page_title: Viscoelasticity
section_title: Background
hierarchical_section_title: Viscoelasticity / Background
context_page_description: Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.
  Viscoelastic materials have elements of both of these properties and, as such, exhibit time-dependent strain. Whereas elasticity is usually the result of bond stretching along crystallographic planes in an ordered solid, viscosity is the result of the diffusion of atoms or molecules inside an amorphous material.
context_section_description: In the nineteenth century, physicists such as Maxwell, Boltzmann, and Kelvin researched and experimented with creep and recovery of glasses, metals, and rubbers. Viscoelasticity was further examined in the late twentieth century when synthetic polymers were engineered and used in a variety of applications. Viscoelasticity calculations depend heavily on the viscosity variable, η. The inverse of η is also known as fluidity, φ.  The value of either can be derived as a function of temperature or as a given value (i.e. for a dashpot).
  Depending on the change of strain rate versus stress inside a material the viscosity can be categorized as having a linear, non-linear, or plastic response.  When a material exhibits a linear response it is categorized as a Newtonian material. In this case the stress is linearly proportional to the strain rate.  If the material exhibits a non-linear response to the strain rate, it is categorized as Non-Newtonian fluid. There is also an interesting case where the viscosity decreases as the shear/strain rate remains constant. A material which exhibits this type of behavior is known as thixotropic. In addition, when the stress is independent of this strain rate, the material exhibits plastic deformation. Many viscoelastic materials exhibit rubber like behavior explained by the thermodynamic theory of polymer elasticity. 
  Some examples of viscoelastic materials include amorphous polymers, semicrystalline polymers, biopolymers, metals at very high temperatures, and bitumen materials. Cracking occurs when the strain is applied quickly and outside of the elastic limit. Ligaments and tendons are viscoelastic, so the extent of the potential damage to them depends both on the rate of the change of their length as well as on the force applied.
  A viscoelastic material has the following properties:
  hysteresis is seen in the stress–strain curve
  stress relaxation occurs: step constant strain causes decreasing stress
  creep occurs: step constant stress causes increasing strain
caption: Different types of responses (
    
      
        
          σ
        
      
      {\displaystyle \sigma }
    
  ) to a change in strain rate (d
    
      
        
          ε
        
      
      {\displaystyle \varepsilon }
    
  /dt)