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Senior Scientist John Tibballs attends SIAM conference on “Mathematical aspects of materials science” in Philadelphia, USA, 8-12 May 2016.

The conference otherwise ranged widely, with presentations on mathematics applied in material science from vibrational behaviour to thermodynamics.

The mechanical behaviour of dental polymers involves relaxation mechanisms that can only be fully described with relatively complex mathematics.

John Tibballs presented a poster “Phase delay for b-function model of visco-elastic behaviour” that arose in analyzing fatigue testing of bulk-fill composites.

Empirically, resin composites under steady loading relax according to:

ψ(t; β, τ) = exp[-(t/t)β }]; β < 0,5

In fatigue testing, this anelasticity causes a time delay Δt between load and measured displacement.

Expressing ψ(t; β, τ) as a sum of exponential decays, scaled by τn =tau ×10n/4β, the weighting is virtually independent of β. The Laplace transformation relating Δt to τ and β is derived and applied.