Nonlinear mechanical response of finite-length soft composites with random dislocations

Abstract The effects of random dislocations on the vibrational properties of finite-length RNA and DNA macro-structures have been investigated by means of a harmonic Hamiltonian and the Green’s function method. The RNA molecule has been modeled using a half ladder model, and three models (a fishbone model and two different strand models) have been employed to model the structure of DNA. The lengths of the finite and cyclic systems are gradually increased to more accurately approximate the structures of RNA and DNA. Springs whose behaviors are governed by Hooke’s constitutive law have been used to represent the bonds between the masses, with the stiffness of the vertical springs randomly changing along the length of each model. This results in a more realistic representation of the inherent randomness of the studied structures. To investigate the effect of random dislocations on the mechanical response of the studied systems, it has been assumed that a random mass-spring ensemble has been knocked out of place by an external force. It has been found that increasing the number of building blocks along the length of the models suppresses the influence of dislocations on the vibration spectra of RNA and DNA. It was also observed that at low frequencies, the influence of dislocations becomes more pronounced. Besides, taking into account the collective mass of the sugar-phosphate backbone results in the appearance of gaps in the vibration spectra. By introducing dislocations into the models, additional dislocation-induced vibrational states appear in the DOS curves. What stands out from the results is that the responses of the studied systems to these changes are strictly nonlinear. The employed methodology can be applied to investigate the mechanical response of damaged RNA and DNA.