Liste de grandeurs viscoélastiques

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Cette liste répertorie les grandeurs viscoélastiques (ou caractéristiques/propriétés viscoélastiques) d’un matériau viscoélastique, utilisées en mécanique des milieux continus. Ces résultats quantitatifs peuvent être donnés par un analyseur mécanique dynamique (DMA) ou, hors mesures en traction, compression et flexion, par un rhéomètre. Les grandeurs dépendent de la fréquence de sollicitation (dans le cas des essais périodiques), de la vitesse de sollicitation (cas par exemple d’un essai de traction) ou du temps. Un essai au cours duquel la contrainte (ou la déformation) est appliquée de façon sinusoïdale, à une fréquence f, équivaut à celui (quasi statique) de fluage ou de relaxation de contrainte à un temps t = 1/ω.

Nom Symbole ou relation Remarque et/ou relation
Tangente de l’angle de phase, tan delta tan δ(ω)[1] tan δ(ω) = E’’(ω) / E’(ω) = D’’(ω) / D’(ω)[2]
Module de conservation en traction-compression, en flexion E’(ω) Caractérise la rigidité du matériau viscoélastique ; indique l’énergie conservée[3]
Module de perte en traction-compression, en flexion E’’(ω) Indique l’énergie dissipée
Module complexe en traction-compression, en flexion E*(ω) E*(ω) = E’(ω) + i E’’(ω) ; |E*| = (E’2 + E’’2)½
Module de conservation en cisaillement, en torsion G’(ω) Caractérise la rigidité du matériau viscoélastique ; indique l’énergie conservée[3]
Module de perte en cisaillement, en torsion G’’(ω) Indique l’énergie dissipée
Module complexe en cisaillement, en torsion G*(ω) G*(ω) = G’(ω) + i G’’(ω) ; |G*| = (G’2 + G’’2)½
Complaisance de conservation[4] en traction-compression, en flexion D’(ω) Indique l’énergie conservée[3]
Complaisance de perte en traction-compression, en flexion D’’(ω) Indique l’énergie dissipée
Complaisance complexe en traction-compression, en flexion D*(ω) D*(ω) = D’(ω) - i D’’(ω) = 1 / E*(ω)
Complaisance de conservation[4] en cisaillement, en torsion J’(ω) Indique l’énergie conservée[3]
Complaisance de perte en cisaillement, en torsion J’’(ω) Indique l’énergie dissipée
Complaisance complexe en cisaillement, en torsion J*(ω) J*(ω) = J’(ω) - i J’’(ω) = 1 / G*(ω)
Module de relaxation de contrainte en traction E(t)
Module de relaxation de contrainte en cisaillement G(t)
Complaisance de relaxation de contrainte en traction 1 / E(t)
Complaisance de relaxation de contrainte en cisaillement 1 / G(t)
Complaisance de fluage en traction D(t)
Complaisance de fluage en cisaillement J(t)
Module de fluage en traction 1 / D(t)
Module de fluage en cisaillement 1 / J(t)
Viscosité dynamique η’(ω) η’(ω) = G’’(ω) / ω ; indique l’énergie dissipée
Viscosité complexe η*(ω) η*(ω) = η’(ω) - i η’’(ω) = G*(ω) / i ω = (G’’(ω) / ω) - i (G’(ω) / ω)

Notes

  1. ↑ δ est aussi appelé angle de déphasage ou angle de perte. Pour un solide élastique parfait, δ et le module de perte sont nuls ; pour un liquide newtonien parfait, δ = 90° et le module de conservation est nul.
  2. ↑ Relation correspondant à une expérience en traction-compression ou en flexion. En cisaillement ou en torsion, le facteur de perte ou facteur d’amortissement s’écrit : tan δ(ω) = G’’(ω) / G’(ω) = J’’(ω) / J’(ω).
  3. ↑ a b c et d Énergie mécanique conservée puis restituée par l’échantillon pendant un cycle de déformation sinusoïdale.
  4. ↑ a et b Ou complaisance instantanée.

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