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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H. E. Huntley, Applications of a Constitutive Equation for Microstructural Change in Polymers, Ph.D. dissertation, The University of Michigan, 1992
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K. R. Rajagopal, On Constitutive Relations and Material Modelling in Continuum Mechanics, Report #6, Institute for Applied and Computational Mechanics, The University of Pittsburgh, 1995
K. R. Rajagopal and A. S. Wineman, A constitutive equation for nonlinear solids which undergo deformation induced microstructural changes, Internat. J. Plast. 8, 385–395 (1992)
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A. S. Wineman and H. E. Huntley, Numerical simulation of the effect of damage induced softening on the inflation of a circular rubber membrane, Internat. J. Solids Structure 31, 3295–3313 (1994)
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M. M. Carroll, Controllable deformations of incompressible simple materials, Internat. J. Engrg. 5, 515–525 (1967)
M. M. Carroll, Pressure maximum behavior in inflation of incompressible elastic hollow spheres and cylinders, Quart. Appl. Math. 45, 141–154 (1987)
H. E. Huntley, Applications of a Constitutive Equation for Microstructural Change in Polymers, Ph.D. dissertation, The University of Michigan, 1992
H. E. Huntley, A. S. Wineman, and K. R. Rajagopal, Chemorheological relaxation, residual stress, and permanent set arising in radial deformation of elastomeric hollow spheres, Math. Mech. Solids 1, 267–299 (1996)
K. R. Rajagopal, On Constitutive Relations and Material Modelling in Continuum Mechanics, Report #6, Institute for Applied and Computational Mechanics, The University of Pittsburgh, 1995
K. R. Rajagopal and A. S. Wineman, A constitutive equation for nonlinear solids which undergo deformation induced microstructural changes, Internat. J. Plast. 8, 385–395 (1992)
A. J. M. Spencer, Continuum Mechanics, Longman Mathematical Texts, New York, 1980
A. S. Wineman and H. E. Huntley, Numerical simulation of the effect of damage induced softening on the inflation of a circular rubber membrane, Internat. J. Solids Structure 31, 3295–3313 (1994)
A. S. Wineman and K. R. Rajagopal, On a Constitutive Theory for Materials Undergoing Microstructural Changes, Arch. Mech. (Arch. Mech. Stos.) 42, 53–75 (1991)
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© Copyright 2001
American Mathematical Society