Publication 23-CNA-008
Statistical Field Theory for Nonlinear Elasticity of Polymer Networks with Excluded Volume Interactions
Pratik Khandagale
Department of Mechanical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
pkhandag@alumni.cmu.edu
Timothy Breitzman
Air Force Research Laboratory
timothy.breitzman.1@us.af.mil
Carmel Majidi
Department of Civil and Environmental Engineering
Department of Mechanical Engineering
Department of Materials Science and Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
Kaushik Dayal
Center for Nonlinear Analysis
Department of Civil and Environmental Engineering
Department of Materials Science and Engineering
Scott Institute for Energy Innovation
Carnegie Mellon University
Pittsburgh, PA 15213
Kaushik.Dayal@cmu.edu
Abstract: Polymer networks formed by cross-linking flexible polymer chains are ubiquitous in many natural and synthetic soft matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum-scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the endtoend vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in 3-dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (1) the linearized Poisson’s ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (2) despite the harmonic Gaussian chain as a starting point, there is an emergent strainsoftening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (3) the emergence of a deformation-sensitive localization instability at large excluded volumes.
Get the paper in its entirety as 23-CNA-008.pdf
« Back to CNA Publications
