Deriving Ogden Constitutive Parameters from Biaxial Stretch Testing Data
Deriving Ogden constitutive parameters pairs non-linear biaxial stretch data with Drucker stability constraints to ensure reliable finite element simulations.
Rubber Elasticity
Meaning
Entropic mechanical behavior enables lightly crosslinked polymer networks to exhibit high strain capacity and reversible elastic recovery. Thermodynamically governed rubber elasticity explains how uncoiling molecular chains generate restorative forces upon stretching without undergoing permanent molecular slip. The physical model applies strictly to amorphous polymers operating above their glass transition temperature with intact crosslinked networks, ceasing to apply when chain scission or plastic flow takes place.
Entropic Thermodynamics
Stretching an elastomer forces random polymer chain conformations into ordered, aligned arrangements, reducing internal entropy. Exhibiting rubber elasticity, the material generates retractive force primarily driven by the thermodynamic drive to maximize conformational entropy rather than changes in internal energy. Releasing applied loads permits thermal agitation to randomly recoil chain segments back into high-entropy configurations.
High strain levels trigger crystallization in natural rubber, increasing stiffness temporarily before complete recovery occurs upon unloading.
Network Crosslinking
Vulcanization creates covalent bonds between polymer chains that prevent permanent viscous slip under load. Crosslink density determines shear modulus, where higher crosslink frequencies increase stiffness while reducing maximum elongation at break.
Temperature Dependence
Restorative entropic forces increase proportionally with absolute temperature, causing stretched rubber to contract when heated. Cooling below glass transition freezes chain mobility, suppressing elastic recovery completely.