Stress–softening and recovery of elastomers

A constitutive model is developed for the mechanical response of elastomers at finite strains. A polymer is treated as a network of linear chains linked by permanent (chemical crosslinks) and temporary (entanglements and van der Waals forces) junctions. Temporary junctions are assumed to be in two states: loose (passive) when they impose only topological constrains on available configurations of chains, and tight (active) when their effect is tantamount to that for crosslinks. Stretching of a specimen implies that some loose junctions become active, which decreases the average length of a chain. A long chain is treated as an ensemble of inextensible strands connected in sequel. Two neighboring strands are bridged by a bond which may be in two conformations: flexed (trans) and extended (cis). A bond in the flexed conformation is modeled as a linear elastic solid, whereas the mechanical energy of a bond in the extended conformation (two rigid rods directed along a straight line) is disregarded. For a virgin specimen, all bonds are in the flexed conformation. Under loading some bonds are transformed from flexed to extended conformation. Stress–strain relations for a rubbery polymer and kinetic equations for the trans– cis transition are derived using the laws of thermodynamics. Governing equations