  Finite Element codes used for solving the mechanical equilibrium equations in
transient problems associated to (time-dependent) viscoelastic media generally
relies on time-discretized versions of the selected constitutive law. Recent
concerns about the use of non-integer differential equations to describe
viscoelasticity or well-founded ideas based upon the use of a behavior's law
directly derived from Dynamic Mechanical Analysis (DMA) experiments in
frequency domain, could make the Laplace domain approach particularly
attractive if embedded in a time discretized scheme. Based upon the inversion
of Laplace transforms, this paper shows that this aim is not only possible but
also gives rise to a simple algorithm having good performances in terms of
computation times and precision. Such an approach, which fully relies on the
Laplace-defined Behavioral Transfer Function (LTBF) can be promoted if it uses
ARX parametric models perfectly substitutable to the real LTBF. They avoid the
hitherto prohibitive pitfall of having to store all past data in the computer's
memory while maintaining an equal computation precision.
