Ignore You can use at the bottom of the first question next

Ignore \"You can use\" at the bottom of the first question next to (15 points). Also it says \"Question 1\" two times, but they are two SEPERATE questions!!

Question#1-Compare elastic, viscous and viscoelastic materials in terms of time-dependency and recovery of deformation. You can use (15 points) Question#1-Choose two of the four viscoelastic materials models you know (ie, Maxwell, Kelvin, Solid, Burgers), identify model parameters and derive the corresponding creep responses. Explain how the response evolves from time =0 to later times. (20 points)

Solution

(1)Answer:-Comparison of elastic, viscous and viscoelastic material:-

Elastic material:- That material which regain its original shape and size after removal of load, called elastic material. This type of material is time independent.

Viscous material :- In viscous , stress is proportional to strain rate making behavior time dependent .Recovery of shape is nil when load is removed.

Viscoelastic material :- Viscoelasticity is the property of material that contains both elastic and viscous properties. Making behavior is time dependent and regain its original shape and size after removal of load.

(2) Answer:- Maxwell model:- Maxwell model represented by viscous damper and purely elastic spring connected in series.

d/dt = d_D/dt + d_s/dt   = / + 1/E*d/dt

The Maxwell predict that stress decays exponentially with time which is accurate for most polymer. One limitation of this model is that it does not predict creep accurately.

Maxwell model for creep postulates that strain will increase linearly with time.

Kelvin Model:- It consist of a Newtonian damper and Hooks elastic spring connected in parallel. This is used to explain the creep behavior of polymer.

(t) = E(t)+ * d(t)/dt

When stress is removed the material gradually relaxes to its un deformed state. At constant stress ,the model is quite realistic as it predicts strain to tend to /E as time continues to infinity. The model is extremely good with modeling creep in materials