Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Load maximum behavior in the inflation of hollow spheres of incompressible material with strain-dependent damage

Authors: H. E. Huntley, A. S. Wineman and K. R. Rajagopal
Journal: Quart. Appl. Math. 59 (2001), 193-223
MSC: Primary 74B20
DOI: https://doi.org/10.1090/qam/1827811
MathSciNet review: MR1827811
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Abstract: Carroll has shown three qualitatively different cases of behavior in the load-expansion relation for the inflation of hollow incompressible isotropic elastic spheres. Each of these cases was related to material response in uniaxial compression (or equal biaxial extension). For ``type A'' materials, load increases monotonically with expansion; for ``type B'' materials, load increases monotonically and then decreases; for ``type C'' materials, load increases monotonically, decreases, and again increases. The present work discusses the monotonicity properties of the load-expansion relation when rubbery materials undergo microstructural change or damage. The analysis is carried out using a constitutive equation for materials undergoing continuous scission and reformation of macromolecular junctions. Results are presented for the case when this leads to softening of response. For ``type A", sufficient softening can cause loss of monotonicity; for ``type B", the softening leads to loss of monotonicity at smaller levels of inflation and lower loads.

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DOI: https://doi.org/10.1090/qam/1827811
Article copyright: © Copyright 2001 American Mathematical Society

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