Why does the stress curve suddenly shoot upward at high stretch in the Gent model?

The Gent model divides by Jm minus (I1 minus 3), where I1 is the first strain invariant. As the stretch ratio grows, that difference shrinks toward zero, so stress diverges, modelling the physical limit where polymer chains between cross-links become fully extended.

What does the cross-link density slider change?

Cross-link density n sets how many polymer strands exist per unit volume between vulcanization points. Since shear modulus G equals n times R times T, raising n directly raises G and stiffens every curve at once.

Why does rubber get stiffer when heated?

Because G equals n times R times T, shear modulus is directly proportional to absolute temperature. Higher temperature drives chains back toward disordered, high-entropy coils, increasing the entropic restoring force.

Home▸Materials Science▸Rubber Network Elasticity (2D)

Rubber Network Elasticity (2D)

2D stress-stretch chart of a cross-linked rubber network comparing Neo-Hookean, Mooney-Rivlin and Gent constitutive models as cross-link density and temperature change.

Materials Science2DModerate60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion plots the same three constitutive stress-stretch models as the 3D version — Neo-Hookean, Mooney-Rivlin and Gent — on a flat Canvas2D chart, so the curves themselves are the whole simulation. Drag cross-link density and temperature to recompute the shear modulus G = nRT live, blend in the Mooney C₂ term, and tighten the Gent finite-extensibility limit Jₘ to watch stress diverge as chains run out of slack at λ_max.

⚙ Under the hood

2D stress-stretch plotter for cross-linked rubber networks: Neo-Hookean, Mooney-Rivlin and Gent models drawn live from the same closed-form equations as the 3D version, with a numeric readout of shear modulus and the Gent limiting stretch.

rubber elasticityneo-HookeanMooney-RivlinGent modelcross-link density

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install