Hyperelastic constitutive model

Figure 2. Schematic depiction of load and extension responses of a typical polymer tested in simple tension tests

Examples of sealant behavior

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Figure 5. Schematic illustration of the variation of the coefficient

Figure 4. Variation of the simple tension

of volume expansion α with temperature T for polymers, and the

stressstrain curves of an elastomer with

glass transition temperature Tg. (After Eisenberg 1984.)

strain rate and temperature, and an enve-

lope of failure points. (After Ward 1983 and

Smith and Stedry 1960.)

data can be formed that reflects this influence. Fig-

chemical interaction between the rubber and the

ure 4 shows a schematic illustration of their data.

liquid has occurred, however. For rubbers the pro-

Brittle fracture of an elastomer after large de-

cess is simply a physical mixing process in which

formations should be distinguished from brittle

the molecules of the liquid diffuse into the mo-

fracture of the same material in a glassy state. The

lecular structure of the rubber (Treloar 1975). Vol-

use of the "brittle fracture" to describe rubber fail-

ume changes due to shrinkage during curing of

ure can be misleading and is not often used. In

the rubber formulation can be significant, particu-

addition, the transition from rubber-like behavior

larly if the curing process includes evaporation of

to glassy behavior should be distinguished from

solvents (Panek and Cook 1984). As mentioned

a ductile to brittle transition. The terms ductile and

above, if the volumetric strains are constrained,

brittle describe primarily the failure response at

the material stresses will be affected.

large strains, whereas the terms rubbery and glassy

encompass mechanical response behavior of a

Hyperelastic

greater extent.

constitutive model

Although elastomers generally behave as in-

To characterize the stressstrain response of an

compressible materials in a mechanical loading

elastic body undergoing large deformations, it is

context, thermally induced volumetric strains can

sufficient to specify the form of the strain energy

be significant and, if constrained, can have a sig-

function W as a function of the deformation or cur-

nificant influence on the stresses in the material.

rent strain (e.g., Rivlin 1956, Green and Adkins

The thermal coefficient of volume expansion of a

1960). The derivative of the strain energy function

polymer is another property that varies with tem-

with respect to a strain component gives the cor-

perature such that the glass transition tempera-

responding stress component. The term hyperelas-

ture is revealed. Figure 5 illustrates this variation

tic has been used to describe such an ideal elastic

schematically.

material (Malvern 1969).

Volume changes in rubbers can also be caused

The form of strain energy functions of rubbers

by exposure to organic liquids such as hydrocar-

has been deduced from both molecular consider-

bons (Treloar 1975). Rubber materials can swell and

ations and phenomenological experiments, and

contract with the exposure and expulsion of the

similarities between the forms have been found

liquids, and the volume compressibility can in-

(Treloar 1975, Green and Adkins 1960). Based on

crease with exposure such that an assumption that

experimental measurements, Rivlin and Saunders

the rubber is incompressible is no longer valid

(1951) have suggested that, for vulcanized natural

(Treloar 1975). Swelling does not imply that any

rubber,

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