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Chemorheological Relaxation, Residual Stress, and Permanent Set Arising in Radial Deformation of Elastomeric Hollow Spheres

Department of Mechanical Engineering, University of Michigan-Dearborn, Dearborn, MI 48128

Alan S. Wineman

Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, MI 48109

K. R. Rajagopal

Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA 15261

Recently, a constitutive theory for rubber-like materials has been developed by which stress arises from different micromechanisms at different levels of deformation. For small deformations, the stress is given by the usual theory of rubber elasticity. As the deformation increases, there is scission of some junctions of the macromolecular microstructure. Junctions then reform to generate a new microstructure. The constitutive equation allows for continuous scission of the original junctions and formation of new ones as deformation increases. The macromolecular scission causes stress reduction, termed chemorheological relaxation. The new macromolecular structure results in permanent set on release of external load.

The present work considers a hollow sphere composed of such a material, also assumed to be incom-pressible and isotropic, which undergoes axisymmetric deformation under radial traction. There develops an outer zone of material with the original microstructure and an inner zone of material having undergone macromolecular scission, separated by a spherical interface whose radius increases with the deformation. The stress distribution, radial load-expansion response, residual stress distribution, and permanent set on release of traction are determined. It is found that a residual state of high compressive stress can arise in a thin layer of material at the inner boundary of the sphere.

Mathematics and Mechanics of Solids, Vol. 1, No. 3, 267-299 (1996)
DOI: 10.1177/108128659600100301


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