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### Axial Compression of a Rectangular Rubber Ring Composed of an Incompressible Mooney-Rivlin Material

#### Abstract

The problem of finite deformation of a rectangular rubber ring composed of an isotropic incompressible Mooney-Rivlin material is considered, where both ends of the ring are subjected to static axial compression loads. After formulating the mathematical model based on the nonlinear theory of elasticity, a system of implicit analytical solutions is derived. Then, the influences of axial load and structure parameters on the deformation of the ring are discussed in detail. It is proved that the theoretical results are similar to those in actual applications. The deformation of the ring becomes increasingly apparent with the decreasing ratio of material constants. The axial displacement and the axial compression ratio take the minima at the central cross-section of the ring, respectively, but take the maxima at the endpoints.