A hybrid model of rubber elasticity in simple extension

Abstract

A thermodynamically related model is developed for describing elastic rubber-like behavior of amorphous and crystallizing polymers and demonstrated on example of simple extension. Both the "entropic" and "energetic" motions of polymer chains that contribute in macroscopic elastic deformation are taken into account. The model displays a continuous transition from entropy to energetic elasticity, without common singularity caused by finite extensibility of polymer chains. A multi-scale molecular approach, based on recent literature concepts has been employed for evaluations of continuum parameters.For crystallizing polymers, a simple model is developed for the stress-induced crystallization, which describes the stress reinforcement caused by the formation of long, needle-like polymer crystals.

The entropy of the rotational conformations of (poly)isoprene molecules and its relationship to rubber elasticity and temperature increase for moderate tensile or compressive strains

“…The internal energy of every isoprene unit will, on average, include a contribution from its accessible rotational conformations given by Eq. (6). As the chains are extended under an applied strain, the conformations accessible to isoprene units will be restricted to some subset of the extended rotational states.…”

“…Historically, the development of elasticity models 1-4 for rubber networks has followed two approaches: empirical engineering models, 5,6 with parameters fit to experiments, and highly mathematical polymer physics models, 7-10 relying on thermodynamic assumptions for the end-to-end distributions of individual chains. Numerous theories have been proposed over the past 80 years but none of them has achieved a consensus as the correct physical description of elasticity.…”

Experimental Characterization and Modified Constitutive Modeling of the Strain Rate Dependent Compressive Behavior of Adhesives

“…The various constitutive material models have been proposed to represent the stress–strain response of adhesives . An elastoplastic constitutive formula has been developed to simulate both the reversible elastic and irreversible inelastic deformation of a ductile polymeric adhesive in adhesively bonded aluminum components .…”

“…Hyperelastic adhesive materials exhibit the large nonlinear deformation; their behavior can be quantified by the strain energy function. The physics‐based hyperelastic model using the statistic mechanics approach characterizes the deformation by assuming a structure of randomly oriented long molecular chains . The phenomenological hyperelastic material model was developed in terms of strain energy density that is a power series in the strain invariants .…”

“…[ 2,[4][5][6] adhesives. [19][20][21][22][23][24][25][26][27][28][29] An elastoplastic constitutive formula has been developed to simulate both the reversible elastic and irreversible inelastic deformation of a ductile polymeric adhesive in adhesively bonded aluminum components. [ 19 ] The rheological [ 20 ] or time-hardening [ 21 ] models were applied to quantify the nonlinear viscoelastic behavior of epoxy-based adhesives in sandwich structures.…”