Integral approach for time dependent materials using finite element method

In this work, we present the development of a mathematical approach for the solution of linear, non-ageing viscoelastic materials undergoing mechanical deformation. We use an integral approach based on a discrete spectrum representation for the creep tensor in order to derive the incremental viscoelastic formulation. Integral operators are discretized using finite difference techniques. The incremental viscoelastic constitutive model contains an internal state variable which represents the influence of the whole past history of stress and strain, thus the difficulty of retaining the stress-strain history in numerical solutions is avoided. A complete general formulation of linear viscoelastic stress-strain analysis is developed in terms of increments of stresses and strains. Numerical simulations are included in order to validate the incremental constitutive equations.