On the simultaneous elongation and inflation of a tubular membrane of BKZ fluid

This work considers a viscoelastic fluid membrane which is initially tubular and bonded at each end to a rigid circular disc. The membrane is subjected to prescribed elongational and internal pressure histories causing it to undergo quasi-static axisymmetric deformation. This example is intended to simulate an experiment which has been recently proposed for the determination of constitutive properties for viscoelastic fluids as well as some polymer sheet forming process.The constitutive equation is presumed to be of integral type. The formulation of the problem leads to a basic system of equations which is intended for numerical solution. It has the structure of a two-point boundary value problem for a system ordinary differential equations at each time. The formulation has the advantage that the equations do not have to be rederived if the constitutive equation is changed. A change in the sub-program for computing stress from stretch history is all that is needed.A numerical method of solution is presented. In a numerical example, the material is taken to be polyisobutylene, modeled as a BKZ fluid.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23674/1/0000643.pd

Torsion of an Elastomeric Cylinder Undergoing Microstructural Changes

A constitutive theory which accounts for scission and cross linking processes in polymers during deformation is used to analyze the torsion of a circular bar. In each increment of deformation at a material element of the torsion bar, some volume fraction of material undergoes scission and then re-cross links to form a new network with a new reference state. The scission process reduces the ability of the material to transmit stress. The newly formed networks restore the ability of the material to transmit stress. The total stress is assumed to be the superposition of the stress in the remainder of the original material, determined by its deformation from its original configuration, and the stress in each newly formed network, determined by the deformation in that network from the configuration at which it formed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42685/1/10659_2004_Article_357410.pd

Branching of strain histories for nonlinear viscoelastic solids with a strain clock

An important class of constitutive equations for nonlinear viscoelastic response utilizes the concept of a strain clock. The clock takes the form of a material time variable which is defined in terms of the strain history and which increases faster than physical time. Important consequences of the strain clock are that stress relaxation and creep occur faster as strain increases, and the stress may not increase monotonically with time. In this work, we discuss whether this non-monotonic response implies that strain histories may branch into multiple histories.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41708/1/707_2005_Article_BF01177047.pd

Bifurcation of response of a nonlinear viscoelastic spherical membrane

The quasistatic inflation of a nonlinear viscoelastic spherical membrane by monotonically increasing pressure is considered. The deformation is assumed to be spherically symmetric. For the constitutive equation assumed, circumstances are shown to exist when the radius history must either have a jump discontinuity or bifurcate. A necessary condition for bifurcation and its dependence on material properties and radius history is analysed. Examples of bifurcation for various pressure histories are presented. Post-bifurcation branches are constructed and the possibility of secondary bifurcation is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22721/1/0000276.pd

Large axially symmetric stretching of a nonlinear viscoelastic membrane

Two problems of large planar axisymmetric deformations of an annular membrane consisting of a nonlinear viscoelastic material are solved, one with prescribed deformation at the outer boundary and one with prescribed force. These problems serve as examples to illustrate the extension to a class of viscoelastic membrane problems of a formulation of the corresponding elastic membrane problem suggested by Yang [1], which is especially convenient for numerical solution. The formulation uses radial and circumferential stretch ratios as dependent variables, which in the present case are found by solving a system of first order nonlinear partial differential-integral equations. The numerical procedure is such that at each time step, the problem is equivalent to a system of first order nonlinear ordinary differential equations for the current stretch ratios. This system is then integrated by the same numerical procedure as in the corresponding elastic problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34093/1/0000375.pd

Stress transfer modeling in viscoelastic polymer matrix composites

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76784/1/AIAA-1999-1344-540.pd

The evolution of anisotropies in the elastic response of an elastic-plastic material

The problem of determining the change in a material's symmetries as it undergoes an elastic-plastic deformation is considered. This is interpreted as the problem of evaluating the anisotropies of the current elastic response. The discussion is presented in the context of a particular form of constitutive equation which relates the Cauchy stress to the current value of the deformation gradient and a second order tensor quantity which is a function of the deformation gradient history. A sufficient condition is established for a transformation to be a material symmetry transformation of the current elastic response. This condition relates the minimum symmetries of the current elastic response to the initial material symmetry, the given deformation history, and the structure of the constitutive equation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30354/1/0000756.pd

Modeling the mechanical response of a material undergoing continuous isothermal crystallization

The gradual transition seen in polymer crystallization is modeled. A constitutive equation is developed to follow the mechanical behavior of a crystallizing polymer before, during, and after the completion of crystallization. The post-crystallization response of the material is studied and shown to be "elastic". The symmetries of the post-crystallization response are defined and calculated for crystallization under several deformation histories.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29975/1/0000338.pd

A note on the temperature dependence of the normal stress moduli

In this analysis we establish necessary and sufficient conditions which the normal stress modulus [alpha]1([theta]) and its derivative d[alpha]1([theta])/d[theta] ought to satisfy if a homogeneous incompressible second grade fluid is to meet the requirement that the specific internal energy of the fluid be a minimum when the fluid is locally at rest. We also require that all arbitrary motions of the fluid meet the Clausius-Duhem inequality. It is found that requiring that the specific internal energy of the fluid be a minimum when the fluid is locally at rest is not equivalent to a similar requirement on the specific Helmholtz free energy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24533/1/0000812.pd