Compression of Bonded Blocks of Soft Elastic Material: Variational Solution

Abstract

The problem of a block of nearly incompressible elastic material, bonded on its top and bottom parallel faces to rigid end plates, against which any slip is prevented, and subjected to direct compression, is examined. Approximate solutions are obtained using the minimum potential energy and Hellinger-Reissner variational principles. Bulk compressibility is naturally included in these solutions. The necessity of avoiding a severe overestimation of the effective compressive stiffness of thin blocks is demonstrated. For such blocks, the results confirm solutions, extensively used in engineering design, which are based on the assumption of a pressure distribution within the block.