Application of an Innovate Energy Balance to Investigate Viscoelastic Problems


  • Saeed Shahsavari Isfahan University of Technology, Department of Mechanical Engineering0
  • Mehran Moradi



Energy Balance; Residual Energy; Non-inertial energy; Viscoelasticity


Modeling and investigating of energy distribution especially the wasted one is very important in viscoelastic problems. In this article, an applied energy model based on separation of energy components of the system is extracted and expanded to apply in linear viscoelastic problems, although this method is applicable in nonlinear problems as well. It is assumed that the whole energy of the system can be divided into two parts: Residual and non-inertial energies. The non-inertial energy is the sum of the energies that do not depend on the inertia of the system, while residual energy is the remaining of total energy. When an amount of energy is applied to the system, by determining the non-inertial energy from a novel energy conservation equation, the residual energy can be calculated. Some basic viscoelastic examples are investigated and obtained results will be compared with the expected ones.



Caputo, Michele, and Francesco Mainardi. "A new dissipation model based on memory mechanism." Pure and Applied Geophysics 91.1 (1971): 134-147.

Del Piero, Gianpietro, and Luca Deseri. "On the concepts of state and free energy in linear viscoelasticity." Archive for Rational Mechanics and Analysis 138.1 (1997): 1-35.

Colinas-Armijo, Natalia, Mario Di Paola, and Francesco P. Pinnola. "Fractional characteristic times and dissipated energy in fractional linear viscoelasticity." Communications in Nonlinear Science and Numerical Simulation 37 (2016): 14-30.

Bland, David Russell. The theory of linear viscoelasticity. Courier Dover Publications, 2016.

Hongbin, Yang, et al. "Energy dissipation behaviors of a dispersed viscoelastic microsphere system." Colloids and Surfaces A: Physicochemical and Engineering Aspects 487 (2015): 240-245.

Fabrizio, Mauro, and Angelo Morro. Mathematical problems in linear viscoelasticity. Vol. 12. Siam, 1992.

Deseri, Luca, Giorgio Gentili, and Murrough Golden. "An explicit formula for the minimum free energy in linear viscoelasticity." Journal of elasticity 54.2 (1999): 141-185.

Tschoegl, Nicholas W., Wolfgang G. Knauss, and Igor Emri. "Poisson's ratio in linear viscoelasticity–a critical review." Mechanics of Time-Dependent Materials 6.1 (2002): 3-51.

Lei, Zhen, Chun Liu, and Yi Zhou. "Global existence for a 2D incompressible viscoelastic model with small strain." Communications in Mathematical Sciences 5.3 (2007): 595-616.

Ghayesh, Mergen H. "Dynamics of functionally graded viscoelastic microbeams." International Journal of Engineering Science 124 (2018): 115-131.

Likhtman, Alexei E., Sathish K. Sukumaran, and Jorge Ramirez. "Linear viscoelasticity from molecular dynamics simulation of entangled polymers." Macromolecules 40.18 (2007): 6748-6757.

Gentili, Giorgio. "Maximum recoverable work, minimum free energy and state space in linear viscoelasticity." Quarterly of Applied Mathematics 60.1 (2002): 153-182.

Colby, Ralph H. "Structure and linear viscoelasticity of flexible polymer solutions: comparison of polyelectrolyte and neutral polymer solutions." Rheologica Acta 49.5 (2010): 425-442.

Pettermann, Heinz E., and Antonio DeSimone. "An anisotropic linear thermo-viscoelastic constitutive law." Mechanics of time-dependent materials 22.4 (2018): 421-433.




How to Cite

Shahsavari, S., & Mehran Moradi. (2020). Application of an Innovate Energy Balance to Investigate Viscoelastic Problems. Asian Journal of Engineering and Technology, 8(4).