Finite element modeling of viscoelastic materials on the theory of fractional calculus

Three-dimensional viscoelastic finite element formulation based on the fractional derivative constitutive relation has been developed in the time and frequency domain. This formulation allows a consistent treatment of a structure encompassing both elastic and viscoelastic materials. A two-dimensional finite element computer code is developed in the real time domain for carrying out structural analyses. Substantial computer time is saved by a pure marching in time algorithm in which updating of material/stiffness matrix is not required. Verification of the formulation and computer code are conducted by comparing several simulation results with theoretical, experimental or extant numerical data in the literature. As a result, the fractional derivative constitutive models are capable of characterizing the real world materials in a much more simpler and accurate manner.