A coSSliTt TIVE model i, proposed for tho: deformation of rubber materials which is shnwn tn rcpres..:nt successfully the response of these materials in uniaxial extension. biaxial extension. uniaxial compression. plane strain compression and pure shear. The developed constitutive relation is based on an eight chain representation of the underlying macromokcular network structure of the rubber and the non-Gaussian behavior of tho: individual chains in the proposed network. The eight chain model accurately captun:s the coorx:rativc nature of network d..:formation while requiring only two material parameters. an initial modulus and a limiting chain extensibility. Since these two parameters arc mechanistically linked tn the physics of molecular chain orientation involved in the deformatinn nf rubber, the proposed model rcprcs..:nts a simple and accurate constitUtive model ol rubber ddimnatwn. The chain extension in this network model reduces to a function of the root-mean-square of tho: principal applied stretches as a result of effectively sampling eight orientations of principal stretch space. The results of the proposed eight chain model as well as thos..: of several prominent models arc compared with cxperim..:ntal data of TRELOAR ( 1944. Trans. hm1day Soc. 40, 59) illustrating the superiority. simplicity and pr..:dictivc ability of tho: proposed modd. Additionally. a new set of experiments which captures the state of deformation dependence of rubber is described and conduct~'<.! on three rubber materials. The eight chain model is found to model and prL-dict accurately {he behavior of the three tested materials further conlirming its superiority and ctf..:ctiveness over earlier models.

A review of constitutive models for the finite deformation response of rubbery materials is given. Several recent and classic statistical mechanics and continuum mechanics models of incompressible rubber elasticity are discussed and compared to experimental data. A hybrid of the Flory—Erman model for low stretch deformation and the Arruda—Boyce model for large stretch deformation is shown to give an accurate, predictive description of Treloar's classical data over the entire stretch range for all deformation states. The modeling of compressibility is also addressed.

A combined experimental and analytical investigation has been performed to understand the mechanical behavior of two amorphous polymers-polycarbonate and poly(methyl methacrylate)-at strain rates ranging from 10 À4 to 10 4 s À1 . This range in strain rates was achieved in uniaxial tension and compression tests using a dynamic mechanical analyzer (DMA), a servo-hydraulic testing machine, and an aluminum split-Hopkinson pressure bar. DMA tension tests were used to characterize the viscoelastic behavior of these materials, with focus on the rate-dependent shift of material transition temperatures. Uniaxial compression tests on the servo-hydraulic machine (10 À4 to 1 s À1 ) and the split-Hopkinson pressure bar (10 3 to 10 4 s À1 ) were used to characterize the rate-dependent yield and post-yield behavior. Both materials were observed to exhibit increased rate sensitivity of yield under the same strain rate/temperature conditions as the btransition of the viscoelastic behavior. A physically based constitutive model for large strain deformation of thermoplastics was then extended to encompass high-rate conditions. The model accounts for the contributions of different molecular motions which become operational and important in different frequency regimes. The new features enable the model to not only capture the transition in the yield behavior, but also accurately predict the post-yield, large strain behavior over a wide range of temperatures and strain rates.

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