The present state of development of the statistical mechanics of rubber elasticity is reviewed and analysed, starting from some problems and controversial results drawn from recent experimental progress in this area. Attention is focused on the tube model as a mean field approach to the statistical mechanics of polymer systems with topology conservation. In particular, a new model for simulating the topological constraints in polymer networks and melts is presented which allows the order and the deformation dependence of the tube dimensions to be calculated. Conclusions resulting from the description of large-strain and small-strain behaviour of dry, completely crosslinked networks are discussed and compared with experimental data where all modes of deformation usually employed can be described with similar accuracy. Further, the concept of relaxed microscopic deformation much smaller than the macroscopic deformation of the sample is introduced, which allows explanation of mechanical and thermodynamic properties as well as the scattering results for networks at higher swelling degrees. Similarly, constraint release effects are expected to be responsible for the different experimental results collected for end-linked networks and for networks prepared by cross-linking of long primary chains. The different degrees of completeness of crosslinking have to be considered as the main reason for these differences.

Rubber elasticity of polymer networks: Theories

Liquid crystalline thermosets (LCT's) were prepared by curing a difunctional LC epoxy monomer, diglycidyl ether of 4,4‘-dihydroxy-α-methylstilbene, with the tetrafunctional cross-linker 4,4‘-methylenedianiline (MDA). A commercial, non-LC epoxy monomer of similar starting molecular weight was also cured with MDA to produce an isotropic thermoset for comparison. Dynamic mechanical analysis revealed reduced glassy moduli, increased stiffness in the rubbery state, and broadened and lowered glass transitions for the LCT's compared to the isotropic thermoset based on the non-LC monomer. At room temperature, the true stress versus true strain curves of the LCT's under uniaxial compression showed no strain softening region, substantial plastic deformation (ef ≈ 50%), and increased strain hardening compared to the isotropic thermoset. LCT's with a smectic type of local order exhibited bulk, homogeneous plastic yielding, which led to slow, stable crack propagation and an increased fracture toughness (GIc = 1.62 kJ/...

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Deformation of a polydomain, liquid crystalline epoxy-based thermoset

http://saifulamin.info/publication/journals/j5.pdf

An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification

Hyperelastic constitutive modeling under finite strain

Abstract Rubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behavior of such randomly oriented microstructures, several phenomenological and micromechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in the finite element framework for solving a boundary value problem, one would require two important ingredients, i.e., the stress tensor and the consistent fourth-order tangent operator, where the latter is the result of linearization of the former. In our previous work, 14 such material models are reviewed by deriving the accurate stress tensors and tangent operators from a group of phenomenological and micromechanical models at large deformations. The current contribution will supplement some further important models that were not included in the previous work. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e., uniaxial tension, equibiaxial tension, and pure shear, have been derived and the performances of the models are analyzed.

K. Tei

Papers

Experimental survey of the strain energy density function of isoprene rubber vulcanizate