For hydrogels, their elasticity comes from the solid polymer matrix while the viscosity originates from the polymer network mobility and the water and other components that make up the aqueous phase. Viscoelastic properties of a hydrogel is highly dependent on the nature of the applied mechanical motion. Thus, the time dependence of these applied forces is extremely important for evaluating the viscoelasticity of the material.
Physical models for viscoelasticity attempt to capture the elastic and viscous material properties of a material. In an elastic material, the stress is proportional to the strain while in a viscous material, the stress is proportional to the strain rate. The Maxwell model is one developed mathematical model for linear viscoelastic response. In this model, viscoelasticity is modeled analogous to an electrical circuit with a Hookean spring, that represents the Young's modulus, and a Newtonian dashpot that represents the viscosity. A material that exhibit properties described in this model is a Maxwell material. Another physical model used is called the Kelvin-Voigt Model and a material that follow this model is called a Kelvin–Voigt material. In order to describe the time-dependent creep and stress-relaxation behavior of hydrogel, a variety of physical lumped parameter models can be used. These modeling methods vary greatly and are extremely complex, so the empirical Prony Series description is commonly used to describe the viscoelastic behavior in hydrogels.
In order to measure the time-dependent viscoelastic behavior of polymers dynamic mechanical analysis is often performed. Typically, in these measurements the one side of the hydrogel is subjected to a sinusoidal load in shear mode while the applied stress is measured with a stress transducer and the change in sample length is measured with a strain transducer. One notation used to model the sinusoidal response to the periodic stress or strain is:
in which G' is the real (elastic or storage) modulus, G" is the imaginary (viscous or loss) modulus.