neo-Hookean Behavior Research Articles

Irreversible growth of a spherical cavity in rubber-like material: A fracture mechanics description

A fracture mechanics analysis is performed to get a criterion for irreversible growth of cavities in rubber-like materials. The limit of reversible growth of a hole is calculated using the Griffith fracture criterion for a hyperelastic incompressible material (neo-Hookean behavior law) submitted to a hydrostatic tension under the assumptions of large deformations. It leads to an expression of the energy released rate G for the crack-like hole. This expression is shown to be different from results obtained by other authors. The reversible deformation of the cavity under finite triaxiality is also examined by considering a particular field of kinematically admissible displacements. The so obtained approached solution is used to extend the expression of the energy released rate G to various triaxial tension loadings.

Strain-hardening behavior of polycarbonate in the glassy state

This paper presents an experimental characterization of the three-dimensional strain-hardening response of polycarbonate in the glassy state. Using a special mechanical conditioning technique, large homogeneous deformations were obtained in tension, compression, and shear. The experimental results are compared to a number of existing network models. It was found that the state-of deformation dependence of the strain-hardening response was adequately described by neo-Hookean behavior with a shear modulus G=26 MPa. Up to the deformations applied in this study, no sign of a finite extensibility of the entanglement network was observed.

Dynamic inflation of hyperelastic spherical membranes

The dynamic inflation of hyperelastic spherical membranes of a Mooney–Rivlin material is analyzed in this study. Various inflation regimes are identified through ranges of the material parameters and driving pressure. In particular, the conditions for oscillatory inflation around the static fixed point are examined. It is found that, for a given material, the frequency of oscillation exhibits a maximum at some pressure level, which tends to increase for materials closer to neo-Hookean behavior.

Rubber elasticity of cross-linked networks with trapped entanglements and dangling chains

This is a theoretical study on the effects of the network structure and deformation on the stress response of permanent elastomeric networks containing trapped entanglements and chain defects. In these systems, elastically active chains with both ends cross-linked coexist with segments that are tethered at one end only. It is assumed that under strain, internal strands preserve their deformation with time while dangling segments restore their initial length by retraction and continue their conformational renewal through chain fluctuations. The dynamics of the tethered branches cause disengagement of untrapped entanglements on neighboring segments, thus undermining the structural solidity of the elastomer. The calculated stress under constant deformation depends on the strain value, the molecular weight between cross-links and between entanglements, the relative participation of the tethered chains in the network, and the degree of the relaxation completion. The theory accommodates the observed deviations from neo-Hookean behavior, and the predicted effects of the network architecture are consistent with the experimental evidence.

Contribution of entanglements to rubber elasticity

Uncrosslinked polymers show rubber-like properties above the glass transition temperature and at times short enough to prevent flow. This effect is thought to be due to a temporary entanglement network. Several studies indicate large entanglement contributions to the equilibrium elastic modulus of crosslinked networks. Three methods are discussed in greater detail: stoichiometric crosslinking with a suitable peroxide, the Langley method, and the two-network method. The two latter methods give equilibrium entanglement modulus contributions which are equal to the pseudo-equilibrium modulus of the uncrosslinked polymer. They also indicate that the entanglement contribution to the stress is responsible for departures from neo-Hookean behaviour observed in simpler extension.

Stress–strain behavior in polymer networks containing nonlocalized junctions

Two models of entanglement interaction in polymer networks are examined. One is based on Edwards’ principle of topological classification, the other on interstrand links which are free to slip along the strand contours. Relationships between stress and strain in simple elongation are developed for networks which contain such elements as well as permanent crosslinks. In each case departures from neo-Hookean behavior are found. The apparent modulus decreases with strain in uniaxial tension and remains approximately constant in uniaxial compression as observed in real networks. If the network is expanded, such as would occur through addition of a swelling solvent, the departures from neo-Hookean behavior become smaller, again as observed experimentally. It thus appears that chain entanglements, portrayed here by two different nonlocalized junction models, may account for many of the differences in behavior between real networks and predictions of the phantom network theories.

Stresses near a crack in a rubber sheet

The principal stresses in the vicinity of the crack tip in a rubber sheet have been determined experimentally by measuring the strain field with the aid of an imprinted grid work and calculating the stresses by assuming neo-Hookean material behavior. The principal stresses in the crack-tip vicinity are presented graphically. A correlation between the measured maximum tensile stress on the crack axis and that obtained from infinitesimal-elasticity theory is established. Information is given which provides bounds on the loading and deformation within which a large-deformation elastic analysis is valid before geometric deformations due to tearing must be considered.