Three topics of mechanics of elastomers: constitutive models, load-deflection relations, and instabilities, are covered in this dissertation.; First, methods for the determination of the strain energy function for a specific elastomer are discussed. The strain energy function is obtained by fitting the experimental data of uniaxial tension and compression, equi-biaxial extension, and pure shear tests. The equi-biaxial test is done in a novel way, by inflating a thin circular rubber sheet and measuring the displacements using moire techniques. The obtained strain energy function is then incorporated into a finite element (ABAQUS) program, and the load-deflection of an electric connector spring is calculated.; The next topic of study is the establishment of compressive load-deflection relations for bonded rubber blocks. The problem of a bonded thin rubber cylinder under small compression is rigorously solved by an eigenfunction expansion method. Various techniques of tackling the stress singularities at the corner of the cylinder are discussed; a thorough understanding of the problem is achieved. For large compression, approximate methods are proposed to calculate the nonlinear load-deflection relations of bonded circular disks, rectangular slabs, and annular blocks; the approximate solutions are evaluated by finite element methods, and good correlation is obtained.; Finally, instability of hyperelastic columns is investigated. The problem of buckling of a thick rectangular slab under a plane-strain deformation is solved exactly; the focus here is to study the bifurcation behaviors of columns made of materials other than the familiar neo-Hookean and Mooney-Rivlin ones. A simple engineering method is developed to calculate the critical load for general rubber columns; the results for circular bars compare favorably with finite element analyses, and experiments.
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