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We use coarse-grained molecular dynamics simulations to study deformation of networks and gels of linear and brush strands in both linear and nonlinear deformation regimes under constant pressure conditions. The simulations show that the Poisson ratio of networks and gels could exceed 0.5 in the nonlinear deformation regime. This behavior is due to the ability of the network and gel strands to sustain large reversible deformation, which, in combination with the finite strand extensibility results in strand alignment and monomer density, increases with increasing strand elongation. We developed a nonlinear network and gel deformation model which defines conditions for the Poisson ratio to exceed 0.5. The model predictions are in good agreement with the simulation results. 

We develop a forensic-like framework for network structural characterization based on an analysis of their nonlinear response to mechanical deformation. For model networks, this methodology provides information about the strand degree of polymerization between cross-links, the effective cross-link functionality, the contribution of loops and entanglements to network elasticity, as well as the fraction of stress-supporting strands. For networks with trapped entanglements, we identify a transition from cross-link-controlled to entanglement-controlled network elasticity with increasing degree of polymerization of network strands between cross-links and show how specific features of this transition are manifested in changes of entanglement and structural shear moduli characterizing different modes of network deformation. In particular, this cross-link-to-entanglement transition results in saturation of the network shear modulus at small deformations and renormalization of the degree of polymerization of the effective network strands determining nonlinear elastic response in the strongly entangled networks. The developed approach enables the classification of networks according to their topology and effectiveness of stress distribution between network strands.