A model for the stability and creep of organic materials

A model is presented for the thermally assisted breaking of a number of bonds arranged in parallel and stressed by an individual soft spring each. Using a simplified potential for the bond it is shown that in equilibrium there are two definite regions of elastic behavior: one with all bonds intact, the other with a variable fraction of bonds broken, therefore with a tangent modulus steadily decreasing with applied stress. Criteria are given for the existence of these regions. Beyond these regions time-dependent creep to rupture is found, limited, in turn, by the theoretical fracture strength, the stress necessary for fracture without any thermal assistance, beyond which a bound state is impossible. The time-to-fracture for creep rupture is calculated and an example of the time evolution of the accelerating creep given. The results of the calculations are applied to experimental data on Wallaby tendons by Wang and Ker (J. Exp. Biol. 198 (1995) 831) and data estimated for the bond potential depth, the theoretical fracture strength and the number density of bonds involved as well as the elastic modulus of the ensemble. Values are derived under the assumption of one deformation mechanism being dominant—e.g., (sub-)fibril sliding or sliding of collagen molecules along one another—but the model cannot definitely distinguish between mechanisms.