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Finite Element codes used for solving the mechanical equilibrium equations intransient problems associated to (time-dependent) viscoelastic media generallyrelies on time-discretized versions of the selected constitutive law. Recentconcerns about the use of non-integer differential equations to describeviscoelasticity or well-founded ideas based upon the use of a behavior's lawdirectly derived from Dynamic Mechanical Analysis (DMA) experiments infrequency domain, could make the Laplace domain approach particularlyattractive if embedded in a time discretized scheme. Based upon the inversionof Laplace transforms, this paper shows that this aim is not only possible butalso gives rise to a simple algorithm having good performances in terms ofcomputation times and precision. Such an approach, which fully relies on theLaplace-defined Behavioral Transfer Function (LTBF) can be promoted if it usesARX parametric models perfectly substitutable to the real LTBF. They avoid thehitherto prohibitive pitfall of having to store all past data in the computer'smemory while maintaining an equal computation precision.

Solving viscoelastic problems in a step-inverse Laplace transform  approach supplanted with ARX models: a way to upgrade Finite Element or  spectral codes