Nonlinear Elasticity: From Single Chain to Networks and Gels

Journal Article · Thu Apr 25 04:00:00 EDT 2013 · Macromolecules

DOI:https://doi.org/10.1021/ma400478f· OSTI ID:1564987

Carrillo, Jan-Michael Y. ^[1]; MacKintosh, Fred C. ^[2]; Dobrynin, Andrey V. ^[3]

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1. Polymer Program, Institute of Materials Science and Department of Physics, University of Connecticut, Storrs, Connecticut 06269, United States; Scientific Computing Department, National Center for Computational Sciences, Oak Ridge National Laboratories, Oak Ridge, Tennessee 37831, United States
2. Department of Physics and Astronomy, VU University, Amsterdam 1081 HV, The Netherlands
3. Polymer Program, Institute of Materials Science and Department of Physics, University of Connecticut, Storrs, Connecticut 06269, United States

Biological and polymeric networks show highly nonlinear stress–strain behavior manifested in materials that stiffen with increasing deformation. Using a combination of the theoretical analysis and molecular dynamics simulations, we develop a model of network deformation that describes nonlinear mechanical properties of networks and gels by relating their macroscopic strain-hardening behavior to molecular parameters of the network strands. The starting point of our approach is a nonlinear force/elongation relation for discrete chains with varying bending rigidity. The derived expression for the network free energy is a universal function of the first deformation invariant and chain elongation ratio that depends on a ratio of the unperturbed chain size to chain dimension in a fully extended conformation. The model predictions for the nonlinear shear modulus and differential shear modulus for uniaxial and shear deformations are in very good agreement with both the results of molecular dynamics simulations of networks and with experimental data for biopolymer networks of actin, collagen, fibrin, vimentin, neurofilaments, and pectin.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
• Sponsoring Organization: USDOE Office of Science
• OSTI ID: 1564987
• Journal Information: Macromolecules, Journal Name: Macromolecules Journal Issue: 9 Vol. 46; ISSN 0024-9297
• Publisher: American Chemical Society
• Country of Publication: United States
• Language: English

Related Subjects

Polymer Science