Deformation Model of Chains and Networks with Extendable Bonds

The nonlinear stress-strain behavior of polymer networks, manifested in the monotonically increasing instantaneous modulus, is a product of the nonlinear deformation of individual network strands. This nonlinear network response to external deformations is described in the framework of a network model relating macroscopic stress-strain response to force-elongation behavior of individual network strands with finite bending rigidity and extendable bonds. The developed approach correlates network shear modulus, bond deformation modulus and extensibility ratio with the strands’ Kuhn length, bond elastic constant, and their dimensions in undeformed and fully extended states. The model’s accuracy is tested in coarse-grained molecular dynamics simulations of chain and diamond network deformations covering both linear and nonlinear deformation regimes. The model is used to describe different deformation regimes of DNA molecules and biological networks of fibrin, collagen, and neurofilaments and to obtain elastic constants characterizing these systems’ mechanical responses.