The proposed mathematical model of nanomechanics for rubbery materials provides seven parameters to characterize the stress-strain response of rubbery materials as a function of time and temperature. Especially, two parameters of an attractive energy, k, and an internal variable, xi, are newly introduced to describe the departures from the classical thermodynamics of rubber elasticity. The mathematical model can reproduce the entropy and energy components on stress with various conditions such as the degree of cross-links, the extent of swelling, the temperature dependence and the strain rate dependence. It also offers physical insights represented by the quantitative molecular structural parameters such as the number of non-bonding interactions and its potential energy. As a conclusion the energy component can be associated with the non-bonding potential energy of the dipole-dipole interaction (0.3-0.9 kJ/mol) and the steric interaction to rotation about the chain backbone (16-20 kJ/mol). (C) 2017 Elsevier Ltd. All rights reserved.