Principal Investigator Franz-Josef Ulm
By using the concept of fractional-order derivative (derivative of an arbitrary order), we bridge the time-dependent response of a viscoelastic solid at its material level to that at its macroscopic level. The constitutive differential equation governing the time-dependent indentation response of a half-space solid is derived; together with its creep and relaxation functions suitable for back-analysis of experimental data to optimize the fractional-viscoelastic model parameters.
As an another application of fractional derivatives in materials which follow hereditary integral response, the time-dependent governing equation of a viscoelastic DNA is derived at the macro level. This formalism enables to use an optimization scheme in Laplace domain to find the viscoelastic model parameters.
Past research project includes determination of the spectral (i.e. frequency dependent) finite element of an alpha helix. We treat an alpha helix as a straight elastic element, exhibiting coupling between axial and torsional motions. Next, we derive all component of its dynamic stiffness tensor as a function of the frequency and the parameter describing the said coupling. The growth of that parameter leads to a progressively denser occurrence of the resonances of both axial and torsional motions.