3. State Variables Approach

The State Variables approach is an alternative to the history dependent integral representation given in Chap.​ 2. It has a physical basis because of its origin in thermodynamic formulations and shows computational advantages. The creep and relaxation functions are approximated by exponential series. The introduction of state variables leads to n differential equations of first order in place of the differential equation of order n linked to a generalized model. This formulation leads to exponential expressions that make incremental integration easier, allowing the determination of the viscoelastic strains at time t + Δt as a function of the viscoelastic strains and stresses at time t. Then, there is no need to store the whole history of stress or strain. In this chapter, we introduce the basic formulation that is later extended to 3D, aging and nonlinear situations.