Maxwell and kelvin voight models of viscoelasticity presentation

A better understanding of the Maxwell and Kelvin Voight models of Viscoelasticity when measuring analysing certain materials.

1. Maxwell and Kelvin Voight models of Viscoelasticity Presentation by Hope Mungwariri and Nyamuronda Marshal

2. Viscoelasticity It may be defined as the behavior exhibited by a material that has both viscous and elastic elements in its response to a deformation or load T he application of stress causing temporary deformation if the stress is quickly removed but permanent deformation if it is maintained . However, many liquids (including water) will briefly react like elastic solids when subjected to sudden stress. Conversely, many "solids" (even granite) will flow like liquids,

3. Elastic Response

4. Viscous Response

5. Maxwell Model A spring and a dashpot is connected in series in the model Suggests that there is uniform distribution of stress in the model Predicts that stress decays exponentially with time Can also describe stress relaxation

6. Maxwell Model

7. Stress Relaxation due to Maxwell

8. Maxwell Model Represented by a purely viscous damper and a purely elastic spring connected in series The model can be represented by the following equation: Predicts that stress decays exponentially with time Model doesn’t accurately predict creep (constant stress). Predicts that strain will increase linearly with time. Actually strain rate decreases with time Stress relaxation experiment

9. Kelvin Voight model Suggests that there is uniform distribution of strain The spring and Dashpot will be in parallel in the model Gives a retarded elastic response but does not allow for ‘ideal’ stress relaxation since the model cannot be instantaneously deformed for a given strain Creep is constant

10. Voigt Model

11. Model Comparison Maxwell Good for predicting stress relaxation Poor at predicting creep Used for soft solids (materials close to the melting point Kelvin-Voigt Good for predicting creep Not accurate with predicting stress relaxation Used for organic polymers, rubber, wood when the load is not too high

12. Kelvin-Voigt Model Represented by a Newtonian damper and Hookean elastic spring in parallel. The model can be expressed as a linear first order differential equation: Represents a solid undergoing reversible, viscoelastic strain. At constant stress (creep), predicts strain to tend to σ/E as time continues to infinity The model is less accurate with relaxation in a material Creep and recovery response

13. Creep due to Voigt Relaxation

14. Combination of Maxwell and Voigt

15. References Tanner, Roger I. (1988).  Engineering Rheologu . Oxford University Press. p. 27.  Silbey and Alberty (2001):  Physical Chemistry , 857. John Wiley & Sons, Inc. Roylance , David (2001); "Engineering Viscoelasticity“ S.A. Baeurle , A. Hotta , A.A. Gusev , Polymer  47 , 6243-6253 (2006). Rosato , et al. (2001): "Plastics Design Handbook", 63-64 .   E. J. Barbero . Finite Element Analysis of Composite Materials. CRC Press, Boca Raton, Florida, 200 Rod Lakes (1998).  Viscoelastic solids . CRC Press.