Yieldlike response of a compressible nonlinear viscoelastic solid

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Abstract
Several authors have shown that many aspects of the yieldlike response of polymers can be described by the constitutive framework of nonlinear viscoelasticity. This arises through the use of a reduced time which causes stress relaxation to be accelerated by increasing deformation. Moreover, the history dependence inherent in the constitutive equation leads to different yield response under strain and stress control conditions, as is observed experimentally. Previous work has been concerned with yield during large extensional deformations under elongation control conditions, or small shear deformations under strain or stress control. The present work is concerned with a numerical study of yieldlike response under large shear deformations. Of particular interest is the influence of volume changes associated with the normal stress effects induced by shear deformations. A nonlinear single integral constitutive equation for a viscoelastic compressible solid is developed for the purpose of the study. Its initial elastic response and the long time equilibrium response are given by a Beatty–Blatz–Ko model for a nonlinear elastic compressible solid. A reduced time is introduced in which the shift function depends on the volume change and/or the shear deformation. Results are presented of numerical simulations of experiments involving simple shear deformations and shear deformations in the absence of normal tractions. The latter allows the influence of volume changes arising from the absence of normal tractions to be studied. Both the shear deformation and shear stress control conditions are examined.

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