D metamaterial has two significant Mie-type eigenmodes, monopole and dipolar resonances. Large blocking of sound waves in the low-frequency range between monopole and dipolar resonances is observed numerically and experimentally. The effective properties extracted from the reflection and transmission coefficients show negative bulk modulus around the monopole resonant frequency and negative mass density around the dipolar resonant frequency. By employing the proposed two-scale model, the metamaterial system demonstrates the functionalities of sound cloaking and super-tunneling within a finite space.